H-DnLI Division of Agricultural Science! — A- ( \ — UNIVERSITY OF CALIFORNI A The First Report in a Series on Prices and Marketing Margins for Fruits and Vegetabies DAILY PRICES AND RETAIL MARGINS- ORANGES, LEMONS, AND GRAPEFRUIT * Denver, August 1948-Jul/ 1949 m • Sidney Hoos UNIVERSITY OF CALIFORNIA DAVIS AUG 2 * iyo4 LIBRARY m • CALIFORNIA AGRICULTURAL EXPERIMENT STATION GIANNINI FOUNDATION OF AGRICULTURAL ECONOMICS Mimeographed Report No. 168 July 1954 Unireraity of California Division of Agricultural Sciences Agricultural Experiment Station Berkeley, California DAILY PRICES AND RETAIL MARGINS- GRANGES, LEMONS AND GRAPEFRUIT Denver, August 1948- 1, the xisual situation, the product of and can be sufficiently less than unity so that is the right-hand side of (3) would be less than unity. If Pr Pf greater than unity and the slopes of the two demand functions are equal, then, E^>E^, but this is clearly not a general case. It is clear that no unique general relation need exist between and — =■ nor between E and E». The outcome as to the relative price 9 we now turn to measures of variability shown in Table 6: 1/ At this point, it is pertinent to note that in January 19li9 there occurred a rather severe freeze in California, The market evidence sug- gests that as a result of the January 19U9 freeze in California the gen- eral price level for citrus, rather than the price structure, was affected. -22- TABLE 6 Measure of Average Variability in Daily Price Spreads of Oranges August 19li8-July 19U9 lype of spreads be- tween daily First six months, August I9ii8- January 19li9 Second six months, February 19ii9- July 19li9 Year, August 19li8- July 19U9 retail and wholesale Standard devia- Coefficient of Standard devia- Coefficient of Standard devia- Coefficient of prices tion variation 1 tdon variation tion variation cents cents cents per pound per cent per pound i per cent per pound per cent Absolute ; spreads 1 Retail and i current 1 wholesale 0.88 2U 0.77 19 0.85 22 ! Retail and lagged wholesale 1 0,h6 13 0.51 12 o.Sh Ui 1 per cent ! Relative i spreads Retail and current wholesale 7.12 23 5.02 16 6.17 20 Retail and lagged wholesale 2.60 8 1 L 1.1U h 1 2.12 1 7 These statistical measures indicate that different patterns of varia- bility are characteristic of the several different types of dally spreads. The major differences may be described in the following terms. The spreads based on daily retail and current wholesale prices tend to vary more widely than do the spreads based on daily retail and lagged wholesale prices,* this generalization applies to both absolute and relative spreads. When the ab- solute and relative spreads between the retail and current wholesale prices are considered, it appears that they fluctuate in about the same degree. Vlhen the spreads between the daily retail and lagged wholesale prices are considered, however, we find that the absolute spreads have a greater de- gree of variability over time than do the relative spreads. The absolute -23- and especially the relative spreads between the daily retail and current wholesale prices tend to fluctuate about a horizontal trend. However, the absolute and relative spreads between the daily retail and lagged whole- sale prices also fluctuate but around a varying trend rather than a hori- zontal one. There is little doubt that different types of spreads having different behavior characteristics emerge, depending on whether daily lagged or current wholesale prices are compared with the daily retail prices. Daily Variation in Store Operations in Oranges. — Before proceeding further with the discussion of spreads between daily retail and wholesale prices of oranges, it may be appropriate here to insert a tangential dis- cussion of patterns of variation during the week. Since we are dealing with daily prices and spreads, the question arises as to whether the data should be adjusted in some way for the regular patterns of daily variation within the veek,^ Such an adjustment may be necessary if pronounced regu- lar patterns do exist in the daily prices aiMi spreads. To determine whether regular patterns in the daily prices and spreads are present, indexes of daily variation were constructed,^ They are shown in Figure U for the two 6-month periods as well as for the year as a whole. Also included in Figure k are indexes of daily purchases and sales of or- anges which were constructed to indicate not only the timing of purchases and sales by the stores but also to detemine whether those indexes bear any relation to the indexes of daily prices and spreads. The indexes for the first and second halves of the year differ, mainly in that the day with lowest store purchases occurs on Tuesday in the first half of the year but shifts to Wednesday in the second half. In store sales, Friday and Saturday are of about equal inqportance in the first half of the year; but in the second half, Saturday sales are of substantially greater volume than those on Friday. Checking with the stores and witl» 1/ Patterns of seasonal variation in f.o.b. prices and shipments of or- anges are analyzed in Sidney Hoos and J, N. Boles, Oranges and Orange Products, Changing Econoinic Relationships . Berkeley, 1953." S7p^ (Calif, Agr. Exp. Sta. Bui, 73l) 2/ The indexes of daily variation in store operations were constructed as follows: For a given operation, the figure for each day was expressed as a percentage of the daily average of that operation during the respec- tive week. The resulting daily percentages for all of the Mondays were then averaged to obtain the index value for Monday} the same was done to obtain the index values for Tuesday and the remaining days of the week through Saturday. FIGURE 4. ORANGES; DAILY VARIATION IN RETAIL STORE OPERATIONS, STORE SALES. PURCHASES, RETAIL AND CURRENT WHOLESALE PRICES AND PRICE SPREADS (DAILY AVERAGE = 100) MON TUE WED. THU. FRI. SAT MON TUE. WED THU. FRI. SAT MON I I TUE WED. THU. FRI. SAT -25- wholesalers confirms that Tuesday and Wednesday are the "slow" days with respect to the purchasing of oranges by the stores. Checking with the stores also confirms that, although Saturday usually is the day of largest retail sales of oranges with Friday next largest, in some periods the re- verse holds. Some retailers maintain that in recent years the Friday vol- ume of sales has tended to increase relatively more than that of other days, even Saturday; but we do not have the data to check that view. Nevertheless, it is clear that Friday and Saturday are the "busiest" days, while Tuesday is the "slowest" day in the retail sale of oranges. Using the indexes based on the entire year and to supplement the in- formation visible in Figure U, the following measures are set forth in Table 7s TABLE 7 Indexes of Daily Variation in Retail Store Operations in Oranges August 19li8-July 19U9 Business day Retail price Current wholesale price Store sales Store pvirchases Retail and lagged wholesale price spread Retail and current wholesale price spread average of business days during week ■ • 100 Monday 1 100.6 100.1 83.8 1U3.2 101.0 99.7 Tuesday 100.2 98.U 78.1; 90.7 100.8 103.8 Wednesday 99.8 98.3 85.8 87.3 99.2 102.9 Thursday 100.0 IOI.I4 95.0 111;. 5 100.0 97.1 Friday 99.0 98.8 119.3 139.7 99.8 101.6 Saturday 99.8 i03.lt 138.2 13.5 99.2 91.1 No regular variation within the week is noticeable in the daily re- tail prices. The differences between the daily values of that index are so minute that they can be disregarded. Apparently, the practice of the stores having "week end specials" is not sufficiently regular and pro- nounced in the retail price data for all stores combined so that week-end prices can be said to be significantly lower than those of the earlier days of the week. -26- THhen we examine the daily indexes of current wholesale prices, we find only a very slight decrease in level on Tuesday and Y/ednesday, the days on which store purchases are slack. The current wholesale price on Saturday apparently averages a little higher than on the other days, but study of the primary basic data shows that relatively few stores purchase on Saturday, and those that do are the very small stores which may purchase only irregularly on that day. The tendency for the current wholesale prloe to be somewhat higher on Satxirday than on other days is due primarily to purchases by small stores on that day and, as shown in the next report, the wholesale prices paid by the small stores average higher than those paid by the larger stores. Ttie daily sales of fresh oranges by the stores exhibit a fairly regu- lar pattern of variation within the week. The Monday volume of sales is followed by lower sales during the next day, and by Wednesday sales have picked upj they then continue to increase and reach a peak at the end of the week. This pattern of daily sales does not appear to be induced to any significant extent by a pattern of daily retail prices. Rather, the pattern of daily sales of oranges seems to be related to habits or prac- tices of households in their purchase of food supplies. Most households purchase heavily on the week ends for use during the next several days, and a not inconsiderable number of households purchase on the week ends for consumption during part of the following week. Daily purchases of oranges by stores follow a clear pattern of varia- tion during the week. On Monday, at the very beginning of the business week, the stores purchase oranges to restock their supplies which had be- come depleted during the preceding week end. On Tuesday and Wednesday, store purchases are below those of Monday, On Thursday, purchases pick up and increase to a peak on Friday to provide supplies for the week-end busi- ness. But on Saturday, store purchases of oranges are generally very lowj very few stores do any extensive buying of oranges on Saturday when they are bugy with the week-end rush in their sales. "Whfen we examine the daily indexes of the price spreads, we find no distinct patterns of variation within the week. In the spread between the retail and lagged wholesale prices, all of the daily indexes hover closely about the daily average, indicating no significant pattern. In the spread between the retail and current wholesale prices, several of the daily in- dexes depart from the weekly pattern to some extent, namely, Tuesday, -27- V/ednesday, Thursday, and Saturday. To the extent that such departures are significfmt, they suggest relatively more favorable spreads, from the view of the store, on Tuesday and Wednesday but less favorable spreads on Thurs- day and Saturday. Yet, a rationalization of such behavior is not readily apparent except for Saturday when the current wholesale price advances rela^ tive to the retail price; but, as noted earlier, the Saturday current whole- sale price cannot be very significant in view of the relatively small volume of store purchases on that day. Relations Between Daily Orange Prices and Spreads — We now return to a review of relations between the daily spreads and prices of oranges. Earlier, attention was given to relations between the daily retail and wholesale prices, and in those results relationships among the prices and spreads were implied. We now can consider such relationships explicitly. First, let us look at correlations between the daily prices and spreads between them shown in Table 8. TABLE 8 Coefficients of Correlation Between Daily Spreads and Wholesale Prices of Oranges August 19U8-.July 19U9 Correlation between tjrpes of daily prices and spreads First six months, August I9I48- January 19U9 Second six months, February 19U9- July 19U9 Year, August I9U8- JuXy 19U9 Prices and absolute spreads Lagged wholesale price and spread between it and retail price +0.62 ♦0.8$ ♦0.79 Current wholesale price and spread between it and retail price -o.oU ♦0.16 ♦O.lli Prices and relative spreads Lagged wholesale price and spread between it and retail price -0.36 -0.33 -O.3U Current wholesale price and spread between it and retail price -0.U2 i -0.51 i , , . ... -0.U2 i ~- -28- The above statistics clearly indicates that the higher degree of as- sociation is between the daily lagged wholesale price and the absolute spread between it and the daily retail price and that correlation is not of an unusually high order, although it does show that the daily lagged wholesale price and the absolute retail and lagged wholesale price spread generally change in the same direction. Another correlation meriting specific comment is the one between the daily current wholesale price and the relative spread between it and the daily retail price. That correla- tion, hoT/ever, is only of a fairly low order, alttough it does suggest a noticeable tendency for the daily current wholesale price and the relative retail and current wholesale price spread to change in opposite directions. Figure 5 is a scattergram of daily lagged wholesale prices and corre- sponding absolute retail and lagged wholesale price spreads, with the fomer measured along the horizontal axis and the latter on the vertical axis. Each business day is represented by a small circle. A number in the circles means that that many different days had the same combination of lagged wholesale price and absolute retail and lagged vfholesale price spread. The solid heavy upward-sloping straight line represents the aver- age relationship during the year between the daily prices and spreads. As noted above, the daily lagged wholesale prices ani retail and lagged whole- sale price spreads tend to change in the same direction. Yet, the rela- tionsMp is far from a perfect one as reflected by the scatter of the daily observations about the line of average relationship. Figure 6 shows graphically the relationship of the relative retail and lagged wholesale price spread and the lagged wholesale price. The relative spread decreases on the average very slightly (about 0.6 per cent) with a one-cent-a-pound increase in the daily lagged wholesale price, and the relationship is significant in a probability sense. But the relative retail and current wholesale price spread decreases on the average about 2 per cent with a one-cent increase in the current wholesale price. There is a reasonably clear tendency for the relative spreads to become smaller as the wholesale prices increase; and there is a fairly clear tendency for the absolute retail and lagged wholesale price spread to become larger as the lagged wliolesale price increases. Less pronounced evidence is fo\md for the absolute retail and current wholesale price spread to change as the current wholesale price changes. -29- FI6URE 5. ORANGES; RELATION BETWEEN ABSOLUTE RETAIL- LAGGED WHOLESALE PRICE SPREAD AND LAGGED WHOLESALE PRICE, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 4.0 5.0 6.0 7.0 8.0 9.0 10.0 110 LAGGED WHOLESALE PRICE (4/LB.) FIGURE 6. ORANGES; RELATION BETWEEN RELATIVE RETAIL- LAGGED WHOLESALE PRICE SPREAD AND LAGGED WHOLESALE PRICE, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 !«2 o < 4.0 e 0 0 ® o o 6 ( - o ® o ® o'o o ® o °o® » 0 0 o 0 o 0 ® e o 1 o ■ 1 1 1 5.0 6.0 7.0 8.0 9.0 LAGGED WHOLESALE PRICE U/LB.) 10.0 1 1.0 -30- Quantitative measures of related changes in the lagged wholesale prices and the spreads between the retail price and lagged wholesale price are summarized in Table 9.^ From the data in Table 9, using the results for the entire year, we see that, as the daily lagged wholesale price changes by 1 cent a pound, the absolute retail and lagged wholesale price spread changes in the same direction in an amount of about O.h cent a pound. This relationship was inferred earlier from relations of the daily retail price to the daily lagged wholesale price. Between the current wholesale price and the spread between it and the retail price, there is only a slight quantita- tive relationship, although it is statistically signi.ficant. 1/ Because of the algebraic relationships between the retail and wholesale prices and their spread, the following relations among their associated changes hold: d8_ . ^ ds ^ , dPr % , dPj, ^ " dp^ ' ^ ■ dp^ - dT - dT " where p^ represents the retail price, p^ represents the wholesale price, and s represents the spread between the retail and wholesale prices. In terms of regression, the relations may be expressed as follows! (regression of the spread on the retail price) ■ 1 - (regreseion of the wholesale on the retail price) (regression of the spread on the wholesale price) - (regression of the retail on the wholesale price) - 1 (regression of the retail price on the spread) - 1 + (regression of the wholesale price on the spread) The regression statistics in this report were computed from the basic series and the above relationships were used for checking some of the results. Due to computational rounding, the two procedures may not alvfays give precisely the same results, although when they do differ it is so only by an Insignificant amount. The preceding equations are here noted more to emphasize the interrelationships between the retail and Trholesale prices and their spread than to indicate short-cut computa- tional procedures. -31- TABIE 9 Equations of linear Regression of Daily Retail and T/Vholesale Price Spreads on Daily Miolesale Prices of Oranges August 19148-Juay 19U9 First six months, August I9U8- January 19U9 Second six months, February 19U9- July 19U9 Year, August 19li8- JuOy I9U9 Regression of daily spreads on daily wholesale prices Constant Regres- sion coef- ficient Constant Regres- sion coef- ficient Constant Regres- sion coef- ficient cents per pound ADSOxuxie spreaas on wholesale prices Retail and lagged wholesale price spread on lagged wholp^alfl 'Drice ( 5.23)^ +0.31 (9.75) * 0.72 ( U.37) 0.38 (20.58) 4 0.92 ( 6.91) + 0.36 (22.59) Retail and cur- rent wholesale price spread on current whole- sale price ♦ 3.91 ( 6.31) -0.03 (o.UU) + 3.15 ( 6.61) ♦ 0.06 ( 1.77) ♦ 3.02 ( 8.63) + 0.05 ( 2.28) per cent Relative jjpreads on r" wholesale prices Retail and lagged wholesale price spread on lagged wholesale price +39.69 (2ii.97) -0.95 (li.65) +35.61 (iil.23) - 0.U2 ( U.3U) +37.13 (h5.97) - 0.61 ( 6.27) Retail and cur- rent wholesale price spread on current whole- sale price 5U.99 (12.12) -3.00 (5.19) ♦U8.75 (16.06) 1 1- 2.00 ; ( 6.63) 1 ; +118.36 1 (20.71) - 2.05 ( 7.38) a/ Figures in parentheses are t-ratios. Sensitivity of Retail to "Wholesale Prices of Oranges . — The results discussed so far provide a basis from which to approach one of the most widely spread ideas among citrus marketers concerning relationships be- tween wholesale and retail prices of fresh fruits and vegetables in gen- eral and oranges in particular. Many producers and distributors of -32- oranges, particularly shippers, believe that retail prices are tied to wholesale prices in a very special way: TWhen the wholesale market price advances, the retail market price also advances and does so iiranediatelyj but when the ■wholesale market price declines, the retail market price lags behind. According to this view, retailers are supposed to be sensitive in making upward adjustments in retail prices, but the same retailers are sup- posed to be sluggish in making downward adjustments in their retail prices. It is views such as the one just set forth which are behind the attitude of some producers toward "middlemen retailers" who are supposed to be holding back the flow of oranges to consumers by not reducing retail prices ade- quately during periods when f.o.b. and auction prices are declining. If such a view is valid, it would help to explain why supplies at times con- tinue to accumulate at supply points viiile orange prices are declining at f.o.b. auction and wholesale levels of distribution. Let us first look at the scattergram in Figure 7. The horizontal axia represents the day-to-day change in the current wholesale prd.ce, and the vertical axis represents the day-to-day change in the retail price. Each small circle represents the simultaneous changes from one day to the next in the daily retail and current wiiolesale prices. All of the changes be- tween successive business days during the year are included in Figure 7. Cases where the same pair of changes in the two prices occur more than once are shown by numbers in the small circles, with the number indicating the frequency with which the particular pair of changes in the two prices oc- curred during the year. Even a casual examination of the scattergrajn in Figure 7 suggests that no systematic relationship exists between day-to-day changes in the retail and current wholesale prices. Practically no correlation exists (r - 0.03) and no trend or drift of average relationship is apparent. Figure 7 clearly y A somewhat similar hypothesis is considered by H. W. little and A. L. Meyers in: U. S. Bureau of Agricultural Economics. Estimated Lags Between Farm, Wholesale, and Retail Prices for Selected Foods" Washington, June 19U3« The results of that study, particularly for oranges, are subject to serious limitations. For an item such as oranges, daily data are necessary for the type of analysis undertaken. Also, the authors were not in a posi- tion to take advantage of distinction between current and lagged wholesale prices in their analyses. The authors did recognize and engage a hypothesis very meaningful for pricing and marketing policy, even though they failed to test the hypothesis with appropriate analyses. 3.0 2.5 2.0 FIGURE 7 ORANGES; RELATION BETWEEN DAY TO DAY CHANGES IN RETAIL PRICES AND CURRENT WHOLESALE PRICES AUGUST 2, 1948 TO JULY 30, 1949 o 2 '5 ui u c 0. d 10 4 »- UI a < X u a -.5 ■1.0 O -o- ® o o o o o o o o o o o o o o o OO OOOOOO ( o (3)0(2)0 o@ o@ o( @ o 00 ®o®o(S dMD — ft^ o 00 0(3)0^ I o (Do@oi o(D o @ ® ° o c o I o o o o o o 00 o(Do (2) 000 ®o@(D o(D(2)ooo o So o@ o o o@ @o-o dXI® — ° — ® (3)o@ (D o @ o o(S)o o o o@ o @o 00 o ® 00 o (D o o o o 00 -0-0-0- 000 o o o -4.2— O -1.5 _l_ O— •4.7 ■3.5 -3.0 -2.5 -2.0 -1.5 -1.0 "-.5 O .5 1.0 1.5 OAY TO DAY CHANGE IN CURRENT WHOLESALE PRICE (4/LB) 2.0 2.5 3.0 3.S -3k- indicates that day-to-day changes in the retail price of oranges occur independently of the simultaneous day-to-day changes in the current wholesale price. If the current wholesale price increases from one day to the next, the retail maricet price at the same time is about as likely to decrease as not; or, if the current wholesale price decreases from one day to the next, the retail market price is about as likely to increase as not. There is little doubt that the daily retail and cur- rent vrholesale prices change independently from one business day to the next, and it is clear that daily changes in the current wholesale price do not dominate or set the pattern of daily changes in the retail price of oranges. In Figure 8 is shown a scattergram of day-to-day changes in the re- tail and lagped wholesale prices of oranges. Figure 8 is constructed exactly the same as Figure 7 except that in Figure 8 the horizontal axis represents day-to-day changes in the lagged wholesale price. With in- spection of Figure 8, one is immediately made aware of the existence of a high degree of association (r ■ 0.90) between the day-to-day changes in the retail and lagged wholesale prices of oranges. As the lagged wholesale price changes from one day to the next, there is a strong ten- dency for the daily retail price also to change and in the same direc- tion as that in which the lagged wholesale price changed. There are exceptions to this tendency, but they are in a small minority; the gen- eral tendency is clear smd strong. It is evident that a systematic re- lationship exists between the daily changes in the retail and lagged wholesale market prices, which is in sharp contrast to the lack of any systematic relationship prevailing between daily changes in the retail and current wholesale market prices. The relation of the daily changes in the retail prices to the daily changes in the lagged wholesale price 1 -35- FIGURE 8. ORANGES; RELATION BETWEEN DAY TO DAY CHANGES IN RETAIL PRICES AND LAGGED WHOLESALE PRICES AUGUST 2, 1948 TO JULY 30, 1949 y o o o o o o ■ ' 1 * -.5 0 .5 1.0 1.5 20 2.5 3.0 DAY TO DAY CHANGE IN LAGGED WHOLESALE PRICE (♦/LBi -36- is linear within the range of experience encountered during the entire year investigated,-^ How do these findings check uri-th the hypothesis stated above, ex- pressive of the view held by many producers and shippers of oranges con- cerning the relation of changes in the retail price to changes in the wholesale price? Our findings are inconsistent with this hypothesis at two points. ■When the hypothesis is tested with reference to day-to-day changes in the retail and current wholesale prices, it must be rejected because no relationship is found between theraj the daily changes in those two series of prices occur independently of each other (Figure 7). When we considered day-to-day changes in the retail and lagged wholesale prices, a systematic relationship is found, but it differs markedly from that specified by the hypothesis. The relationship found (Figure 8) is linear between the daily changes in the retail and lagged wholesale prices. For 1/ To check further the hypothesis being examined and to uncover what are the relationships for various groups of stores> a similar analysis was made by store groups. The results, sximmarized below, confirm the conclu- sion that day-to-day changes in retail prices of oranges in the separate store groups are correlated substantially with the day-to-day changes in the lagged wholesale prices but not at all significantly with the day-to- day changes in the current wholesale prices of oranges. Day-to-day changes in retail and lagged wholesale prices Day-to-day changes in retail and current wholesale prices Store group Correlation coefficient Regression / coefficients' Correlation coefficient degression / coefficient^^ Very small stores 0.72 0.86 (17.68) -0.U+ -0.07 (0.i;7) Small stores 0.83 l.W (26.51) 0.22 0.11 (3.25) Medium stores ■ 0.92 l.h3 (li0.]42) O.lli 0.06 Large stores ■ 0.89 l,kl (33.00) 0.15 0.07 (1.90) Fruit and vegetable stores 0.81 0.96 ■ (23.85) -0.01 -0.003 i (0.115) All stores combined 0.90 1.27 (3lj.72) 0.03 .... .. 1 1 0.01 (0.53) 1 a/ Regression of day-to-day change in retail price (in cents per pound) on day-to-day change in wholesale price (in cents per pound )j figures in parentheses are t-ratios. -37- the hypothesis to be supported by the evidence, a scattergram such as that in Figure 8 should reflect the following: in the southwest quadrant, the line of average relationship would be horizontal or have a slight upward slope, and the line would pass through or near the originj and, then, in the northeast quadrant, the line of average relationship would have an up- ward slope steeper than that in the southwest quadrant. A simple model of that type might be represented by a linear but kinked line of average re- lationship with the kink occurring at or near the origin. A more sophis- ticated model of that type might be represented by a curvilinear average relationship passing through or near the origin and with the slope of the curvilinear function being positive in both the southwest and northeast quadrants but less steep in the former than in the latter quadrant. It is reasonably clear that such models, either the simple or more sophisticated, are not suggested by the actual relationships found to exist between day- to-day changes in the retail and lagged wholesale prices. INhen the daily changes in the retail price of oranges are related to the daily changes in either the current or lagged wholesale prices, we find no evidence to sup- port the notion that, when the wholesale market price of oranges advances, the retail price also advances and does so immediately, but when the whole- sale price declines, the retail price lags behind.^'' 1/ Ihis conclusion is based on analysis of prices of all oranges in- cluding a mixture of sizes, grades, and different states of origin. Analy- sis of the prices of a more homogeneous product, medium-sized California oranges, yields the following results* p« - 0.003 + 1.08 P' , r„, p, - 0.75j ^ (0.19b-) (19.33) Pr' ^ pt . _o.008 - 0.02 p • , r„, . - -O.Olij ^ (0.251) (0.67) Pi where p^ represents day-to-day changes in the retail price, P* represents day-to-day changes in the lagged wholesale price, w p' represents day-to-day changes in the current wholesale price, and the figures in parentheses are t-ratios. These statistics for medium-sized California oranges indicate results which are in line with those from the analysis of day-to-day changes in the retail and. wholesale prices of all oranges combined. -38- Lead-Lag Relations Among Daily Retail and "Wholesale Prices of Oranges . — Additional results bearing on the tendency of the daily prices to be related over time are now considered. Three sets of lagged corre- lations were computed: one set for the first half of the year, another set for the second half of the year, and a third set for the entire year. Below is summarized the third set which reflects the experience, of the year as a whole i TABIE 10 Lagged Coefficients of Correlation Between Daily Wholesale and Retail Prices of Oranges August l^Ue-JuOy 19h9 Number of Number of days ciu:rent Number of days current ■ wholesale days lagged wholesale price pre- wholesale price pre- cedes (+) and price pre- cedes (+) and follows (-) cedes (+) and ! follows (-) Correlation lagged whole- Correlation^ follows (-) Correlation 1 retail price coefficient sale price coefficient 1 retail price coefficient > +5 +0.7h +5 +0.75 +5 +0.86 *h ♦0.75 +u +0.76 +U +0.88 1 ♦3 +0.78 *3 +0.79 i +3 +0. 91 +2 +0.77 +2 +0.79 +2 +0.92 +1 +0.77 1 ♦1 +0.79 ♦1 +O.9I1 i ; 0 +0.75 : +0.77 0 +0.98 ! ; -1 +0.72 j -1 . 1 +0.7li , -1 +0.9li 1 ; -2 +0.70 i ■-2 j +0.72 -2 +0. 91 ! ! -3 • i +0.70 -3 1 +0.72 -3 +0.89 i +0.69 1 -u ■ i +0.72 -h +0.86 1 -5 I 1 +0.68 -5 1 +0.71 j, -5 +0.83 I i All of the above correlation coefficients are of a substantial magni- tude. However, what is of particular interest is the pattern they trace as the leads and lags are varied. The correlations increase and reach a high with a certain lead lag between the prices, then, the correlations decrease. First, consider the intertemporal relations between the daily retail and current wholesale prices of oranges. The first panel of Figure 9 shows the correlation coefficients for the half- and whole-year periods separately as the daily current wholesale price precedes the dally retail FIGURES. ORANGES; CORRELATION BETWEEN DAILY PRICES, RETAIL. LAGGED AND CURRENT WHOLESALE PRICES RETAIL AND CURRENT WHOLESALE PRICES 1.0 |- CURRENT AND LAGGED WHOLESALE PRICES .2 !-- 0 12 3 4 5 NO. OF DAYS CURRENT WHOLESALE PRICE PRECEDES RETAIL PRICE 1.0 .9 - FEB "49 - JULY "49 AUG. 48 - JULY 49 • .6 ) AUG. '48- JAN '49 ' .5 r 0 12 3 4 5 NO. OF DAYS CURRENT WHOLESALE PRICE PRECEDES LAGGED WHOLESALE PRICE RETAIL AND LAGGED WHOLESALE PRICES '0 0 12 3 4 5 NO. OF DAYS LAGGED WHOLESALE PRICE PRECEDES RETAIL PRICE price by different numbers of days. The highest correlation between the daily current wholesale and retail prices occurs with the pairing of the retail prices with the current wholesale prices of three days previously. For leads of more than three days or fewer than three days, lower corre- lations are found; and the correlations tend to decrease as successively greater lags in the current wholesale price are introduced. These rela- tionships suggest that the movements in the current wholesale price tend to lead those in the daily retail price. One may also make the inference that, in the aggregate, most of the oranges sold on a given day by the stores were purchased by them during the previous three or four days. It appears that an average inventory period of oranges in the stores amounts to about three days. The wholesale prices paid by the stores three days earlier are most closely related to the retail prices received by the stores on a particular day. In the correlations between the daily current and lagged wholesale prices, the highest degree of relationship occurs when the current whole- sale price precedes the lagged wholesale price by one to three days. Other leads and lags yield lower correlations which tend to become smaller as that one-to- three-day interval recedes. The significant point here is that the level of the current wholesale price on a particular day is not the best index of the level of the lagged wholesale price on the same day. The wholesale prices which retailers paid for the oranges they sold on a given day are not representative of the wholesale prices the retailers have to pay for oranges they buy on that same day. The correlations be- tween daily current and lagged wholesale prices, where the former precede the latter, are shown in the middle panel of Figure 9, Comparison of the first and middle panels of Figure 9 shows that the correlation patterns for the retail and current wholesale prices are very similar to the pat- terns for the current and lagged wholesale prices, ITe now consider the statistics on the relations among the daily retail and lagged wholesale prices of oranges. The corresponding correlation co- efficients are given in the third set of columns in the preceding tabula- tion, and the correlations in which the lagged wholesale prices precede the retail prices are shown in the third panel of Figure 9, It is clear that the highest correlation occurs when the daily retail and lagged whole- sale prices pertain to the same day, that is, with no introduction of lead or lag, A consistent pattern of decreasing correlation develops as leads are introduced, and the same occurs when lags are introduced. There ap- pears to be no evidence that the daily lagged wholesale price movements lead those of the daily retail prices. It is also of some interest to note that the correlations between the daily retail and lagged wholesale prices are all higher than the correlations in the other two sets. These findings confirm the view, as did evidence reviewed previously, that the behavior of the daily retail price in its movement over time is closely tied to the movement of the daily lagged wholesale price (almost regardless of what the going wholesale price was several days ago or what is to be the going wholesale price several days later). The inference may be made that the price retailers paid for the oranges they sold on a given day is a major factor setting the retail price charged by retailers for oranges on that day. We have uncovered no evidence so far suggesting that the current or going wholesale market price or its expected level plays a significant role in determining the retail market level of orange prices on a specific day. To investigate further the relation between the daily retail and whole- sale prices, the analysis was modified to take into account directly the direction and amount of initial changes in the wholesale prices of oranges. This was done by classifying the changes in the daily wholesale prices into three groT;5)s: large increases, small changes in either direction, and large decreases. First, let us consider the analysis with current wholesale prices. When the current wholesale price of oranges increased by an amount of O.U cent or more, the change is called a "large" positive one/ increases or decreases of less than O.Ji cent, or no change in the current wholesale price, are called "small" changes} and, when the current wholesale price decreases by an ajnount of O.U cent or less, the change is called a "large" negative one,^ For each such group separately, lagged correlations between the daily retail and wholesale prices were computed. This procedure permits noting the extent to which the degree of relationship between the daily retail and current wholesale prices is affected by the type of change in the current wholesale price. 1/ The intervals specifying the three groups were selected, after ex- amining the distribution of daily changes in the wholesale prices, so as to reflect the frequency of various amounts of change and to yield a suffi- cient number of observations in each of the groups such that their statis- tics would be meaningful. -U2- In Figure 10 are summarized the correlation results, -with each of the three panels showing the relationships associated with a given type of change in the current wholesale price. The coefficients are tabulated as follows for the year as a whole. TABLE 11 Lagged Coefficients of Correlation Between Daily Retail and Current Wholesale Prices of Oranges August 19U8-July 19U9 Number of days current wholesale price precedes retail price Large positive change in current wholesale price Small or no change in current wholesale price Large negative change in current wholesale price nit/ r n r n r 0 107 +0.65 97 +0.92 . 107 +0.8U 1 107 +0.71 97 +0.91 106 +0.83 2 107 +0.73 97 +0.90 105 +0.8U 3 107 +0. 71 96 +0.89 105 +0.8U k 106 +0.70 96 +0.90 105 +0.77 5 106 +0.68 95 +0.90 105 +0.79 a/ n indicates number of paired changes on which the corresponding correla- tion coefficients are based. It is evident from Table 11 that, when the current wholesale price changes by a small anount in either direction, the daily retail and cur- rent wholesale prices of oranges show a closer relationship than when the change in the current wholesale price is a large positive one or a large negative one. The statistics also suggests that, when the current wholesale price of oranges decreases by a large amount, the daily retail and current wholesale prices retain a closer relationship than when the change in the current wholesale price is by a large positive amount. When the current wholesale price change is a large positive one, some lag of several days . occurs in the subsequent partial adjustment of the retail price. But, when the current wholesale price change is a large negative one, the short-run partial adjuslanent which occurs in the retail market price oc- curs almost immediately, and then some four or five days later, a lower relationship prevails between the daily retail and current wholesale prices. Similar statistics is presented in Table 12 for lagged wholesale prices. As previously, three groups are established according to the di- rection and amount of change in the lagged wholesale price. The criteria "13- FIGURE 10. ORANGES; CORRELATION BETWEEN RETAIL AND CURRENT WHOLESALE PRICES, BY TYPE OF DAY TO DAY CHANGES IN CURRENT WHOLESALE PRICE LARGE POSITIVE CHANGE IN CURRENTWHOLESALE PRICE - FEB. '«» ■ JULT '4» III C g.3 u .z .1 0 SMALL CHANGE IN CURRENT WHOLESALE PRICE FEB. 4»- JULY 49 AUO '46 - JULY '49 AUO. 4a- JAN 49 I LARGE NEGATIVE CHANGE IN CURRENT WHOLESALE PRICE :i .8 .7 .6 .S .4 - FEB '49 JULY '4t AUO '4« - JULY '49 »" I NUMBER OF DAYS CURRENT WHOLESALE PRICE PRECEDES RETAIL PRICE FIGURE II. ORANGES; CORRELATION BETWEEN RETAIL AND LAGGED WHOLESALE PRICES, BY TYPE OF DAY TO DAY CHANGES IN LAGGED WHOLESALE PRICE LARGE POSITIVE CHANGE IN LAGGED WHOLESALE PRICE >vrFrr' '49 - JULY '49 N , ^AUB.' 4B • JULY '49 i.7 o 3 1 9 S • U«. '4a ■ JAN '49 SMALL CHANGE IN LAGGED WHOLESALE PRICE I LARGE NEGATIVE CHANGE IN LAGGED WHOLESALE PRICE AUa. '4a - JULY '49 Aua. '49 ■ JAN. '49 1 NUMBER OF DAYS LAGGED WHOLESALE PRICE PRECEDES RETAIL PRICE for these groups are altered because the frequency distribution of daily changes in the lagged wholesale price differed from the frequency dis- tribution of daily changes in the current wholesale price. For the analy- sis with changes in the lagged wholesale price, tJtie following criteria are established for the three groups: daily increases in the lagged wholesale price amounting to 0.2 cent a poimd or more are grouped together as "large" positive changes; no change or a change of less than 0.2 cent a pound, positive or negative, is grouped together and called a "small" changej and daily declines in the lagged wholesale price amounting to 0.2 cent a pound or more are grouped together as "large" negative changes. For each of the three types of changes in the lagged wholesale price, correlations were computed between the daily retail price and lagged wholesale prices of or- anges. The results for the year as a whole are as follows: TABLE 12 . Lagged Coefficients of Correlation Between Daily Retail and Lagged Wholesale Prices of Oranges August 19ii8-July 19k9 Number of days Large positive Small or no Large negative lagged wholesale change in lagged change in lagged change in lagged price precedes wholesale price wholesale price wholesale price retail price ni/ i r n ; r n r 0 83 i +0.98 iii5 +0.98 Bh +0.98 ^ 1 83 ^ +0.95 +0.97 6k +0.93 ; 2 83 +0.92 iliU ; +0.95 83 +0.92 3 83 1 +0.86 lit3 1 +0.93 2^ +0.92 k 83 ! +0.86 1U2 \ +0.92 83 +0.89 5 83 +0,6$ ihl i +0.89 ; 83 +0.86 a/ n indicates number of paired changes oh which the corresponding correla- tion coefficients are based. Examination of the statistics in Table 12, and in Figure 11, suggests that the correlation patterns appear to be veiy similar. No pronounced or distinctive pattern of correlation prevails whether the lagged wholesale price increases or decreases by a large amount or changes slightly. For all three groups considered, the correlation between the daily retail and wholesale prices is highest vdth no lag between the prices; and the corre- lations diminish as lags are introduced so as to yield about similar pat- terns for the three groups. In summary, it appears that the retail market price of oranges is about as responsive to large declines as to large advances which occurred in the going wholesale market price of oranges. The evidence indicates that, if anything, the retail market price may be slightly more responsive to large declines which occurred in the going wholesale price. But, even in this situation, retailers as a group in the short-run setting of their retail prices are guided more closely by the prices they paid for the or- anges than by the going wholesale prices if the latter differ from the former. -ii6- Leiaons: Daily Prices and Retail Margins Fresh lemons, one of the three major citrus fruits, ai-e distributed by shippers and sold by wholesalers and retailers throughout the year. Supplies shipped and sold during the November-April period are commonly called "printer" lesaons, and those shipped and sold during the May-October period are commonly referred to as "summer" lanons. The characteristics of the seasonal patterns in f.o.b. sliipments and prices are analyzed else- where.i'^ In this report we are concerned with the characteristics of the behavior of daily retail and wholesale prices of lemons. From the view of marketing practices and policies, the short-run characteristics of prices, such as the level of and variation of daily prices, are of importance to producers, shippers, wholesalers, and retailers as well as consumers. Also of considerable interest and importance are the relationships prevailing among the daily retail and wholesale prices of lemons and the spread be- tween them. Types of Daily Lemon Prices .— The record of daily prices of lemons analyzed is shown in Hgure 12. The period covered includes the business days from the beginning of August. 19U8 to the end of July 19k9» Three dif- ferent types of average daily prices are shown in Figure 12: retail, cur- rent wholesale, and lagged wholesale. The retail prices reflect the average level of the prices received by the stores for the lemons they sold. For a given day, the average retail price is constructed by weighting that day's retail price of each store by its volume of retail sales of lemons on that day. The current wholesale prices reflect the average level of the prices paid by the stores for the lemons they sold. The average current wholesale price for a given day is constructed by weighting that day's wholesale pur- chase price paid by each store by the volume of lemons purchased by the store on tiiat day. The lagged wholesale prices reflect the average level of prices paid by the stores for the lemons they sold. For a given day, the lagged wholesale price is constructed by weighting the -niiolesale places paid by the stores for the lemons they sold on that by the volume of lemons they sold on that day. The lagged wholesale price thus reflects the aver- age cost to the stores for the lemons sold at retail on a given day, 1/ Hoos, Sidney, and R. E, Seltzer. Lemons and Lemon Products, Changing Economic Relationships, 1951-5 2. Berkeley, 1952. yOp. (Calif, Agr, Exp, Sta. Bui. 129) FIGURE 12 LEMONS; RETAIL AND WHOLESALE PRICES, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 26 24 20 o z O a. a: bJ a. RETAIL PRICE 18 "V 1 u) 16 z UJ 14 12 10 vr • \ V IN I:- A: h k LAGGED WHOLESALE PRICE A CURRENT WHOLESALE PRICE^ — I— I — I — I — I — I — I — I — I — I 1 I I I ■ ■ 1. I ■ ■ 7 21 4 18 2 16 30 13 27 II 25 8 22 5 19 5 19 AUG SEPT OCT NOV. DEC. JAN. FEB. MAR. 1948 i 1 1 1 1 1 1 ! I ! I I I I l_l ■ ■ ■ I ■ ■ l_ 2 16 30 14 28 II 25 9 23 APR. MAY JUNE JULY 1949 -4 I -Ii8- Exanination of Figure 12 indicates that the three types of daily- prices have much in common in their movement over timej yet, certain dif- ferences are also noticeable. In terms of trend and major swings, the three types of daily prices tend to move along together; but, in ternis of short- tern behavior and day-to-day changes, the three prices act differently. It is the latter -type of short-term behavior which is of primary importance frcm the view of this report. From Figure 12 it appears that from the view of day-to-day variation the retail price of lemons behaves more like the lagged wholesale price than the current ;^olesale price. Also noticeable from the figure is that the current wholesale price seems to fluctuate more widely than the lagged wholesale price of lemons. To help clarify the tendencies in the average levels, fluctuations, and interrelationships of the retail and wholesale prices, IJiey will be reviewed in some detail later* First, we review the general trends in the prices during the year. During the year as a whole, there was a general upward trend in ■Uie prices of lemons, but the period began with a price decline during August 19^8 followed by a recovery in the next month. Prices were then fairly stable for about the next four months, m January 19k9f a sharp advance to a higher level occurred reflecting in large part the cold weather and freeze of that year in the lemon-producing area. For about three months the prices remained at the higher level and then declined during April 19k9» Beginning with May 19h9, however, an upward trend developed and continued on to nearly the end of the year investigated. These broad movements, with a mixture of periods of advancing, stable, and declining prices, occurred in the daily retail, current wholesale, and lagged wholesale prices of lemons. Average Pally Lemon Prices .— Following the pattern set earlier in the discussion of daily prices of oranges, we now turn to the comparative average levels of the daily prices of lemons. Although many of the distinctive features of the daily prices are submerged when broad averages are used, such measures can be helpfUl as supplements to information in- herent in Figure 12, Hence, the following average prices are summarized: -U9- TABLE 13 Average Daily Prices of Lemons August 19ii8-July 19k9 Type of daily price First six months, August I9I48- January 19U9 Second six months, February 19U9- July 19U9 Year, August 19U8- July 15li9 cents per pound Retail 18,1 22.3 20,2 Lagged wholesale 12.2 15.U 13.8 Current wholesale 12.3 15.5 13.9 As is to be expected from what is clearly evident in Figtire 12, the prices averaged higher in the second half than in the first half of the yearj and, over intervals as long as six months, the daily lagged and current wholesale prices of lemons have just about equal averages. Yet, Figure 12 clearly indicates that the daily lagged and current wholesale prices behave differently. When the prices are steadily advancing, the current wholesale price tends to be above the lagged wholesale price, and the reverse holds when prices are steadily declining. This occurs because, in fact, ihe lagged wholesale price is in a sense a moving average. Of the lemons sold in a given day, some may have been bought by the store the same day, some may have been bought in the preceding day, and some in earlier days. Such a distribution of the purchases by the stores of the lemons they sell on a given day affect% as will be noted later, the spreads between daily retail and wholesale prices. Variability of Daily Lemon Prices .— To proceed with background informa- tion on the behavior of daily lemon prices, we next review their vartability over time. The six-month and yearly average measures of variability appear in Table lU. In view of the two fairly distinct different levels of prices prevailing in the first and second halves of the year, it is meaningful to give atten- tion to semiannual results. In cents per pound, the daily retail and lagged wholesale prices fluctuated in about equal amounts but less than the daily current wholesale prices. In relative terms as measured by the coefficients of variation, however, the daily current wholesale price of lemons fluctuated -50- sonewhat more than the daily lagged wholesale price and considerably more than the daily retail prices of lemons. It may also be noted that the notion—the closer to the producer, the more variable over time is the price — prevails in lemon prices when the relative variability is consid- ered? but the time period involved and the type of wholesale price consid- ered, as well as the measure of variability used, affect the results. TABLE lU Measures of Average Variability in Daily Prices of Lemons August 19U8-Juny 19U9 Type of First six months, August I9I48- January 19l).9 Second six months, February 19U9- July 19U9 Year, August 19ii8- July 19U9 daily price Standard jCoenicient deviation lof variation Standard deviation Coefficient of variation Standard deviation Coefficient of variation cents per pound per cent cents per pound per cent cents per pound per cent He tail 1.38 7.6 0.95 li«3 2.U2 12,0 LafTf^ed wholesale 1.37 11.3 0.96 6.2 2.02 IU.6 Current xrholesale 1.55 12.6 1.31 1 ' ' 2.16 The greater variability in the daily current wholesale price than in the daily lagged wholesale prices of lemons reflects the fact that the latter price is an average of the preceding current wholesale prices. In terms of the prices the stores pay from day to day, the variability of the current wholesale price is of Interestj but, in terms of the prices the stores paid for the lemons they sold, the variability of the lagged whole- sale price is of interest. Relations Betvreen Daily Lemon Prices .— Inspection of Figure 12 gives a rough idea of the extent to ^rtiich the movements in the daily retail, cur- rent wholesale, and lagged wholesale prices are related. Visual examination suggests that the association betiireen the daily retail and lagged wholesale prices is closer that the association betireen the daily retail and current Triiolesale prices. This suggestion is confirmed by the following correlation statistics: i -51- TUBLE 15 Coefficients of Correlation Between Daily Retail and VJliolesale Prices of Lemons August lPU8-July 19U9 Correlation between types of daily prices First six months, August 19U8- January 19h9 Second six months, February 19lt9- July 19li9 Tear, August 19U8- July 19U9 Retail and lagged wholesale +0.97 +0.87 +0.98 Retail and current wholesale +0.78 +0.56 +0,88 Lagged and current wholesale +0.82 +0.55 +0.88 These measures clearly support the idea that the daily retail prices of lemons are more closely related to the daily lagged wholesale prices than to the daily current wholesale prices. In fact, the relationship between the current and lagged wholesale prices is of about the same order as that between the daily retail and cxirrent wholesale prices. For all three pairs of prices, the coefficients are higher for the first half of the year than the second half. This is accounted for, in part, by the fact that the range betsreen low and high prices in the first half of the year is wider than the corresponding range in the second half. The strong relationship found between the daily retail and lagged wholesale prices of lemons may be viewed as some tentative evidence con- cerning the pricing practices of retailers, in the aggregate, in their merchandising of lemons. With the correlation results as a basis, the following inference can be made. In the setting and changing of retail prices of lemons, the aggregate behavior of retailers is as if they tend to give primary attention to the wholesale prices they paid for the lemons. Apparently, only secondary attention is given to the going or current wholesale price if it differs from the previous wholesale price paid by the retailers for the lemons they are selling. Since it has been shown that the daily retail prices of lemons are related to the daily current and lagged wholesale prices (more to the latter than the former), the next point considered is how much the retail -52- price changes for given changes in the wholesale price. This point is of some interest because marketers often make estimates of how much the retail price is likely to change along with or in response to changes in the whole- sale prices. The average changes in the daily retail prices of lemons associated with their daily wholesale prices are summarized in the following tabula- tion: TABLE 16 Equations of Linear Regression of Daily Retail Prices on Daily Wholesale Prices of Lemons August 19U8-July 19U9 Regression of daily retail prices on daily whole- ,sale prices First six months, August 19h8- January 19U9 Second six months, February 19i49- July 19U9 Year, August 19U8- July 19U9 Constant Regression coefficient Constant Regression coefficient Constant Regression coefficient Retail on lagr^ed wholesale Retail on current wholesale cents per pound 6.20 , (25.66)a/ 9.52 (17.17) + 0.98 (U9.U7) + 0.69 (15. 5U) 8.86 (IU.56) 15.9U (20.96) + 0.87 (22.10) + 0.55 ( 8.37) U.06 (19.63) 6.U8 (15.09) + 1.17 (78.70) + 1.02 (32.22) a/ Figures in parentheses are t-ratios . . The regression statistics support the view that larger changes in the dally retail price of lemons are associated with changes in the lagged wholesale price than with changes in the current wholesale prices of lemons. lihen the results for the whole year are considered, a 1-cent-a-pound change in the lagged wholesale price is associated with an average change in the same direction in the retail price by an amount of almost 1.2 cents a pound; whereas, for a change of 1 cent a pound in the current wholesale price, the retail price changes in the same direction by an average amount of about 1 cent a pound. In other terms, the daily retiail price tends to be more responsive to changes in the daily lagged wholesale price Vcian to changes in the current wholesale price. -53- In the preceding regression, eqixabions, the conatcaat terras can be considered as statistically significant. Hence, the regression Lines of averaf^e relationships between the retail and wholesale prices csnnot be viewed as if, aside from sampling variation, they pass through the origin of the axes. Accordingly, there are no grounds for believing that a con- stant percentage relationship tends to prevail between the daily retail and current or lagged wholesale prices of lemons. l/ To investigate this question further, we turn now to a consideration of the spread betereen retail and wholesale prices. jSpreads Bett-reen Daily Lemon Prices .— 'In Figures 13 and lit are pre- sented various types of spreads betiieen daily retail and wholesale prices. Hie data in Figure 13 include daily absolute spreads, in cents per pound, between the daily retail and current wholesale prices of lemons and also the corresponding relaiive spreads which are the absolute spreads expressed as per cent of the retail prices. Similar spreads are shown in Figure lii between the daily retail and lagged wholesale prices of lemons. As one examines Figures 13 and lU, one finds that the spreads in Figure 13 appear to fluctuate more widely than do the spreads in Figure lit. One also notes that the relative spreads in both figures tend to fluctuate about a horizontal trend during the year, although the level of prices themselves was higher in the second half than in the first half of the year. In both figures the absolute spreads rose to a higher level in the second half of the year than prevailed in the first half of the year. To confirm these broad generalizations, we review some statistical measures. First, we consider average daily spreads for the half years and for the year as a whole: 1/ The Durbin-Watson test ( Biometrika , 19^1) indicates a significant (l-per-cent probability level) positive serial correlation among the residuals of the daily retail prices (for regression of daily retail on lagged whole- sale prices, n " 306, k« " 1, d ■ 0.30j for regression of daily retail on current wholesale prices, n " 289, k« " 1, and d ■ 1.10, Thus, the least- squares formulation is open to some question as a valid statistical model, and the text statement is less acceptable as an inferred generalisation than as a description of the relationships found for the sample data. FIGURE 13 LEMONS; SPREADS BETWEEN RETAIL AND CURRENT WHOLESALE PRICES. ABSOLUTE AND RELATIVE, DAILY, AUGUST 2, 1948 TO JULY 30. 1949 -RELATIVE SPREAD in V ^.jjj _ If/ ' ' ' ' ^ABSOLUTE SPREAD 30H T 21 4 IS 2 16 30 13 27 II 29 B 22 S 19 S 19 2 16 30 14 26 II 23 9- 23 AUG. SEPT OCT NOV DEC. JAN. FEB. MAR. APR MAY JUNE JULY 1948 1949 FIGURE 14 LEMONS, SPREADS BETWEEN RETAIL AND LAGGED WHOLESALE PRICES, ABSOLUTE AND RELATIVE, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 V n RELATIVE SPREAD ABSOLUTE SPREAD ' 21 4 '8 2 16 30 13 27 II 25 6 22 OCT 1948 9 19 5 19 2 16 30 14 28 II 25 9 23 FEB APR. 1949 TABLE 17 Average Spreads Between Daily Retail and Wholesale Prices of Lemons August 19li8-July 19h9 lypes of spreads between daily- retail and whole- sale prices First six months, August 19H8- January 19k9 Second six months, February 19U9- July 19U9 August 19U8- July 19U9 cents per pound per cent of retail price cents per pound per cent of retail price cents per pound per cent of retail price Absolute spreads Retail and current wholesale 6.8 6.3 Retail and lagged wholesale 6,8 6.U Relative spreads Retail and current wholesale 32.0 30.6 31.3 Retail and lagged wholesale 32.9 30.7 31.8 These averages do show that the absolute spreads were higher while the relative spreads were lower in Hie second half of the year as compared with the first half. It is also noted that, in terms of six-month averages, very little difference emerges between the spreads based on current whole- sale prices and the spreads based on lagged wholesale prices, let, from the view of imputing gross profits, the spread between the daily retail prices and lagged wholesale prices is the logical one to use. In this connection, it may be repeated that the lagged wholesale price measures the wholesale price paid by the stores for the lemons sold on a given day. Variability of Daily Lemon Price Spreads .— To check the comparative variabilities in the two types of spreads over time, the following measures are presented: -56- TABLE 18 Measures of Average Variabili-ty in Daily Price Spreads of Lemons August 19li8-July 19h9 Types of spreads be- tween daily First six months, August 19li8- January 19U9 Second six months, February 19U9- July 19U9 Year, August 19U8- July 19li9 retail and wholesale prices Standard devia- tion Coefficient of variatton Standard devia- tion Coefficient of variation S'tandard devia- tion Coefficient of variation cents per pound per cent cen'ts per pound per cent cents per pound per cent Absolute spreads Retail and current wholesale 0,86 15 0.82 12 1,00 16 ■Retail and lagged wholesale 0.3U o.US 0.62 10 per cent Relative spreads Retail and current wholesale 5.19 16 3.92 13 U.6U 15 Retail and lagged wholesale 2.95 1 9 2.3U 8 2,87 9 These statistics confirm the idea that the daily spreads between the retail and cxirrent wholesale prices of lemons fluctuate more widely than do the daily spreads between the retail and lagged wholesale prices of lemons, and this applies to both the absolute and relative spreads. The generalization holds whether fluctuation is thought of in basic unit terms as measured by the standard deviation or relatively as measured by the coefficient of variation. But it may also be noted that generally little difference is found In the relative variabilities of the absolute and relative spreads for the retail and current wholesale prices and, likewise, for the absolute and relative spreads between the retail and lagged wholesale prices of lemons. Daily Variation in Store Operations in Lemons .-- -To analyze the systematic variation of store operations within the week, various indexes were constructed. They were computed for daily store purchases of lemons, retail sales and prices, current wholesale prices paid by stores for lemons, and the two types of spreads between daily retail and wholesale prices. The resulting indexes for each half of the year and for the year as a whole are shown in Figure l5j below are given the sets of indexes for the entire year: TABLE 19 Indexes of Daily Variation in Retail Store Operations in Lemons August 19U8-July 19U9 Business day Retail price Current wholesale price Store sales Store purchases Retail and lagged Wholesale price spread Retail and current wholesale price spread average c )f business days during week " 100 Monday 99.8 100. U 83.5 155.1 99.8 99.0 Tuesday 100.0 100.2 81.5 91.0 99.7 100.0 Wednesday 99.9 99.U 86.2 82.1 99.9 101.0 Thursday 100.0 99.6 9U.5 99.9 99.6 101.5 Friday 100.1 99.5 112.5 12U.8 100.3 101.9 Saturday 100.2 lOl.U 1U2.3 25.3 100.7 9U.8 Examination of the daily indexes of the retail prices of lemons pro- vides strong evidence that the stores, in the aggregate, show no systematic daily variation in the retail prices during the week. All of the daily indexes in that set are just about equal to the daily average. No sugges- tion is found of the practice of "week end specials" in a regular way. To the extent that such special sales prevail, their number and volume are not sufficient to have a noticeable impact on the aggregate daily indexes for all stores combined. When we examine the indexes of daily variation in the current whole- sale prices of lemons, some systematic variation is noticeable but it is only very slight, There may be a minor tendency for the current wholesale prices early in the week and at the very end on Saturday to average minutely 160 FIGURE 15 LEMONS, DAILY VARIATION IN RETAIL STORE OPERATIONS; STORE SALES, PURCHASES, RETAIL AND CURRENT WHOLESALE PRICES, AND PRICE SPREADS (DAILY AVERAGE - 100) 160 140 120 100 80 60 \ \ \ 40 ' 20 FEB. "49 - JULY "49 SPREAD BETWEEN RETAIL \ AND CURRENT WHOLESALE \ ) /A a tut>Tnjiyi» >%i Mi^ i ^ji. ' jS * Cl'.. ' jiJi.i i il» «*MMa — c;> / t SPREAD BETWEEN RETAIL AND LAGGED WHOLESALE PRICE ISO 140 120 100 80 60 40 20 AUG. '48 - JULY '49 CURRENT WHOLESALE PRICE t I MON. TUE. WED. THU. FRL SAT MON. TUE. WEO. THU. FRI. SAT MON. TUE. WED. THU. FRI. SAT -69' higher than during the week. The Saturday index may be on shaky ground and not fully meaningful in view of the low volume of purchases ocourilng on that day as will be noted below, Oie may suspect that the differences among the daily indexes of the current wholesale prices of lemons are not sufficiently marked to be viewed as significant differences. The next set of indexes reviewed describes the variation in daily sales of lemons by the stores as a group. There, a pronounced pattern of variation within the week is noticeable. Store sales of lemons early in the week are relatively low* This is due to the fact that households apparently have a slack demand for lemons early in the week because they have supplies left over from week-end purchases. As the week progresses, however, households restock their supplies and purchase lemons at an in- creasing rate. This occurs at an increasing tempo with the week end having the largest volume of sales, especially on Saturday. The relatively heavy sales of lemons on Fridays, followed by even heavier sales on Saturdays, take place because households then obtain their supplies for use during the week end and the next several days. Thus, the pattern of daily varia- tion in store sales of lemons is tied closely to purchase habits of households, rather than being induced by price considerations as such. It may also here be noted that, when extreme variations in the temperature occur, unusually warm in the summer months or unusually cold in the winter season, households increase their purchase of lemons. This tendency in the summer months occurs because of the popular use of lemons in the home- making of cool drinks, while in the winter months when unusually low temperatures prevail and respiratory difficulties may be fairly wide- spread, there is a popular use of lemons in the homemaking of hot drinks to alleviate "colds" and similar ailments .V But purchases for such uses, either in the summer or winter, have no impact on the indexes because there is no systematic pattern within the week in the occxirrence of extreme temperatures , When we examine the daily indexes of store purchases of lemons, we find a different pattern than was characteristic of the store sales of lemons. In the daily sales, the week begins with a higher volume of 1/ For evidence, see U. S. Bureau of Agricultural Economics, Consumers' Use^of a nd Opinions About Citrus Products , October, 195l« (Agr. Inf, Bui. -60- purchaaes than occurs in any of the following days of the week. As the week progresses, store purchases tend to decrease, reaching a low on Wednesday, After that day, store purchases of lemons increase, reaching a peak on Friday but a lower one 'Uian that of Monday, On Saturday, store purchases tend to be very low and much smaller in volume than any of the previous days of the week. The relatively high purchases of lemons by the stores on Monday take place then because the stores buy their supplies to replace those sold during the »rush" days of the preceding Friday and Saturday and also to provide inventory for use during the next several days. Ch Thursday the purchases increase in getting ready for the week-end business and even more are purchased on Friday for the same reason. By the end of Friday, practically all of the week's purchases by the stores have been completed. Saturday purchases are made only by some very small stores or sporadically by some other stores to obtain particular sizes or grades to fill in their inventories. Considering the daily indexes of store purchases of lemons together with the indexes of current wholesale prices and store sales, it appears that the pattern of store purchases is based in large part on the pattern of sales and appears to be induced hardly at all by the pattern of current wholesale prices, ihe store purchase pattern can be said to be derived from the sales pattern and, hence, results primarily from habitual and traditional behavior of households in their purchase of lemons. As in store sales, the purchases of lemons by the stores are irregularly and sporadically influenced by extreme variations in temperature. But these influences are not reflected in the pattern of daily purchases of lemons by stores, probably for the reasons noted above in connection with the discagsion of the pattern of daily sales. There now remains to be considered the patterns of daily variation in the spreads between the retail and wholesale prices of lemons. Examina- tion of the sets of indexes for the retail and lagged wholesale prices and the retail and current wholesale prices reveals no pronounced patterns. This situation, of course, reflects the lack of pronounced patterns in the variation of the daily retail price and the current wholesale price. There does occur, however, a considerable drop in the Saturday index of the re- tail and current wholesale price spread. That drop reflects the higher -61- index for Saturday in the current wholesale price compared with the corre- sponding index in the daily retail price on Saturday, Yet, it must be noted again that only a very small volume of lemons is generally purchased l>y stores on Saturday. Since the pattern of store gross earnings is reflected by the spread between the retail and lagged wholesale prices and no appreciable pattern is evident in the indexes of that spread, there is little evidence to sup- port the view that stores in the aggregate regularly tend to experience higher earnings, per pound of lemons sold, on certain days as compared with other days of the week. Yet, the high volume of sales during the last two days of the week can mean that, in terms of gross profits, stores in the aggregate do earn more on the week-end days than in previous days of the week. Relations Between Daily Lemon Prices and Spreads .— Having reached the conclusion that no significant systematic patterns of daily variation are evident in the daily retail and wholesale prices and the spread between them, we now turn to a consideration of the relationships among the daily- spreads and prices. Such relationships are implicit in the materials reviewed earlier, but now we attempt to set them forth explicitly, m that connection, we consider relative as well as absolute spreads and lagged as well as current wholesale prices. To indicate the degree and direction of association generally pre- vailing among the daily spreads and wholesale prices, we first review the correlation statistics in Table 20, These correlation coefficients may be better interpreted with the aid of Figures l6 and 17, Figure l6 shows the relationship between the daily absolute spreads and the daily lagged wholesale price, and Figure 17 shows the relationship between the daily relative spreads and the daily lagged wholesale prices. Although similar figures for the spreads and current wholesale prices were prepared for study and analysis, they are not reproduced here. The correlation between the daily absolute spreads and lagged wholesale price for each of the half years turns out to be negative, although the coefficients are small and not considered significant in probability terras, When the year as a whole is considered, the correlation is positive but not of a high order. These statistics, supplemented by Figure 16, suggest that a very loose relation prevails among the daily lagged wholesale price and -62- FIGURE 16 LEMONS, RELATION BETWEEN ABSOLUTE RETAIL- LAGGED WHOLESALE PRICE SPREAD AND LAGGED WHOLESALE PRICE, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 180 5 7 0 , «.0 00 — o o 00 O O 00 o eo o - o o 00 oo o o O (JIO 00 o (JxsSQifioo oooooo - 0®0O ® O ® 01 O OO O® OOO o 0®O o o 00 O 00 00 0 o o o (SD o o® o - - od® ® o (S3)odiolesale price more closely than the daily current wholesale price. We may now proceed with review of the regression relations among the daily retail and wholesale prices of grapefruit. Such relations are suia- mariZGd below for each of the half years and the entire year for the re- gression of the daily retail price on each of the two types of wholesale prices. TABIE 27 Equations of Linear Regression of Dally Retail Prices on Daily VJholesale Prices of Qrapefrult August 19li8-Juljr 19U9 Regression of daily retail prices on daily whole- sale prices First six months, August 19U8- Januaiy 19U9 Second Febra Jul; six months, ary 19U9- f 19U9 I Augu Jul ear, St 19U8- 7 19U9 Constant Regretsion coefficient Constant Regression coefficient Constant Regression coefficient Retail on lagged wholesale Retail on cuiTxnt whole Gale cents per pound 2,02 ^/ 3.53 (11.60) 1.20 (28,09) 0.95 (19.27) 1.32 (lit.32) 1.98 ( 8.00) 1.28 (loU.oo) 1.18 ( 35.68) 1.81 (13.98) 2.82 (15.03) 1.23 (6U.3U) 1.07 (39.02) a/ Figures in parentheses are t-ratios. -81- All of the previous statistics are significant in a probability sense. The effects on the retail price of changes in the wholesale prices' were slightly more pronovmced in the latter half than in the first half of the year. For the year as a whole, a change of 1 cent a pound in the daily lagged wholesale price is associated with an average change in the same direction of almost 1.2 cents a pound whereas a change of 1 cent a pound in the daily current wholesale price is accompanied by an average change in the same direction of about 1 cent a pound in the retail price. In each of the half years, as well as for the year as a whole, the daily retail market price of grapefruit responds more to changes in the lagged wholesale price than to changes in the current wholesale price. Since the constant terms in the regression equations are statistically significant, there is no evidence that a constant percentage relationship prevails be- tween the daily retail and wholesale market prices of grapefruit .-'^ This raises questions as to what are the characteristics of the spread between the daily retail and wholesale prices and what are the relations of the spread to the prices. Spreads Between Daily Grapefruit Prices .— In Figures 23 and 2k are shown the daily spreads between the retail and wholesale prices of grape- fruit, with Figure 23 including the absolute and relative spreads between the retail and current wholesale prices and Figure 2k including the abso- lute and relative spreads between the retail and lagged wholesale prices. It is apparent from Figures 23 and 2k that, although the trends in the two absolute spreads are very similar as are the trends in the two relative spreads, the day-to-day changes and the variabilities seem to be different. In the following tabulation are shown the average daily spreads in absolute and relative terms: 1/ The Durbln-Watson test ( BLometrika , 1951) indicates a significant (1-per cent probability level) positive serial correlation among the residuals of the daily retail prices (for regression of daily retail on lagged wholesale prices, n - 307, k' 1, d = 0.77} for regression of daily retail on current wholesale prices, n =• 292, k' » 1, d " O.98). Thus, the least-squares formulation is open to some question as a valid statistical model, and the text statement is less acceptable as an in- ferred generalization than as a description of the relationships found for the sample data. -82- FIGURE 23 GRftPEFROIT; SPREADS BETWEEN RETAIL AMD CURRENT WHOLESALE PRICES, ABSOLUTE AND RELATIVE, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 RELATIVE SPREAD - «0 lis ABSOLUTE SPREAD fi 01 I I ■ ' * ' -i- I I I I ■ TO SO -|40l- z kl 10 1 to 10 T Zl 4 IS t 16 30 15 27 II 25 AUe. SEPT OCT NOV. DEC. 1946 22 S l» S 19 2 16 30 14 28 II 29 9 23 JAN. FEB. MAR. APR. MAY JUNE JULY lt4B nOURE 24 GRAPEFRUIT; SPREADS BETWEEN RETAIL AND LAGGED WHOLESALE PRICES, ABSOLUTE AND RELATIVE, ' DAILY, AUGUST Z, 1948 TO JULY 90, 1949 I CO 90 .RELATIVE SPREAD r . 40 I ■ so 20 S ABSOLUTE SPREAD 10 Ol-< — ' — ' " I ' — I — i— I — I — 1 — I — 1 — 1 — I — 1 — 1 — 1 — 1—1 — I — I — I ■ ■ ■ ■ . ■ . ■ ...» * .,o'5 * «S.r '? " " " 23 • 82 8 19 9 19 2 16 SO 14 2S II tS • tS AUe. SEPT .2SI ■ J*"- FEB- ""R 1948 APR. MAY JUNE JULY 1949 -83- TABIE 28 Average Spreads Between Daily RetaU and Wholesale Prices of Grapefruit August 19U8-July 19U9 Types of spreads between daily retail and whole- sale prices First six months, August 19U8- January 19U9 Second i Februj Julj six months, ary 19U9- 7 19U9 Year, August 19U8- July 19U9 Absolute spreads Retail and current wholesale Retail and lagged wholesale Relative spreads Retail and current wholesale Retail and lagged wholesale cents per pound per cent of retail price cents per pound per cent of retail price cents : per pound per cent of retail price 3.2: 3.2 35.U 35.3 3.3 3.U 31.3 32.1 3.2 3.3 33.U 33.7 The absolute spreads averaged very slightly higher in the second half of the year than in the first half, although the relative spreads averaged lower In the second half compared with the first half of the year. As an over-all average, the absolute spread between the retail and wholesale prices of grapefruit is about 3.3 cents a pound while the relative spread is about 33 per cent of the retail price. As may be expected when six- month or yearly averages are compared, veiy little difference is found between the spreads based on current and lagged wholesale prices. Variability of Daily Grapefruit Price Spreads .— We next look at the comparative variabilities over time in the daily spreads as described by the following statistics t -Bh- TABLE 29 Measures of Average Variability in Daily Price Spreads of Grapefruit August 19U8-July I9I49 Type of spreads be- tween daily First six months, August I9U8- Januaiy 19k9 Second six months, Februasry I9U9- July 19U9 I'ear, August I9U8- July 19U9 retail and wholesale prices Standard devia- tion Coefficient of variation devia- tion of variation oT>euiaaru devia- tion \jO exi 1 c xeni> Ox variation cents cents cents per pound per cent per pound per cent per pound per cent Absolute spreads Ketail and current wholesale 0.72 22 0.61 18 0.67 20 Retail and lagged wholesale 0.71 22 0.U8 2k 0.61 18 per cent Relative spreads Retail and current wholesale 7.07 20 U.UO lit 6.2U 19 Retail and lagged i^olesale U.77 lU 2.36 7 ij.07 12 The statistics for the absolute spreads, in terms of cents per pound, indicates only a slightly lower average variability in the retail and lagged wholesale price spread than in the retail and current wholesale price spread. But the statistics for the relative spreads suggests that the variability in the retail and current wholesale price spread is sig- nificantly greater than the variability in the retail and lagged whole- sale price spread. Daily Variation in Store Operat ions in Grapefruit . -¥e consider now variability of store operations within the week. Pertinent measures are shown in Figure 25 for each of the six months and for the year. Jfi^sures for the entire year are given in Table 30 j r 160 FIGURE 25 GRAPEFRUIT; DAILY VARIATION IN RETAIL STORE OPERATIONS; STORE SALES, PURCHASES, RETAIL AND CURRENT WHOLESALE PRICES, AND PRICE SPREADS (DAILY AVERAGE = 100) 160 AUG. '48 -JAN. '49 140 120 100 80 60 40 20 MON. TUE. WED. THU. FRI. SAT. 0 MON. FEB. '48- JUL. '49 \ -/ \ SPREAD BETWEEN RETAIL / V AND CURRENT WHOLESALE ^/ • \ PRICE-. ^-^/ .. v< / A r / 7 '7 SPREAD BETWEEN RETAIL AND LAGGED WHOLESALE PRICE \ \ \ \ \ \ \ \ 1 1 -J 1 160 140 120 - 100 SO - 60 40 20 AUG. '48 - JUL. '49 CURRENT WHOLESALE ^ PRICE \ TUE. WED. THU. FRI. SAT. MON. TUE. WED. THU. FRI. SAT. -86- TABIE 30 Indexes of Daily Variation in Retail Store Operations in Grapefruit August 19U8-Juaor 19k9 Retail and Retail and Current lagged current Business Retail wholesale Store Store wholesale wholesale day price price sales purchases price spread price spread average of bus; jiess days during week ■ 100 Monday 100.0 101. U 86.7 ll;8.9 99.9 98.0 Tuesday 100.1 100.3 78.7 80.5 99.8 100.1 Wednesday 100.0 100.8 83.14 81.2 100.0 98.6 Thursday 99.8 99.2 100.7 121.6 99.0 100.6 Friday 99.0 99.2 115.2 126«3 99.2 100.6 Saturday 100.7 98.8 138.9 2U.7 102.1 102,9 No significant patterns of daily variation within the week are noticeable in the retail or current wholesale prices. One might suspect that the same conclusion applies to the price spreads, although the spreads on Saturday average slightly higher than on the other days of the week. Inlhen the daily variation in the store sales and purchases are ex-> aminedf pronounced patterns are readily noticeable. In the store sales, the business week begins with purchases on Monday at a higher level than on the following two days. Tuesday appears to be the "slowest" day in the sales of grapefruit. Beginning with Wednesday, sales pick up and continue to increase through the rest of the week. Friday and Saturday are the b\isiest days of the week in the sale of grapefruit, with Saturday sales averaging considerably above those of Friday. In the store pirrchases of grapefruit, Monday is the "high volume" day. Large purchases are made on Monday to replace inventory sold dxiring the previous Friday and Saturday and also to provide working inventoty for the following several days. Purchases of grapefruit drop substan- tially on Tuesday and remain low on Wednesday. Beginning with Thursday and continuing on Friday, store purchases of grapefruit are inade in sub- stantial volume to provide stocks for the busy sales days on Friday and Saturday. Relatively small volumes of grapefruit are purchased by the -87- the stores in the aggregate on Saturday. Although no systematic patterns of daily variation within the week are evident in the prices and spreads, such patterns are found for the store purchases and sales of grapefruit. The purchase and sales patterns not only are pronounced but fit together in a logically consistent manner. Relations Between Daily Grapefruit Prices and Spreads *— •Having con- sidered the variability of store operations within the week, we now re- turn to relationships between the daily prices and the spread between ttiem. Some of these relationships are implicit in the data and results reviewed earlier. Now we can consider the relationships in more explicit terms. The statistics are presented so that they may be con^jared with corresponding results for oranges and lemons. First we consider the degree of association between the daily prices and spreads. In Table 31 are presented some correlation coef f icients t TABLE 31 Coefficients of Coirelation Between Daily Spreads and Wholesale Prices of Grapefrtilt August 19i;8-July 19ii9 Correlation between types of daily prices and spreads First six months, August 19U8- January 19U9 Second six months, Febrmry 19U9- July 19U9 Year, August 19U8- JxHy 19k9 Prices and absolute spreads Lagged wholesale price and spread between it and retail price +0.35 +0.88 +0.55 Current wholesale price and spread between it and retail price -0.03 ♦0.U6 +0.20 Prices and relative spreads Lagged wholesale price and spread between it and retail price -0.59 -0.80 -0.6? Current wholesale price and spread between it and retail price -0.7U -0.63 -0.71 -88- In the second half of the year, there prevailed closer association between the absolute spreads and daily retail prices than was found in the first half of the year. Other than that, diverse results were obtained. When the absolute spreads are related to the wholesale prices, a closer relationship is found with the lagged wholesale price than with the cur- rent wholesale price. But, when the relative spreads are related to the wholesale pidce, the several time periods show differing resultsj for the year as a whole, the relative spread is more closely related to the cur- rent wholesale price than to lagged wholesale price, although the reverse holds in the second half of the year. From these statistics, it is diffi- cult to discern clear and sy strati c relationships which hold uniformly between the spreads and wholesale prices of grapefruit. Figures 26 and 27 are scattergrams of the relative spreads and the wholesale prices, lagged and current, respectively. Although a consider- able amount of scatter is evident, there is also noticeable a tendency for the spreads and prices to be related. To estimate how much the spread tends to change ae the prices vary, the following measures were computed in Table 32. The absolute spread between retail and lagged wholesale prices Is more responsive to changes in the lagged wholesale price than is the ab- solute spread between the retail and current wholesale price to changes in the daily curr^t wholesale price of grapefruit. But the relative re- tail and current wholesale price spread responds more to changes in the current wholesale price than does the relative retail and lagged wholesale price spread to changes in the lagged wholesale price. Considering the year as a irtiole, a change of 1 cent a pound In the daily lagged or curirent wholesale price is associated with an average change in the opposite di- rection of about 1.8 per cent in the relative retail and lagged wholesale price spread and an average change of about 2.75 in the relative retail and current wholesale price spread. Again, for the year as a idiole, a change of 1 cent a pound in the daily lagged or current iriiolesale price is asso- ciated with an average change in the same direction of about 0.20 cent in the retail and lagged wholesale price spread and less than 0.10 cent in the retail and current wholesale price spread. There is no evidence that abso- lute spreads tend to bear a constant percentage relationship to the whole- sale prices. -89- FIGURE 26 GRAPEFRUIT; RELATION BETWEEN RELATIVE RETAIL- LAGGED WHOLESALE PRICE SPREAD AND LAGGED WHOLESALE PRICE, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 90 FIGURE 27 GRAPEFRUIT; RELATION BETWEEN RELATIVE RETAIL- CURRENT WHOLESALE PRICE SPREAD AND CURRENT WHOLESALE PRICE, DAILY, AUGUST 2, 1948 TO JULY 30, 1949 TO, 4.0 5.0 6.0 7.0 8.0 9.0 CURRENT WHOLESALE PRICE («/LB.) -90- TABIE 32 Equations of Linear Regression of Daily Retail and Wholesale Price Spreads on Daily Wholesale Prices of Grapefruit August 19U8-July 19U9 First six months, August I9U8- January 19U9 Second six months, February 19l*9- July I9U9 Yea: August July : 19U8- L9U9 Regression of daily spreads on daily wholesale prices Constant Regres- sion coef- ficient Constant Regres- sion coef- ficient Constant Regres- sion coef- ficient cents per pound Absolute spreads on wholesale prices Retail and lagged wholesale price spread on lagged wholesale price 2.0U / ( l.^hP 0.20 ( U.61) 1»33 (lli.72) * 0.28 (23.11) 1.82 (13.87) + 0.22 (11.67) Retail and cur- rent wholesale price spread on current whole- sale price 3.31 (11.80) - 0.02. ( 0.3U) 1.92 ( 7.95) + 0.18 ( 5.73) 2.69 (15.19) + 0.08 ( 3.22) per Cent Relative spreads on wholesale prices Retail and lagged wholesale price spread on lagged wholesale price ii8.91 (31.3U) - 2.26 ( 8.89) Ul.32 (72.18) - 1.27 (16.36) U5.81 (58.U8) - 1.82 (15.83) Retail and cur- rent wholesale price spread on current whole- sale price (30.75) - 3.69 (12.II4) 1 . . , ii5.oo (29.88) - 1.81 ( 9.0I4) 51.65 (U3.77) - 2.76 (15.9U) a/ Figures in parentheses are t-ratios. Sensitivity of Retail to Wholesale Prices of Qrapefiniit , — Now we shall consider the extent to which day-to-day changes in the daily retail price of grapefruit follow day-to-day changes in the wholesale price. The scattergrams in Figures 28 and 29 bear on this question. In Figure 28, the day-to-day changes in the retail price are plotted against the corresponding day-to-day changes in the current wholesale price* In Figure 29, the day- to-day changes in the retail price are plotted against day-to-day changes in the lagged wholesale price. r\ ■ ■ FIGURE 28 GRAPEFRUIT; RELATION BETWEEN DAY TO DAY CHANGES IN RETAIL PRICES AND CURRENT WHOLESALE PRICES AUGUST 2, 1948 TO JULY 30, 1949 2.0 1.5 1.0 -.5 -1.0 -1.5 o o o o o o ® o o o o® o ®o o(D o- o-o-o (D-o-o (g ® o ©@ o®@(i; 6 o o o o oooo(|)®oo o@ oo ®o®®®®®® o o ®(D®(D ■1.0 -1.5 J- O o o o o o ® .5 0 .5 DAY TO DAY CHArTGE IN LAGGED WHOLESALE PRICE (*/LB.) 1.0 -93- The day-to-day changes in the current wholesale and retail prices of grapefruit appear to be independent of each other. No correlation is found (r ■ 0.06). But there is a noticeable tendency for the day-to-day changes in the lagged wholesale and retail prices of grapefruit to be positively correlated (r ■ 0.31) • Thus, for grapefruit, as was found previously for oranges and lemons, the retail market price changes from one day to the next tend to follow the lagged wholesale price changes but not those of the current wholesale price.— ^ There seems to be no indica- tion that the retail market price quickly follows the current wholesale price when it advances but follows it only sluggishly when it declines. Leads and Lags Among Daily Retail and VJholesale Prices of Grape - fruit .— We turn next to a consideration of lead and lag relations among the prices. In Figure 30 are pictured patterns of lagged correlations between the daily prices for each half of the year and for the entire year. The following table includes the lagged correlation coefficients based on the entire year's dataj l/ The corresponding statistics for store groups, summarized below, indicates that the day-to-day changes in retail prices of grapefruit in the several groups of stores are much less correlated with the day-to-day changes in the current wholesale price than with the day-to-day changes in the lagged wholesale price of grapefruit. Store group Day-to-day changes in retail and lagged wholesale prices Day-to-day changes in retail and current wholesale prices Correlation coefficient Regression / coefficient^' Correlation coefficient Regression / coef ficient^' Very small stores 0,ii6 0.66 -0.27 -0.07 ( 7.5U) (0.8U) Small stores 0.63 0.99 0.11 O.OU (li*.05) (1.26) Medium stores 0.31 0.6U 0.03 0.02 ( 5.7U) (0.56) Large stores 0.65 0.96 0.29 0.20 (lii.77) (3.U1) Fruit and 0.63 mo . 0.55 0.36 vegetable stores (13.78) (3.92) All stores 0.31 0.U8 0.06 0.2U combined ( 5.55) (0.90) a/ Regression of day-to-day change in retail price (in cents per pound) on ~ day-to-day change in wholesale price (in cents per pound)} figures in parentheses are t-ratios« MU- TABLE 33 Lagged Coefficients of Correlation Between Daily Wholesale and Retail Prices of Grapefruit August 19U8-July 19h9 Number of days cur- rent w no a aJLO price pre- cedes re- tall price tion coef- ficient Number of (iavfi cur- rent wholesale price pre- lagged wholesale price Cor re la » tion coef- ficient Nuinber of days lagged wholesale price pre- cedes re- tail price Correla- tion coef- ficient 5 +0.93 ♦0.95 5 +0.97 U +0.92 U +0.95 k ♦0.97 3 ♦0.92 3 +0,96 3 +0.96 2 +0.92 2 +0.96 2 +0.96 1 +0.92 1 +0.96 1 +0.97 0 +0.91 0 +0.95 0 +0.96 The above lagged correlation coefficients reflect a cohesiveness in the structure of retail and wholesale prices of grapefruit* The daily current wholesale prices of grapefruit, as much as of five preceding days, are closely related to the daily retail prices. In fact, as the lead decreases in number of days, there appears to be a slight loosening in the association with the retail prices, although the correlations change very little and probably by insignificant amounts. The set of lead and lag correlations between the daily current wholesale and retail prices suggests a slight tendency for the retail prices to follow the daily cur- rent wholesale prices, but the evidence is not strong* The lead and lag correlations between the daily current and lagged wholesale prices displ^ no definite pattern. The degree of association between the prices is about the same whether the current wholesale price precedes the retail price by five days, by only one day, or not at all. The set of lead and lag correlations between the daily lagged wholesale and retail prices of grapefruit also displays no definite pattern. 1 FIGURE 30 GRAPEFRUIT; CORRELATION BETWEEN DAILY PRICES, RETAIL, LAGGED AND CURRENT WHOLESALE PRICES RETAIL AND CURRENT WHOLESALE PRICES FEB. '49- JUL-Y '49 ■AUG. 48- JULY 49 AUG. '48 -JAN. '49 0 I 2 3 4 5 NO. OF DAYS CURRENT WHOLESALE PRICE PRECEDES RETAIL PRICE CURRENT AND LAGGED WHOLESALE PRICES FEB.'49- JULY '49 AUG. "48 - JULY '49- -AUG. '48- JAN. '49 0 1 2 3 4 5 NO. OF DAYS CURRENT WHOLESALE PRICE PRECEDES LftGGED WHOLESALE PRICE RETAIL AND LAGGED WHOLESALE PRICES 1.0 .6 J- FEB. '49 - JULY '49 • ••••• AUG. '48- JULY '49 -AUG. "48 - JAN. '49' 1 vo 0 12 3 4 5 NO. OF DAYS LAGGED WHOLESALE PRICE PRECEDES RETAIL PRICE -96- To examine in greater detail the lead and lag relations between the daily current wholesale and retail prices of grapefruit, three sets of correlations were computed. One set is based on days for which the daily current wholesale price increased by a "large" positive amount of at least 0.2 cent per poxind. The second set was calculated for days for which the daily current wholesale price increased or decreased by a "small" amount less than 0.2 per pound. And the third set was based on days for which the daily current wholesale price decreased by a "large" positive amount of at least 0.2 cent a pound. The correlation coefficients are pictured in Figure 31, and those for the year as a whole are summarized in Table }h» TABLE 3U Lagged Coefficients of Correlation Between Daily Retail and Current Wholesale Prices of Grapefruit August 19li8-July 19h9 Number of days current wholesale price precedes Large positive change in current wholesale price Small or no change in current wholesale price Large negative change in current trtiolesale price retail price r n r n r 0 105 +0.95 101 +0.93 105 +0.89 1 105 +0.96 101 +0.96 loU ♦0.87 2 105 +0.93 100 +0.97 loU +0.90 3 105 +0.96 99 +0.93 loU ♦0.91 U. 105 +0.97 98 +0.96 loU +0.88 5 105 +0.93 1 J 98 +0.97 103 +0.90 a/ n indicates number of paired changes on which the corresponding ~ correlation coefficients are based. When the previous sets of correlation coefficients are examined, no systematic patterns are uncovered related to the number of days by which the daily current wholesale price precedes the daily retail price of grapefruit. Attention should be drawn, however, to the fact that all the correlation coefficients in the group "large negative changes in current >rtiolesale price" are consistently lower than the corresponding coefficients in the other two groups. This suggests that the retail price of grapefruit follows the current wholesale price less closely when the latter decreases by a "large" amount than when it increases by a "large" amount. r FIGURE 31 GRAPEFRUIT; CORRELATION BETWEEN RETAIL AND CURRENT WHOLESALE PRICES BY TYPE OF DAY TO DAY CHANGES IN CURRENT WHOLESALE PRICES -98- Summary and Comparison of Findings To provide the reader with a resume of the preceding sections, here is a summary of some of the findings. There is, however, another reason for making available such a summary at this point. That is to compare the respective findings for the three citrus fruits— oranges, lemons, and grapefruit. Wholesale and Retail Prices, Their Interrelations .— Below are summa- rized the average levels of the prices during the year investigated. TABIE 35 Average Daily Prices August 19U8-July 191+9 Types of daily price Oranges Lemons Grapefruit cents per pound Retail 12.1 20.2 9.9 Lagged wholesale 8.2 13.8 6.6 « Current wholesale 8.U 13.9 6.6 The daily prices of oranges lie between those of lemons and grape- frviit, and this holds for both retail and wholesale prices. The prices of grapefruit are nearly half, in cents per pound, of the lemon prices, and the prices of oranges are about 60 per cent of the lemon prices. In all three citrus fruits, the average daily lagged and current wholesale prices for the year are about equivalent. This may be expected for periods as long as a year and even for six-month periods. Absolute variability, in cents per pound, and relative variability, in per cent of the average prices for retail and wholesale prices, are shovm in Table 36. -99- TABLE 36 Measures of Average Variability in Daily Prices August 19U8-July 19U9 Oranf^es Lemons Grapefruit Types of daily price Standard deviation Coefficient of variation Standard deviation Coefficient of variation Standard variation Coefficient of variation cents per pound per cent cents per pound per cent cents per pound per cent Retail 1.6U 13 2.U2 12 1.92 19 Lagged wholesale 1.18 Hi 2.02 ■ 15 1.51 23 Current wholesale 1.29 15 2.16 16 1.63 2U As measured by the standard deviation, the daily retail prices tend to fluctuate more than the daily wholesale prices and the daily current wholesale prices tend to fluctuate somewhat more than the daily lagged wholesale prices for each of the three fruits. But, as measured by the coefficient of variation, the daily retail prices tend to fluctviate a lit- tle less than the daily lagged wholesale price which, in turn, tends to fluctuate slightly less than ths daily current wholesale price. It is commonly understood that retail prices tend to fluctuate less over tiire than do wholesale prices which are supposed to fluctuate l^ss than f.o.b. prices, and they, in turn, are supposed to fluctuate less than farm prices. Such a view is consistent with the above measures of relative variability. But, in terms of absolute variability or in cents per pound, the daily retail prices fluctuate more than do the wholesale prices. The correspondence in the general movements of the daily prices is summarized by the following correlation coefficients: -100- TABLE 37 Coefficients of Correlation Between Daily Retail and Wholesale Prices, August l^US-July 19U9 Correlation between types of daily prices Oranges Lemons Grapefruit Retail and lagged wholesale Retail and current whole sals Lagged and current wholesale cents per pound +0.98 ■K).75 +0.77 +0.98 +0,88 +0.88 +0.96 +0.91 +0.95 In all three citrus fruits— oranges, lemons, and grapefruit— there is a high degree of association in the general movements of the daily re- tail and lagged wholesale prices. Although the correlations between the retail and lagged wholesale prices for oranges and lemons are a little higher than that for grapefruit, the difference between the coefficients is not sufficient to be deemed highly significant. For all three fruits, but particularly for oranges and lemons, retail and lagged wholesale prices are substantially hi^er than between the retail and current whole- sale prices. The preceding correlation coefficients suggest that the re- tail market prices of oranges, lemons, and grapefruit follow the lagged wholesale price more closely than the current or going wholesale price. To indicate the average changes in the daily retail prices associated with changes in the daily wholesale prices, the following regression rela- tionships are presentedj TABIE 38 Eqviations of Linear Regression of Daily Retail Prices on Daily Wholesale Prices, August 19U8-July 19U9 Regression of daily retail prices on daily wholesale prices Oranges Lemons Grapefruit Constant Regression coefficient Constant Regression coefficient Constant Regression coefficient Retail on lagged wholesale Retail on current 'vrtiolesale cents per pound 0.93 , ( 7.002/ U.21 (10, Ul) + 1.36 (85.U9) + 1.03 (19.87) U.06 (19.63) 6.U8 (15.09) + 1.17 (78.70) + 1.02 (32.22) 1.81 (13.98) 2.82 (15.03) + 1.23 (6U.3U) + 1.07 (39.02) a/ Figures in parentheses are t-ratios. -101- Flrst, one may note that the constant terms in the regression equa- tions are statistically significant. This suggests that a constant per- centage relationship between the daily retail and wholesale prices does not prevail. This applies to oranges and lemons as well as to grapefruit. Second, the results indicate that the daily retail prices of each of the three fruits respond more to changes in the daily lagged wholesale prices than to changes in their daily current wholesale prices. This evidence again suggests that retail market price tends to follow more closely the historical wholesale cost than the replacement wholesale cost of the fruit. Spreads Between Wholesale and Retail Prices .— First are the average daily spreads between the prices as shown in Table 39 and measures of variability in Table UO. TABLE 39 Average Daily Spreads Between Daily Retail and Wholesale Prices, August 19U8-July 19U9 Types of daily spreads Oranges Lemons Grapefruit cents per pound per cent of retail price cents per pound per cent of retail price cents per pound per cent of retail price Absolute spreads Retail and current, wholesale 3.7 6.3 3.2 Retail and lagged vrtiolesale 3.9 6.U 3.3 Relative spreads Retail and c\xrrent wholesale 31.2 31.3 33 .1* Retail and lagged wholesale 32.1 31.8 33.7 i The average daily absolute spreads for oranges, in cents per pound, lie between those for lemons and grapefruit, with lemons the highest and grapefruit the lowest. The average absolute spread for grapefruit is about half of that for lemons, and the average absolute spread for oranges -102- is about 60 per cent of that for lemons. These relations among the aver- age daily spreads of the three citrus fruits are similar, to those noted earlier for the percentage relations among the average daily prices of or- anges, lemons, and grapefruit. It will be noted, however, that the abso- lute spreads expressed as a percentage of the retail price are of about the same magnitude for the three fruits. TABIE UO Measures of Average Variability in Daily Price Spreads August 19U8-Juay 19k9 Types of spreads be- tween daily Oranges Lemons Grapefruit ffltai 1 and whole sal3 prices Standard devia- tion Coefficient of variation Standard devia- tion Coefficient of variation Staiidard devia- tion Coefficient of variation cents per pound per cent cents per pound per cent cents per pound per cent Absolute spreactg Retail and current ^diolesale 0.85 22 1.00 16 0.67 20 Retail and lagged wholesale o.Sh 2h 0.62 10 0.61 18 , „ P®^ cent Relative spreads Retail and current wholesale 6.17 20 U.6U 6.2U 19 Retail and lagged wholesale 2.12 7 2.87 9 U.07 12 As presented in Table UO, it will be observed that the spread between the retail and current wholesale prices has greater variability over time than does the spread between the retail and lagged wholesale price. -103- This holds for variation measured in actual units or relatively and char- acterizes both the daily absolute spreads and the daily relative spreads " for all three of the fresh citrus fruits. Daily Variation in Store Operations .— While on the topic of varia- bility over time in the price spreads, it is appropriate here to review the tendencies found viith respect to systematic variation during the week in the retail store operations concerned with merchandising fresh citrus. In that connection, indexes of variation with the business week are pre- sented in Tables kit ^» k3 for the prices, spreads, purchases, and sales of the three citrus fruits. TABIE hi Indexes of Daily Variation in Retail and Current TOiolesale Prices, August l^l^S-July 19h9 Oranges Lemons Gra pefruit Current Current Cuirent Business Retail wholesale Retail wholesale Retail T^olesale day price price price price price price average of business days during week - loo Monday 101 100 100 100 100 101 Tuesday 100 98 100 100 100 100 Wednesday 100 98 100 99 100 101 Thursday 100 101 100 100 100 99 Friday 99 99 100 100 99 99 Saturday • 1 , , i 100 103 100 101 101 99 The above indexes of the daily retail prices indicate that no regu- lar and systematic pattern of variation within the week tends to prevail. Although some stores may have "week end specials," they are not regular or widespread enough to be reflected in the indexes. In the daily cur- rent wholesale prices, also, no pronounced or clearly ascertainable pat- tern of weekly variation is apparent. TABIE h2 Indexes of Daily Variation in Spreads Between Daily Retail and Wholesale Prices August 19i48-July 19k9 Oranges Lemons Grapefruit Spread Spread Spread Spread Spread Spread betiveen bettveen between between between between retail retail retail retail retail ratal 1 and and and and and and lagged current lagged current lagged current whole- whole- whole- whole- whole- whole- OUSXXIcSS sale sale sale sale sale sale day prices prices prices prices prices prices average of business c lays durir ig week - 100 Monday 101 100 100 99 100 98 1 Tuesday 101 lOU 100 100 100 100 i 1 "Wednesday 99 103 100 101 100 99 ! Thursday i 100 97 100 102 99 101 i Friday . 100 102 100 102 99 101 I Saturday 1 i 99 9k \ \ 101 9$ i c 1 102 103 For oranges, lemons, and grapefruit, no systematic patterns of varia- tion within the -week seem to prevail in the spread between the daily re- tail and lagged wholesale prices. Whatever departures do occur from the daily average during the week are not sufficiently pronounced to be con- sidered as reflecting significant variation. In the spread between the daily retail and current wholesale prices of oranges, Tuesday and Wednes- day may tend to be higher than the weekly average, but that is not fully cl^arj and the lower average spread on Saturday for oranges and lemons is not fully meaningful in view of the very low volumes of purchases made on that day by the stores. From the above indexes, no strong evidence is found for regular and systematic patterns of variation within the week in the behavior of the spreads. -10$- TABLB U3 Indexes of Daily Variation in the Purchases and Sales August 19U8-July 19k9 Oranges Lemons Grapefruit Business Store Store Store Store Store Store day purchases sales purchases sales purchases sales avera ge of business day s durin g week = 100 Monday lli3 155 8U 1U9 87 Tuesday 91 78 91 82 80 79 Wednesday 87 66 82 86 81 83 Thursday llU 95 100 9h 122 101 Friday iko 119 125 112 126 U5 Saturday 111 138 25 ll;2 25 139 In both the store purchases and sales of fresh citrus, we find pro- nounced patterns of daily variation, and the patterns for oranges, lemons, and grapefruit correspond to a considerable extent. In the purchases, the week begins with the highest volume of purchases by the stores on Monday to replace inventory sold during the previous week end and provide inventory for the early part of the week. As the week progresses through Wednesday, purchases by the stores tend to decrease. But, by Thursday, the volume of purchases has strengthened markedly and increases even fur- ther on Friday to build up working stocks for the week-end trade. On Saturday, only a slight volume of citrus purchases is made by the stores which are busy in their sales operations, and those small purchases are made to fill in stock with particular sizes and grades. The pattern of sales variation is different from but consistent with the purchase pattern. The week begins with a moderate volume of sales on Monday and falls off somewhat during the next day or two. By Wednesday, sales of fresh citrus generally begin to increase and continue to do so during the rest of the week, with Friday and Saturday being "the busy days" of the sales week. Saturday sales usually are greater than Friday's although on both those days households build up their stocks for use dur- ing the week end and the beginning of the following week. -106- The patterns of purchases and sales reviewed previously reflect the aggregate operations of all the stores* It may well be that particular stores, or groups of stores, experience different patterns of variation, especially in the retail prices for those stores which frequently have "week end specials." But, from the view of total market effects, the above patterns of variation within the week reflect the operations of the stores in the aggregate. Relations Between Spreads and Prices . — Statistics bearing on the re- lations between spreads and prices are given in Tables hk and ii5* TABLE hh Coefficients of Correlation Between Daily Spreads and Wholesale Prices, August 19U8-July 19h9 Correlation between types of daily prices and spreads Oranges Lemons Grapefruit Prices and absolute spreads Lagged wholesale price and spread between it and retail price +0.79 +0.53 +0.55 Current wholesale price and spread between it and retail price +0.1U +0.08 +0.20 Prices and relative spreads Lagged wholesale price and spread between it and retail price -0.3ii -0.76 -0.67 Current wholesale price and spread between it and retail price -0.i;2 -0.67 -0.71 First, it may be deduced from Table hh that practically no correla- tion exists between the daily retail price and the absolute spread be- tween the daily retail and current wholesale prices. Also, it may be observed that, for oranges, there are only low correlations between the daily retail price and the relative spread between the retail and whole- sale prices, lagged or current. The remaining correlations are of a moderate magnitude, sufficient to be viewed as significant but not highly so. Generally, the absolute spread is positively related to the whole- sale prices, and the relative spread is negatively related to the whole- sale prices. For lemons and grapefruit, higher correlations prevail -107- between the relative spread and the wholesale prices than between the absolute spread and the wholesale prices, but, for oranges, the highest correlation is between the absolute spread and the lagged wholesale price. TABLE U5 Equations of Linear Regression of Daily Retail and Wholesale Price Spreads on Daily Wholesale Prices August 19U8-July 19k9 Regression of daily spreads on daily wholesale prices Or an ges Lemons Grapefruit Constant Regres- sion coef- ficient Constant Regres- sion coef- ficient Constant Regres- sion coef- ficient _ Absolute spreads on wholesale prices Retail and lagged wholesale price spread on lagged wholesale price Retail and current wholesale price spread on current wholesale price Relative spreads on cents per pound + 0.92 , ( e.9iw * 3.02 ( 8.63) + 0.36 (22.59) + 0.05 ( 2.28) + U.12 (19.75) + 5.76 (13.83) + 0.16 (10.9U) + O.Oli ( 1.25) + 1.82 (13.87) + 2,69 (15.19) + 0.22 (11.67) + 0.08 ( 3.22) per cent +37.13 (U5.97) +I48.36 (20.71) - 0.61 ( 6.27) - 2.05 ( 7.38) +U6.63 (63.00) +51.78 (35.87) - 1.08 (20.27) - I.ll7 (lli.3U +U5.81 (58.1^8) +51.65 (U3.77) - 1.82 (15.83) - 2.76 (15.9U) wholesale prices Retail and lagged wholesale price spread on lagged wholesale price Retail and current wholesale price spread on current wholesale price a/ Figures in parentheses are t-ratios« It can be inferred from Table U5 that, for all three of the citrus fruits, the absolute spread between the daily retail and current whole- sale prices is insensitive to changes in the daily current wholesale price. -108- For all three of the citrus fruits, the relative daily spreads are some- what more responsive to changes in the current wholesale price than to changes in the lagged wholesale prices. Also, for all three fruits, the regression statistics provides no basis for believing that a constant per- centage relationship prevails between the daily spreads and wholesale prices. Sensitivity of Retail Prices to Changes in Wholesale Prices .— The be- lief is held by some producers and marketers that retail prices respond differently when wholesale prices are rising than when they are fallingo It is claimed that, vhen wholesale prices advance, retail prices follow along qidcklyj but vrtien wholesale prices decline, retail prices lag behind and follow sluggishly. To check the idea, day-to-day changes in the re- tail prices were correlated with simultaneous day-to-day changes in the wholesale prices. When the daily changes in the current wholesale prices are related to the simultaneous changes in the daily retail prices, we find no system- atic relationship. When the daily changes in the lagged wholesale prices are related to the simultaneous changes in the daily retail prices, we find a pronounced tendency towards a positive and linear relationship (r = 0.90 for oranges, 0.U6 for lemons, and 0.U8 for grapefniit). The day- to-day changes in the retail prices are associated with the simultaneous day-to-day changes in the lagged wholesale prices. Such I'elationship prevails for all three of the citrus fruits, although to a lesser extent in lemons and grapefruit than in oranges. When the daily changes in the current wholesale prices are related to simultaneous changes in the daily prices, practically no correlation is found (r • 0.03 for oranges, -0.01 for lemons, and 0.06 for grapefruit). The results do not support the view that the retail prices of the three citrus fruits respond differently to advances than to declines in the wholesale market prices. To probe the subject further, additional calcula- tions are reported in Table hS to uncover the existence of lead-lag rela- tions among the retail and wholesale prices. Sensitivity of Retail to Wholesale Prices . — In the following tabiaa- tion is summarized some statistics on intertemporal relations among the daily retail and wholesale prices 1 -109- TABLE k6 Lagged Coefficients of Correlation Betvreen Daily TWiolesale and Retail Prices of Oi'anges August 19ii8-July 19h9 Number of days current wholesale price pre- cedes retail price Citrus fruit if 3 2 1 0 Oranges 0.7li 0.75 0.78 0.77 0.77 0.75 Lemons 0.91 0.91 0.90 0.90 0.90 0.88 Grapefruit 0.93 0.92 0.92 0.92 0.92 0.91 Number of days curren ■j wholesale price pre- cedes lagged wholesale price k 2 1 Oranges 0.75 0.76 0.79 0.79 0.79 0.77 Lemons 0. 92 0.92 0.92 0.91 0.90 0.88 Grapefruit 0.91 0.91 0.90 0.90 0.90 0.88 Number of days lagged wholesale price pre- ' cedes retail pric e ! 5 h 3 2 1 0 Oranges 0.86 0.88 0.91 0.92 0.9li 0,98 Lemons 0.96 0.97 0.97 0.97 0.97 0.98 1 Grapefruit ,1 ., , 0.97 0.97 0.96 0.96 0.97 0.96 i . ) These lagged correlation coefficients suggest some tendency for the retail prices of oranges, lemons, and grapefruit on a given day to be less related to the current wholesale price of that day than to the cur- rent wholesale price which prevailed several days previously. The tend- ency is not a strikingly strong one, but it is noticeable and does fit in well with the view that the daily retail prices tend to lag behind the current or going wholesale prices. The previous set of correlations also indicates a tendency for the daily lagged wholesale prices of oranges, lemons, and grapefruit to fol- low behind the daily current wholesale prices of the three citrus fruits. The correlation between the current and lagged wholesale prices on a particular day tends to be less than the correlation between the lagged wholesale price of a given day and the current wholesale price of several -no- preceding days. The tendency for the movement of the cui'rent wholesale prices, although not a strong tendency, to precede the movement of the lagged wholesale prices derives from the fact that the inventory which stores have on hand and sell on a given day was purchased by the stores, in the main, during the several preceding days. The lagged wholesale price, which represents the produce cost to the stores for the citrus they sell on a given day, is an average of the preceding days' current wholesale prices which represent the produce cost to the stores for the citrus purchased on those days. From the previous correlation statistics, we conclude that, in or- anges, there is a pronounced tendency for the retail price to be more closely related to the lagged wholesale price of a given day than to the lagged wholesale price of the preceding days* Such a tendency is only slightly noticeable for lemons, to a considerably lees extent than for or* anges. In grapefruit, the situation is still less clear. It appears that the structural lead and lag relations between the daily retail and lagged wholesale prices of lemons and grapefruit are more rigid than are the structural lead and lag relatione between the daily retail and lagged wholesale prices of oranges. This differential behavior may be due In part to the varying degrees of perishability of oranges compared wLth lemons and grapefruit and to the individual practices in the timing of purchases and holding of Inventory by the stores with respect to oranges compared with lemons and grapefruit* But It should be noted that| for each of the three citrus fruits, the intertemporal correlations between the daily retail and lagged wholesale prices are hi^er than the correla- tions between the daily lagged and current wholesale prices or the oorre- lations between the daily retail and current i^olesale prices; and the correlations between the lagged and current wholesale prices are higher than the correlations between the daily and current wholesale prices. These results pertaining to the lead and lag relations among the dally retail and wholesale prices of oranges, lemons, and grapefiniit do not differentiate as to the effects which may be associated with the di- rection and amount of change in the daily current wholesale prices. To throw some light on that question, the following summary correlation sta- tistics 1 s presentedi -111- TABIE U7 Lagged Coefficients of Correlation Between Daily Retail Prices and Changes in Current V/holesale Prices August 19l^8-July 19k9 Citirus fruit and types of Nuniber of days current wholesale price precedes retail price U 3 1 0 px 1 CeS na/ r ' n r n r n r n r n r Positive and large 106 ♦0.68 106 ♦0.70 107 +0.71 107 ♦0.73 107 ♦0.71 107 ♦0.65 Small or no change 95 +0.90 96 +0.90 96 +0.89 97 +0.90 97 +0.91 97 +0.92 Negative and large 105 +0.79 105 +0.77 105 +0.8U 105 +0.8U 106 +0.83 107 +0.8U Lemons Positive and large 105 +0.93 106 +0.93 106 +0.93 106 ♦0.92 106 +0.92 106 +0.91 Small or no change 99 +0.95 99 +0.95 99 +0.95 99 +0.9U 100 +0.9U 100 +0.93 Negative +0.89 lOU and large 102 +0.90 102 +0.90 103 +0.90 lOU •K).88 105 +0.86 Grapefruit Positive and large 105 +0.93 105 +0.97 105 +0.96 105 +0.93 105 +0.96 105 ♦0.95 Small or no change 98 +0.97 98 +0.96 99 +0.93 100 +0.97 101 +0.96 101 +0.93 Negative and large 103 +0.90 loU +0.88 lOU +0.91 lOii +0.90 loU +0.87 105 +0.89 a/ n indicates number of paired changes on ^ich the corresponding " correlation coefficients are based. The correlation coefficients for oranges suggest a sotoevhat closer relationship between the daily current wholesale prices and the following daily retail prices when the current wholesale price changes only by a small amount than when it changes by a large anaunt. And the irelationship is closer between the current wholesale price and the retail price on the following days when the current wholesale price decreases by a large amount than when it increases by a large amount* -112- i For lemons, as for oranges, a closer relationship exists between the current wholesale price and the retail price on the following days when the current wholesale price changes by no more than a small amount. But, for lemons, the relationship is closer between the current wholesale price and the retail price on the following days when the current wholesale price increases by a large amount than when it decreases by a large amomt. For grapefruit, no clear differentiation is suggested in the rela- tionship between the current wholesale price and the retail price on succeeding days whether the current wholesale price has increased by a large amount or changed by no more than a small amount. Yet, the rela- tionship between the current wholesale price and the retail price on suc- ceeding days tends to be less yAien the current wholesale price decreases by a large amount than when it increases by a large amount or changes in either direction by only a small amount. These relationships suggest somewhat differing reactions in the daily retail market prices of oranges, lemons, and grapefruit to changes in their current wholesale prices of several days previously. The retail mar- ket prices of oranges are more responsive to earlier negative and large decreases in the current wholesale price than to its earlier negative large increases. The opposite tends to prevail in the responsiveness of the retail prices of lemons and grapefruit to changes vriiich occurred in their current wholesale prices. These tendencies are not strong nor sharpy but they exist to some extent if only slightly. It is seen that the daily retail market prices of oranges raaintajji a closer relationship with the current wholesale prices when they had de- clined substantially several days ago than when they had advanced substan- tially. In lemons and grapefruit, there is a slight tendency for the retail prices to respond less to marked declines than to marked advances in the current wholesale prices. Above all, however, there is a strong tendency for the retail prices of oranges, lemons, and grapefruit to be more closely related to the lagged than to the current wholesale prices. The over-all evidence is reasonably clear that the daily retail market price of oranges, lemons, and grapefruit follows more closely the histori- cal cost of the fruit already purchased and being retailed (the lagged wholesale price) than the present or current wholesale replacement cost of the citrus finiit. -113- Appendix Note DESIGN OF SAMPLE by G. M. Kuznet^ The sample used in the study is a stratified list sample of $3 stores. Strata were defined with reference to (l) areas within the city limits of Denver, (2) type of store (grocery and combination, fruit and vegetable), and (3) volume of sales (OPA rating subsequently modified). The number of stores drawn from each stratum was in proportion to the estimated volume of sales handled by the outlets. This approximates an optimum (least variance) design to estimate such parameters as weighted average prices and weighted average margins provided that the listing is reasonably complete, that esti- mates of volume of sales are fairly accurate, and that the standard deviations of the variables measured (prices and margins) do not vary markedly over strata. 1. The primary information for the sample was provided by the listing of stores in Denver procured from the regional office of the Bureau of Labor iStatistics in San Francisco. This list gave the information on food stores in Denver by type of outlet, by location, and by OPA size classification. Two other lists were obtained and used for partial checking of the primary list — a secondary OPA list and the Denver Post route listing. Table U8 gives the distribution of food stores in Denver by type of outlet, by location, and by OPA size classification based on the primary list. While some fresh fruits are handled by meat markets, dairy stores, and other types of outlets such as delicatessen stores, inspection of a small sample of these stores indicated that the volume of fresh fruit sold by these types of outlets is very small. The population of stores from which the sample would be drawn was therefore restricted to grocery and combination stores and to fruit and vegetable stores. Because some 70 per cent of the grocery and combination stores in Denver were classified into the smallest size class (OPA-l) it appeared desirable 1/ Professor of Agricultural Economics and Economist in the Experiment Station and on the Giaiuiini Foundation. -llll- to introduce a finer size breakdom into this category. For this purpose a 20-per cent random sample of OPA-1 grocery and combination stores was dram in the Northivest, Southvrest, Northeast, and Southeast areas of Denver and a UO-per cent sample in the East Central area and the Business district. Because of pressure of time, actual data on volume of sales could not be obtained from these stores. The procedure employed was to obtain two inde- pendent, and in cases of disagreement, four independent, ratings of stores on a three-point scale (large, meditua, small). The rating was assigned on the basis of total volume of business, and absence of produce in the store Tias to be particularly noted. Table h9 gives the results of this prelimi- nary work. In addition to introducing a finer breakdown into the lowest size class, it appeared desirable to check completely the list of the fruit and vegetable stores contacting all the listed outlets since the intention was to assign these outlets a relatively heavy weight. The results of this enumeration are given in Table 50 . A radical revision of the original listing was made necessary largely because many of the entries in the original list repre- sented residences of fruit and vegetable peddlers and the latter were by- definition excluded from the population to be sampled. The succeeding tables indicate step by step the procedure employed in determining the number of stores to be selected randomly from the various strata. Attention should be drawn to the numerous and rather arbitrary as- sumptions (see footnote a. Table ^2) which had to be made in the process of arriving at the sampling rates shown in Table 53. Table 5U indicates the number of stores to be drawn from each stratum for a total sample of 50 stores, the latter number being previously determined largely with reference to the budget available for the study. The distribution of the stores actually in the Denver sample as of August 19U8 is shown in Table 55» The differences apparent between Tables 5U and 55 consist largely of overrepre- sentation of Class II stores and undersampling of Class II fruit and vege- table stores. Neither of these appears to be very serious, particularly the latter since there are definite indications that the size of fruit and vegetable stores was originally overestimated, 2. Information collected in the sample of stores in Denver permits the testing of at least some of the important assumptions made in the calcula- tion of sampling rates and weights. -115- (a) A comparison for August and Septonber of 19U8 of the volume of orange sales per store by size classes and the size in- dicators given in Table 52 (shoivn in Figure 32) indicates that only the size indicator for fruit and vegetable stores Class II is open to serious question. Data for October, November, and December give similar results. (b) Another assumption made in the course of -work is that the size of an outlet does not show a significant variation with geographic areas within the broad size categories which were used. Data permit the testing of this assumption only for Class II stores. An analysis of variance, using volume of sales of oranges for December 19hQ as the size indicator,, revealed no significant differences between the six areas in average size of outlet. Data for pther months are likely to lead to the same conclusion. (c) The equality of the standard deviations of the prices or mar- gins has been tested only with reference to Glass II stores. Test of homogeneity of variance did not show the existence of significant differences in the variability of orange retail prices among the six areas (August X9k& data). Taken together, these partial checks appeared to be quite favorable and led to the decision that a revision of the sample was not necessary. It should be added that, while a systematic check of the com- pleteness and adequacy of the original listing was not made,' the most vulnerable parts of the listing were checked par- tially or completely (Class I and fruit and vegetable stores). TABLE 48 Ntmiber of Independent Retail Food Stores in Denver, Colorado, Classified by Geographic Location, Type of Commodities Handled, and Sales Voliime of stores ex- Grocery and combina- Fruit and vege- Other local types tion stores Meat markets table stores Delica- Fish location local types Glass i; Class 2 | Class 4 Class 1 Class 2 Class 4 Glass 1 Class 2 tessens Dairy markets 2 3 4 5 6 7 8 9 10 11 12 wj-wiULn oiwy limits: i I i 1, Northwest 127 95 j 26 2 4 2 24 3 2* Southwest 142 106 1 15 1 5 1 14 2 9 8 3* Business district 91 i 40 13 i 6 4 3 21 4 4 9 10 4* Northeast 155 ! 121 I 24 5 5 3 22 5 5« East Central 126 75 i S2 i 2 3 10 4 4 28 4 6« Southeast 102 69 i 22 2 9 3 29 8 Total 743 506 ■ 132 1 22 8 3 63 8 18 m 38 Source: OPA Distiribution Center, War Price Board, Denver Retail Growers Association. TABLE 49 Random Sauiple of Class 1 Independent Grocery and Combination Stores in Denver, Colorado Classified by Geographic Location and Sales Volijme January 1948 Rating of stores Geographic Out of Without ——— P.2,ting of stcrss location business produce Small Medium Large Class 2 Total Reject^*/ Total 1 2 3 4 o a 7 c 9 iO 1 T number per cent Within city limits: i I ■ 1. Ncnrbhwest 1 2 Z 8 7 20 15.0 10.0 40.0 35.0 100,0 ■■ 2. Southwest 1 4 9 6 2 1 23 21.7 39,1 26.1 13.1 100.0 3, Business district 4 4 Z 1 9 1 a 38.0 9.5 4.8 47.7 100.0 4. Northeast Z 3 11 5 1 24 16.6 12.5 45.8 25.1 100.0 5. East Central 3 4 2 9 10 6 34 20.6 5.9 26.5 47.0 100.0 6. Southeast 2 5 5 3 15 13.3 33.3 33.3 20.1 100.0 Total 13 16 23 40 36 9 137 21,1 16.8 29.2 52.9 ICO ,0 / Includes stores out of business and stores without produce. / Inclxides stores rated class 2. -118- TABIE 50 Nvmber of Fruit and Vegetable Stores in Denver, Colorado, CJAssified by Geographic locaHon and Sales Volume, January 19kQ^ Geographic location Class 1 CIass 2 Grocery Residence Out of business Total 1 2 3 ? 6 Within city limits: 1. Northirest 1 3 k 2. Southwest 3 2 7 2 lU 3* Business district 11 5 2 8 26 k» Northeast 3 2 ^. East Central I* 2 3 3 3 15 6. Southeast 1 2 6 9 Total 19 7 8 18 21 73 ^ Two fruit and vegetable stores urere added to the list given in Table U8. TJffiLE 51 Estimated Number of Independent Grocery and Food and Vegetable Stores in Denver, Colorado Classified by Geographic Location and Sales Volume, January 1948 Grocery and combination stores Glass 1 Fruit and vege- Geographic Ad 1 lists d table location total total Smnll, Medim Large Glass 2 Glass 4: Class 1 Class 2 Total 1 2 3 4 5 6 7 8 9 10 Within city Hinlts: 1, Northwest 93 79 9 37 33 26 1 106 2* Southwest 106 83 41 28 14 15 ■1 1 3 102 3. Business district 40 25 4 2 19 8 11 5 49 4. Northeast 318 99 15 54 30 24 123 5. East Central 73 58 5 19 34 32 4 2 98 6* Southeast 68 60 23 23 14 22 82 Total 498 404 97 163 144 127 1 19 7 560 Sources: Cd. li Col. 2: Col. 3: Col. 4: Col. 5: Col. 6: Col. Col. Col. 7: 8: 9: Colvnm 2 of Table 48 omitting 8 outlying stores. Column 1 less the proportion of rejects indicated in column 8 of Table 49. Coltmn 9 of Table 49 applied to column 1. Column 10 of Table 49 applied to column 1. Column 11 of Table 49 applied to cdtimn 1. Column 3 of Table 48 except for Business District entry i^ch is based on enumeration in January 1948. Column 4 of Table 48. Column 1 of Table 50. Column 2 of Table 50. Col. 10: Sum of columns 2, 6, 7, 8, and 9, IA.BLE 52 Estimated Distribution of Voliune of Sales of Fresh Fruits and Vegetables Handled by Specified lypes of Independent Bbod Stores in Denver, Colorado Classified by Geographic Location and Tbtal Volume of Sales Grocery and combination stores Fruit and vegetable stores ! Geographic Class 1 Class Class Class Class ! location Small 1 Medium Large 2 4 1 2 Total 1 2 3 4 5 6 7 1944 dollars Within city limits: I ■ ■ ' 1. Horiiiwest 3,600 i i 44,400 .92,400 301,600 10,000 452,000 Z, Southwest 16,400 33,600 39,200 174,000 57,800 30,000 351,000 : 3* Business 1 district 1,600 2,400 159,600 92,800 110,000 345,000 711,400 i 4, Northeast 6,000 64,800 84,000 278,400 433,200 \ 5* East Central 2,000 22,800 95,200 371,200 40,000 138,000 669,200 6. Southeast 9,200 27,600 39,200 255,200 331,200 Total 38,800 195,600 509,600 1,473,200 57,300 190,000 483,000 2,948,000 Assumed annual value o f produce sales per storeV ■ 400 1,200 2,800V 11,600 57,800 10,000 69,000 (Continued on next page.X TlEible 52 continued. a/ Asstuned annual values of produce sales were derived as follows t (1) Bie following estimates of 1944 sales per store were obtained from the Bureau of Labor Statistics in San Francisco; TyTpe Yalue of sales dollars Grocery and combination: Class 1 13,000 Class 2 88,900 Class 4 340,000 Fruit and vegetable 16,900 (2) Assuming the same relative differential between Class 1 and 2 stores cited above for grocery and combination stores gives the following estimates, rounded off, for Classes 1 and 2 of fruit and vegetable stores: Class 1: $10,300 Class 2: 68,800 (3) On the basis of information given in the 1940 Census of Retail Trade, the following relative -weights ■were assigned to sales of produce by type and size of store* Sales of finiits and vegetables Grocery and combination as per cent of total sales Class 1 10 Class 2 IS Class 4 17 Fruit and vegetable Class 1 100 Class 2 100 (Continued on next page,) Table 52 continued, (4) It was assumed that the average sales of grocery. Class 1, snail, mediiaa, and large stores were in the ratio 1:3:7» Diis assumption, taken together with the additional information on frequencies of snail, medium, £ind large stores and the fact that the average sales of all Class 1 stores was known, led to the following estimates of average sales t Grocery and combination stores » Class 1 Average sales tail price Lagged Wholesale | price Cur- rent September 27 10.6 28 ;10.8 29!l0.3 October 8.0 7.6 7.7 7.7 7.6 30 1 2 10.6 10.3 10.2 7.2 7.0! 8.3i 7.7! 8.61 4 10.2 5 110.2 6 10.1 7 jlO.4 8 10.6 9 1 15.0 6.7 6.8 6.6 6.6 6.3 6.4 6.4 6.4 6.3 6.4 6.6 6.4 8.1 13 11.7 7.5 11 '11.2 6.2 8.4 14 11.3 7.3 12 i 9.7 6.6 7.9 15 11.8 7.5 i 8.5! 13 11,5 6.1 8.9 16 11.5 7.3 ; 6.91 14 11.2 7.1 7.5 17 11.1 7.2 7.1! 15 10,9 6.7 8.2 18 11.1 7.2 7.5 i 16i — 8.0 20 11.2 7.4 1 7.4i 1 18:10.8 7.4 8.2' 21 11.4 7.2 7.8 1 19 10.4 6.8 8.6: 22 10.9 7.0 6.8! 20 10.5 6.9 8.3 23 10.5 6.8 6.7j 2lil0.0 6.4 8.8, 24 10.7 7.0 6.9! 22 10.3 6.5 i 25 10.8 7.0 23 10.2 6.5 6.9 6.3 5.8; 6.4! 5.8: 3.9^ 6.8 6.5 6.5i 7.3i 6.4i 6.4j 6.2! 6.6 6.1 6.7 6.7 7.1 7.0! 6.4 i 6.1, 6.2! 4.1 i November cents per pound 25 9.8 ! 6.4 6.4 26 9.7 i 6.4 6.0 27 9.7 , 6.2 6.1 28 10.0 ; 6.2 5.5 29 9.5 ! 6.0 30 9.6 i 6.0 5.8 1 9.2 5.6 5.0 2 9.3 5.6 5.6 3 9.1 5.7 5.3 4 8.8 5,6 5.8 5 8.7 5.4 5.1 6 8.7 5.3 4.3 8 8.6 5.2 5.1 9 8.6 5.2 5.1 10 8.8 5.2 4.6 U 8.6 5.0 4.7 12 8.3 4.9 4.9 13 8.4 5.0 5.6 15 8.5 5.0 4.6 16 8.3 4.9 4.9 17 8.1 4.8 5.0 18 8.0 4.7 3.9 19 8.2 4.7 4.8 20 8.1 4.6 5.4 (Continued on n^ct page.) Table 58 cantinued. ■- Wholesale Wholesale Wholesale — Wholesale Re- price Re- price Re- price Re- price tail C\ir- tail Cur- tail ,Gur- tail Cur- Date price Lagged rent Date price Lagged rent Date price Lagged,' rent Date price Lagged rent cents per poiind cents per pound cents per poxmd cents per pound November 22 8.0 4.7 4.5 December 20 7.1 4.7 4,6 t January 17 ^ 7.5 5.0 5.4 February 14 8.2 5 3 5 A 8.0 4.7 4.6 21 7.3 4.9 4.8 18 7.8 5,1 5,2 15 8.S 5-.3 5.7 OA 8.1 4.6 4,6 M. 7,0 4.6 4,9 19 7.6 4,9 4,8 16 8.2 5-3 5.1 25 23 7,2 4.9 5.0 20 7-6 4.9 4.3 17 8.2 5.2 4.9 26 8.1 4.8 4.8 24 7,3 4,8 4,7 21 7.7 5.0 5.1 18 8.1 5.3 5.1 27 8.1 4.7 5.2 25 22 7.5 5,0 3,4 19 8.1 5.2 29 7.5 4.5, 4.5 27 7,4 4,8 4,5 24 7-7 * • • 5,1 4,9 21 8.1 5,2 5.1 30 7.6 4.6 4.7 28 7.3 4,6 4,4 25 7.6 5,1 5,6 22 8.2 5.3 5.6 7.9 4.6 4.8 7.2 4,6 4,5 26 7.9 5,2 5,3 23 8.2 5-3 5.1 ! 2 8.0 4.7 4.1 30 7.2 4.6 4,5 27 7.8 4.6 24 8.4 5.4 4.9 : 1 3 8.0 4.7 4.4 1949 31 7,0 4.7 4,5 28 7.9 5.1 4.8 25 8.5 5.5 5.1 ! ! 4 7.5 4.6 5.4 Jantiary 1 29 7.7 i 5,1 5.0 26 8.3 5.4 5,3 ; I ! 6 7.7 4.6 4,7 3 7.6 4.6 4.5 31 7.8 ; 5,0 5.1 28 8.1 5.2 5.9 7 7.5 4.6 4,4 4 7,7 5,1 5,0 Febraiary 1 8.0 • 5.1 5.1 March 1 8.4 5.3 5.2 e 0 7.5 4.7 4.4 5 7,2 4.9 4,7 2 7.7 5,0 5,4 2 8.6 5.5 5.5 1 9 7.7 4.7 4.9 6 649 4,3 4,3 3 7.5 i 5,0 4.7 3 8.6 5.5 4.9 10 7.5 4.6 4,3 7 6,4 4.5 4,4 4 7.6 \ 5.0 4.7 4 8.5 5.5 5.8 n 7.2 4,5 4.4 8 7*1 4.6 4.7 5 7.8 5.1 5 8.4 5.4 5.4 13 7.4 4.6 4.4 10 7,5 4.7 5,0 7 7,9 ^ 5,2 5,6 7 8.5 5.7 6,0 14. 7.4 4.6 4.4 11 7.5 4.9 4.3 8 7,9 \ 5,1 4,7 8 8,8 5.7 5,6 15 7.2 4,7 5,1 12 7.4 4.9 5.2 9 8.0 i 5.1 5.7 9 8.8 5.7 6.1 16 7.2 4,6 4.6 13 7.4 4.8 5.1 10 8.1 i 5.2 5.1 10 8.6 5.7 6.1 17 7.2 4.6 4,7 14 7.4 4.9 4.7 n 7.9 i 5,1 5.2 11 9.0 6.0 6.3 18 7.1 4.5 4,4 15 7.4 4,9 5.5 12 8.2 5.4 5.2 12 9.1 6,1 (Coaatlnaed on next page.) > 58 contiimed* Re- Wholesale Wholesale Wholesale Wholesale pri< ie Re- price Re- nrice Re- price Date tail Cur- tail Cur- tail Cur- tail GliT- price Lagged rent Date price Lagged rent Date price Lagged rent Date price Lagged i rent 1 centt J per pound cents per pound cents per pound cents per potmd March 14 1 9.1 6.0 6.1 April 11 9.3 6.3 6.7 May 9 10.8 7.5 7.4 June 6 12.4 9.0 9.0 15 9,2 o.l 6.0 12 9.4 6.3 6.5 10 10.8 7.5 7.6 7 12.4 9.0 8.5 16 9.4 6.2 6.3 13 9.7 6,4 7.0 U 10.8 7.5 7.7 • • • 8 12.2 8,8 8.6 i 17 9,2 6.1 5.7 14 9.5 6,5 6.8 12 10,8 7.5 7.5 9 12.5 8,8 8*4 18 9.4 6.1 ea 15 9.6 6,5 6,7 13 10.9 7.6 7.5 10 12,6 8.7 9,2 i 19 9.1 6.1 5.4 16 10.0 j 6.6 14 10.9 7.6 8.0 U 12.8 8.9 9-2 1 j a 9.1 6.1 6.2 18 10.0 6.7 7,1 16 11.1 7.7 8.0 13 12,2 9.0 9.3 \ 2Z 9.4 6.1 6.2 19 10.0 6.8 7.1 17 11.4 7,7 8,0 14 12.4 8.9 9.1 25 8.9 5.9 5.8 20 10.1 6.8 7.2 18 11.5 7.7 7,7 • • 15 12.3 8.8 8.0 i 24 8,9 6,0 6.0 21 9.7 6.9 7.2 19 n.6 7.7 8.5 16 12.0 8.9 Q I 25 8,3 5.5 5,3 22 10.0 7.0 7.4 20 U.5 7.8 8,5 17 13.0 8.8 9,1 1 26 8.4 5.8 6.7 23 10«2 7.0 7.2 21 11.6 7.9 7.9 18 13,0 8.9 9,3 1 28 9.2 6a 6.3 25 10.2 7.0 7.4 23 n.9 8.1 8.5 20 13.1 9.0 9.1 1 12 9.3 6,1 6.2 26 10.3 7.0 24 o.u o.o 21 9.0 1 E? 9.0 6.1 6,6 27 10.4 7.1 7.0 25 11.9 8.2 7.9 22 13.1 9.1 9.4 ! SI 8,9 6.1 6,4 28 10.6 7.2 7.3 26 11.8 8.2 8,8 23 13.0 9.1 9.6 1 April 1 9,0 6.2 |6.4 29 10.5 7.2 7.3 27 12.1 8.4 8.6 24 13.4 9.1 9.0 2 9.2 6.2 6.5 30 10.6 7.3 8.1 28 12.0 8,2 7.0 25 13«.2 9.0 4 9.3 6,1 6.3 May 2 10.8 7.3 7.5 30 27 13.0 9.0 9,2 ' 5 9.2 6.2 6.2 3 10.6 7.4 7.5 31 12.0 8.3 8,9 28 13.0 9.3 9.2 i 6 9,3 6.2 i 6.3 4 10.7 7.5 7.5 June 1 12.0 8.7 8.8 29 X3ff ^ 9.3 9,3 i 7 9.2 6.3 1 6.0 5 10.7 7.5 7.5 2 12.2 8,8 8.8 30 13.5 9.3 9.4 8 9.0 6.0 i 6.4 6 10.5 7.4 7.5 3 12.4 8,9 9.0 July 1 13.0 9.2 8.9 9 9.2 6.3 \ 6.8 7 10.7 7.5 7.7 4 12,4 8.9 9.1 2 13.4 9.1 9.6 (Contiuoed on next page.) Table 58 continiied Wholesale Wholesale Wholesale Wholesale Re- price Re- price Re- price I Re- price tail Cur- tail Cur- tail Cur- itail Cur- Date price Lagged rent Date price Lagged rent Date price Lagged! rent Date price Lagged rent cents per pound cents per pound cents per poimd ! cents per pound July 4 July 11 l3o2 9.3 9.2 July 18 13,2 9.3 9.5 July 25 1 ! 13.0 8.9 9,5 5 13.1 9.0 7.9 12 13.3 9.2 6,4 19 13,3 9,5 9,5 26 ! 13.4 9.0 8,9 6 13.0 9.1 9.2 13 13.4 9,0 LO.O 20 13,0 9,1 9,1 27 i 13.2 9.1 7 13.0 8.9 9.4 14 13.2 9.0 9.3 21 13.1 9,1 9.4 28 13.1 9.1 8 13.1 9.0 8.5 15 12.9 8.8 9,6 22 12.7 9,0 9.2 29 ; 13.0 8.9 9 13.1 8.8 8.6 16 13.0 9.1 23 13.1 9.0 9.3 30 ! 12.9 9.0 6.7 a/ B l a nk s Indicate holidays. -138- Figure 32. Conparison of Size Indicators and Monthly Sales of Oranges by Sample Stores August 1948 September 1948 Assumed Annual Value of Produoe Sales per Store (1944 dollars In thousands) Type of Store (a) Grocery uid ocmbination Class 1 Small Medium Large Class 2 Class 4 (b) Fruit and Vegetable Class 1 Class Z Original Site Indicator (1944 dollars) 400 1,200 2,800 11,600 57,800 Volume of Oranges Sold (lbs.), 1948 Aug« Sept. Oct» Mot. Deo. 10,000 69.000 102 16^ 499 1,304 7,658 1,351 2,572 71 133 445 1,331 5,471 1,318 2,279 74 116 563 1,638 7,2B9 1,757 2,162 111 125 490 1,679 8,938 2,142 2,902 112 129 692 2.118 8,465 2.366 2,664