630.7 
 U6B 
 no.720 
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University of 
 
 niinois Library 
 
 at Urbana-Champaign 
 
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 Resource Productivity 
 and 
 1^ Income Distribution 
 
 With Implications for 
 
 Farm Tenure Adjustment 
 
 \ 
 
 By Roger W, Strohbehn 
 
 BULLETIN 720 University of Illinois College of Agriculture 
 
 Agricultural Experiment Station — In Cooperation 
 
 With Economic Research Service, U.S. Deportment of Agriculture 
 
CONTENTS 
 
 Theoretical Orientation 4 
 
 Method of Analysis 6 
 
 Model selection and specification 6 
 
 Selection of empirical data 8 
 
 The Analysis 11 
 
 Statistical estimates 11 
 
 Interpretation of Results 15 
 
 Return to real estate 19 
 
 Return to operator 20 
 
 Capital accumulation for land purchase 24 
 
 Capital gains and farm income 24 
 
 Summary and Implications 27 
 
 Literature Cited 30 
 
 Appendix 30 
 
 ACKNOWLEDGMENT 
 
 This study was initiated as a cooperative project between the Natural 
 Resource Economics Division, Economic Research Service, and the Depart- 
 ment of Agricultural Economics, University of Illinois. It supports the North 
 Central Land Economics Research Committee regional research project, 
 "Needed Adjustments in Land Tenure to Meet Changing Agricultural Con- 
 ditions." Major responsibility for the study was assumed by the Economic 
 Research Service. The University of Illinois provided the data and com- 
 putational facilities. 
 
 The author wishes to thank Gene Wunderlich and W. B. Back of the 
 Economic Research Service for their assistance in this study. Dr. Wunderlich 
 provided encouragement and assistance in delineating the research prob- 
 lem, and Dr. Back constructively criticized the presentation of the research 
 findings. Appreciation is also extended to Foike Dovring, Earl R. Swanson, 
 Vincent I. West, C. B. Baker, and Franklin J. Reiss of the University of 
 Illinois for their guidance and counsel throughout the study. If there are 
 errors in the report they remain the responsibility of the author. 
 
 Urbana, Illinois August, 1966 
 
 Publications in the Bulletin series report the results of investigations made 
 or sponsored by the Experiment Station 
 
Resource Productivity and Income Distribution 
 with Implications for Farm Tenure Adjustments 
 
 by Roger W. Strohbehn^ 
 
 RAPID STRIDES IN FARM TECHNOLOGY IN RECENT DE- 
 
 cades have encouraged farm operators to combine more units of capital 
 and land per unit of labor in order to achieve efficient resource use and 
 maintain a competitive position in agriculture. As the per farm capital 
 requirements for efficiently organized farms have risen, farm operators 
 have begun considering alternative tenure arrangements to the time- 
 honored goal of owner-operatorship of the farm resources. 
 
 These new or modified tenure forms include such arrangements as 
 equipment rental, vertical integration, and farm incorporation. One of 
 the perplexing questions in agriculture is whether the tenure system has 
 accommodated the adoption of technology to enable farmers' income to 
 keep pace with urban people, or whether the benefits of more efficient 
 production have been siphoned off in rising land values. 
 
 The role of a tenure system is to provide an institutional framework 
 through which entrepreneurs allocate resources among alternative uses 
 in response to market forces and distribute the ensuing income among 
 the resources. A measure of the effectiveness of a tenure system is its 
 ability to associate resource costs and returns, or more specifically to 
 equate factor costs and factor earnings, and thereby achieve efficient 
 resource use. 
 
 If a dissociation of costs and returns exists among resource owners, 
 the tenure system itself may be jeopardized. Thus the structure of the 
 tenure system, the allocation of resources, and the distribution of income 
 are highly interrelated and must be examined simultaneously. An ap- 
 propriate starting point for an investigation of forces impinging on tenure 
 arrangements would be a historical examination of the factor shares to 
 determine whether the resources used in agricultural production have 
 been properly compensated and whether this compensation is adequate 
 to enable the farmer to acquire ownership of the resources in keeping 
 with the traditional tenure goal. 
 
 If the distribution of farm earnings among the factors results in the 
 
 ^ Dr. Strohbehn is an agricultural economist with the Economic Research 
 Service, USDA. 
 
4 Bulletin No. 720 [August, 
 
 association of factor costs and returns, the problem facing farm operators 
 is one of how to gain access to a quantity of resources that is adequate 
 for an efficient business and that will yield a satisfactory level of living 
 for the operator and his family. On the other hand, if one of the residual 
 claimants (land and operator labor) is overpaid while the other is under- 
 paid, this would suggest the need for a different type of tenure modifica- 
 tion, perhaps a major alteration of the tenure structure rather than a 
 modification of the existing system. 
 
 The objectives of this study were to: (1) analyze the influence of 
 imperfect mobility of farm operators upon farm resource income distribu- 
 tion; (2) examine the relation between imputed land values and actual 
 land values; and (3) analyze the effect of rising land values on the ability 
 of farmers to achieve the goal of owner-operatorship of their land. Two 
 interrelated hypotheses were used to guide the investigation toward the 
 accomplishment of these objectives: (1) the market value of farmland 
 exceeds its imputed value based on the contribution of land to the prod- 
 uct of the farms; and (2) a portion of labor and management earnings 
 of farm operators is capitalized into land values. An analysis of farm 
 account data for different types of farms and regions of Illinois was per- 
 formed in testing the hypotheses. 
 
 Theoretical Orientation 
 
 Application of the usual assumptions of perfect competition and 
 mobility of resources, which underlie micro-static economic theory, results 
 in an equilibrium distribution of income to factors of production in ac- 
 cordance with the marginal contribution of each factor to total output. 
 If one factor such as land is fixed, it becomes a residual claimant to 
 income, otherwise the marginal productivity theory of distribution holds. 
 By considering any residual shares to fixed resources to be consistent with 
 their marginal contributions to output of the firm, an equilibrium situa- 
 tion may be expressed as : 
 
 (1) PyY = PiXi + P2X2 + . . . + PnXn 
 
 In this equation Y is physical output, Xj's are resources, and Pi's are 
 prices for the output and the resources. This expression indicates that the 
 value of the output is exactly exhausted by the sum of the income shares 
 to the resources and is consistent with Euler's theorem expressed in 
 marginal productivity theory as follows : 
 
1966] Resource Productivity and Income Distribution 5 
 
 In this equation Y and Xi's are units of physical output and units of 
 resources, respectively. The latter expression is the same as the first when 
 each term is multiplied by the price of Y(Py) and the resulting marginal 
 value products for the resources are considered equal to the respective 
 resource prices. Empirical implementation of Euler's theorem was ob- 
 tained by use of the Cobb-Douglas form : 
 
 (3) Y = aXibiX2b2 . . . Xn^n 
 
 In this equation 2lbi = 1, and all variables were expressed in dollars. 
 Estimation of marginal productivities of resources used on farms in this 
 manner provided the benchmark for identifying and measuring depar- 
 tures from equilibrium returns to resources. 
 
 The hypothesized existence of disequilibrium in factor shares origi- 
 nates with technological change. The adoption of technology that sub- 
 stitutes capital for land and labor where there is immobility of land and 
 labor will result in excess resources being used and a tendency for output 
 to expand beyond the equilibrium level. If the price flexibility of Y at the 
 farm level is less than — 1.0, as is the case for many farm products, the 
 value of the new total product will be less than the value of the output 
 produced under the old technology.^ Hence the equality sign in (1) will 
 be changed to a "less than" sign as follows: 
 
 (4) PyY < PiXi + P2X2 + . . . + PnXn 
 
 In this new situation, the sum of the distributive shares exceeds the quan- 
 tity to be shared, and reestablishment of equilibrium usually would require 
 an exit of some of the resources made redundant by factor substitutions 
 caused by technological advance. However, if the technological advance 
 created a situation where larger quantities of land per farm would be 
 needed in order to take advantage of the technological advance, land 
 would not be a redundant factor, but the opposite. In this situation the 
 adopting farm operators compete for the available supply of land for 
 farm enlargement with a consequent increase in land prices. 
 
 This places much of the burden upon the farm labor (farm operator 
 and family) to adjust by entry into nonfarm employment. However, farm 
 operator labor tends to be fixed (immobile) because of lack of training 
 for skilled nonfarm jobs, lack of knowledge of possible alternative em- 
 ployment, and nonmonetary values attached to entrepreneurial freedom 
 and farm life. If a farm operator places a high premium on remaining 
 
 ^ See G. E. Brandow, "Interrelations Among Demands for Farm Products 
 and Implications for Control of Market Supply," Pa. State Univ. Bui. 680, 1961, 
 for estimates of price flexibilities of farm products. Price flexibilities at the farm 
 level for selected products are: cattle, — 1.59; hogs, — 2.33; all milk, — 2.64; 
 soybean oil, — 1.77; and corn, — 2.0. 
 
6 Bulletin No. 720 [August, 
 
 a farm operator, and it is hypothesized that most do, he likely will under- 
 value his own labor in order to pay the higher prices for land needed to 
 efficiently utilize new technologies. Under such circumstances, techno- 
 logical advance will be accompanied by land prices rising above the 
 marginal productivity value of land, and correspondingly, the income 
 share of farm operator labor will be below its marginal productivity 
 value. ^ 
 
 Method of Analysis 
 
 Model Selection and Specification 
 
 Whole farm production functions of the Cobb-Douglas type were 
 chosen for this study, since it is concerned with the distribution of returns 
 from the total farm business to the factors of production. A production 
 function, in a sense, becomes an accounting tool when it is used to deter- 
 mine the marginal factor shares for an allocation of the total income of 
 the firm among the inputs. A firm in equilibrium would receive a dollar 
 return for each dollar expenditure that included the opportunity cost of 
 the dollar. In addition, the return to land and operator labor would be 
 equal to their marginal factor shares. 
 
 The Cobb-Douglas function is particularly suited to the study because 
 it specifies diminishing returns to individual inputs and is a homogeneous 
 function that can be easily constrained to be a homogeneous function of 
 degree one, indicating constant returns to scale. ^ The application of 
 Euler's theorem requires constant returns to scale for the sum of the 
 factor payments to just exhaust the total product when the factors are 
 paid according to their marginal value products. The data can be fitted 
 to both an unconstrained function and a constrained function and a 
 statistical test performed to determine if the unconstrained fitted function 
 differs significantly from constant returns to scale. 
 
 Estimates of the marginal productivities of six basic categories of 
 farm inputs were derived from a production function as specified in the 
 following equation: 
 
 (5) Y = aXib.X2b^X3^3X4b4X5b^X6bB 
 
 In the following definitions of the variables, ^ represents the oppor- 
 tunity cost on the capital tied up in the input from the time it was com- 
 
 ^ A more complete theoretical development of the influence of technology 
 and resource immobility on income distribution can be found in R. W. Strohbehn, 
 "Income Distribution on Selected Types of Illinois Farms and Implications for 
 Tenure Adjustments," unpublished Ph.D. thesis, University of Illinois, 1965. 
 
 ^G. Tintner, "Econometrics," pp. 89-91, John Wiley and Sons, New York, 
 1952. 
 
1966] Resource Productivity and Income Distribution 7 
 
 mitted in the production process until a product was forthcoming. 
 Similarly, p represents the rate of interest used to convert an inventory 
 value into an annual service cost. Values of </> and p are shown in Appen- 
 dix Table 1 for the three periods in the analysis. 
 
 Y = Value of production. [(Total cash sales of products and services) 
 — (purchased feed and livestock) + (change in inventory values of 
 grain and livestock) + (value of farm products consumed) — (prop- 
 erty taxes) ]. 
 Xi = Current value of land. A basic value of bare land is established 
 for each farm according to the soil-productivity rating of the land to 
 reflect market value. This value is adjusted each year according to 
 the index of land prices in Illinois, as reported by the USDA. 
 X2 = Total cost of labor. [Operator labor valued at the representative 
 wage rate for the area] + [(actual hired labor cost) + (family labor 
 valued at the representative wage rate for the area)] [1 + </>]. The 
 monthly wage rates used in each area and year are shown in Appendix 
 Table 2. 
 X3 = Land improvement cost. [(Building and fence repairs) + (build- 
 ing depreciation)] [!+</)] + [(depreciated investment in buildings 
 at the beginning of the year) (p)]. 
 
 X4 = Machinery and equipment costs. [(The sum of annual expenses 
 for electricity and telephone, machinery repairs, machinery hire, and 
 gasoline and oil, including the farm share of automobile expenses) + 
 (machinery and the farm share of auto depreciation)] [1 + ^] + 
 [(depreciated inventory value of machinery and the farm share of 
 auto at the beginning of the year) (p)]. 
 
 X5 = Crop expenses. [(The sum of annual expenses for fertilizer and 
 lime, seed and crop expenses, and on grain farms, miscellaneous oper- 
 ating expenses) (1 + <^)] + [(depreciated investment in soil fertility 
 at the beginning of the year) (p) ]. 
 Xg = Livestock expenses. [(Annual livestock expenses, excluding pur- 
 chased livestock and feed, and on livestock farms, miscellaneous oper- 
 ating expenses) (1 + ^)] + [(investment in livestock, feed, and grain 
 at the beginning of the year) (p)]. 
 
 All of the variables were expressed in current dollars. Input variables, 
 except land, represent annual costs including an opportunity cost of 
 income foregone by using the money in the farm business ; or in the case of 
 durable capital items, an annual service cost equivalent to an opportunity 
 cost of income foregone. 
 
8 Bulletin No. 720 [August, 
 
 It may be argued that an opportunity cost should not be included as 
 an explicit cost of the input. However, this is a cost that must be covered 
 if the firm is to obtain the input for production. If the opportunity cost is 
 not included, then the input must yield a marginal value product that is 
 in excess of the dollar expenditure. In an accounting sense, this means 
 that a dollar on the debit side of the ledger is not worth as much as a 
 dollar on the credit side. 
 
 Selection of Empirical Data 
 
 To test the hypotheses stated above, a series of static analyses of farm 
 account data of four types of farms in three separate time periods was 
 used. Four different types of farms — grain, hog, beef and dairy — were 
 chosen to permit selecting farms with similar input-output relationships, 
 while at the same time permitting differences to be detected in the man- 
 ner in which different types of farms combine capital resources with land 
 and labor. 
 
 The different types of farms were selected from areas where the re- 
 spective types of farms prevailed, so that greater uniformity of farms 
 within each type would be achieved. These areas were the east-central 
 area for cash grain farms, the western livestock area for hog and beef 
 farms, and the general farming area in southern Illinois for dairy farms. ^ 
 The counties from which the sample farms were selected are shown in 
 Figure 1. A uniform set of information about farm firms over a wide 
 area and an extended period of time was achieved by utilizing the indi- 
 vidual farm business records of farmers who cooperate with the Depart- 
 ment of Agricultural Economics and the Illinois Farm Bureau Farm 
 Management Service. 
 
 A comparative study of record-keeping farms and a random sample 
 of all farms revealed that record-keeping farms tended to be larger in 
 land size, located on more productive soils, and used capital more inten- 
 sively. The operators possessed superior management ability.^ How- 
 ever, when the random sample farms were grouped to yield a set of farms 
 that was similar to the record-keeping farms in terms of acreage and soil 
 quality, it was found that differences in capital intensity between the two 
 groups diminished and differences in the managerial measures disap- 
 peared. Record-keeping farms cannot be used to represent the entire 
 
 ^ R. C. Ross and H. C. M. Case, "Types of Farming in Illinois." 111. Agr. Exp. 
 Sta. Bui. 601. April, 1956. 
 
 ^ Allan G. Mueller, "Comparison of Farm Management Service Farms and a 
 Random Sample of Farms in Western Illinois," Jour. Farm Econ., 36:285-292. 
 May, 1954. 
 
1966] " Resource Productivity and Income Distribution 
 
 [ j GENERAL FARMING AREA 
 
 Figure 1. — Locations of sample areas in Illinois. 
 
 LIVESTOCK AREA 
 GRAIN AREA 
 
 population of farms in a given area, but they are representative of the 
 
 population of farms that is similar in respect to acreage and soil 
 
 productivity. 
 
 In summarizing the farm account books, each farm is classified by 
 
 type according to the following definitions : ^ 
 
 Grain farms. Farms on which the value of feed fed to livestock was 
 less than one-half of the feed and grain returns and the value of feed 
 fed to dairy or poultry was not more than one-sixth of the feed and 
 grain returns. 
 
 Hog or beef farms. Farms on which the value of feed fed to livestock 
 was more than one-half of feed and grain returns and either hog or 
 beef cattle enterprises received more than one-half of the value of 
 feed fed. 
 
 Dairy farms. Farms on which the value of feed fed to livestock was 
 more than one-half of feed and grain returns and the dairy enterprise 
 received more than one-third of the value of feed fed. 
 
 ^ Illinois Farm Bureau Farm Management Service, "Farm Business Analysis 
 Report on Illinois Farms for 1959," Univ. 111., Dept. Agr. Econ. July, 1960. 
 
10 Bulletin No. 720 [August, 
 
 Dairy-grain farms. Farms on which the value of feed fed to livestock 
 was less than one-half of the feed and grain returns and the value of 
 feed fed to dairy was more than one- sixth of the feed and grain 
 returns. 
 
 Dairy-hog farms. Farms that met the requirements for both dairy and 
 hog farms. 
 
 This classification by type of farm was accepted for this study with 
 the exception that combination dairy-grain or dairy-hog farms were in- 
 cluded as dairy farms in this study. 
 
 To determine trends over time in resource productivity and in the 
 pattern of distributive shares, farm account records were selected to 
 represent the decade from 1949 to 1959. The selection of years for use in 
 detecting changes over time presented a problem because of yield fluctua- 
 tions and price changes. For the sake of simplicity, data from three 
 periods corresponding to the Census of Agriculture taken in 1949, 1954, 
 and 1959 were selected. Data from three consecutive years were averaged 
 to obtain an observation for each individual farm to minimize the effect 
 of "lumpy" investments that appear in the annual farm accounts. Averag- 
 ing may also tend to even out some of the fortuitous consequences 
 occurring to the farm business and provide a more representative account 
 of each farm business. 
 
 Within the specified types of farms and designated periods, farms were 
 identified for possible inclusion in the analysis if they met the follow- 
 ing criteria: (1) the farm was classified as being the same type for the 
 three consecutive years; (2) the operator remained the same during 
 the three years; (3) the operator remained on the same farm during the 
 three years and fluctuations in acreage operated did not exceed the small- 
 est acreage operated by more than one- third; and (4) the farm did not 
 have high-labor enterprises such as truck crops. 
 
 If the total number of qualifying farms in 1948-1950 and 1953-1955 
 exceeded 150, a random sample was drawn to yield at least 150 farms. 
 Because the 1958-1960 data were already processed onto computer cards, 
 the entire groups of farms meeting the selection criteria were used in the 
 analysis for this period. Sample sizes were as follows: 
 
 1948-1950 1953-1955 1958-1960 
 
 Grain farms 149 151 194 
 
 Hog farms 151 150 162 
 
 Beef farms 64 126 99 
 
 Dairy farms 87 119 
 
 In the remainder of this report the mid-years of 1949, 1954, and 1959 
 will be used to refer to data from their respective periods. 
 
1966] Resource Productivity and Income Distribution 11 
 
 The Analysis 
 
 The analysis of factor payments to land and operator labor in this 
 study contains some theoretical characteristics, even though actual farm 
 data were used. In the case of land, the estimated marginal value product 
 of land is compared with an imputed market rate of return to land as 
 reflected in the current market valuation of land. In the case of operator 
 labor, the estimated marginal factor share to operator labor is compared 
 with a "market" return that is computed as a residual return to operator 
 labor after all other factors have been paid according to their imputed 
 market rates. 
 
 Thus the imputed market returns to land and operator labor do not 
 represent what they actually received, but instead what they would have 
 received if the payment to land is based on a percent of its current value 
 and if other non-operator labor inputs receive a payment in accordance 
 with their full market cost. 
 
 This study was not designed to identify or measure the determinates of 
 farm land value. It is recognized that urban people and institutions, as 
 well as farmers, may seek to own farm land, and that for a given tract of 
 land at a given time, a number of factors enter into the determination of 
 its value. Considering farm land in total, however, its valuation for use as 
 an input in agricultural production must ultimately rest on its expected 
 contribution to farm output. 
 
 If a buyer acquires a tract of land and later discovers that the market 
 had underestimated an increase in the productivity of the land, the land- 
 owner would then be in a position to reap some capital gains. If the 
 opposite occurred, however, a capital loss might be experienced. A full 
 examination of the role of expected capital gains, demand for farm land 
 for urban uses, non-farm investors in farm land, and other non-pro- 
 ductivity influences on farm land value was beyond the scope of this study. 
 The focus of this study was to determine the relation between current 
 land value and its estimated productivity value. 
 
 Statistical Estimates 
 
 Only three groups of farms — hog farms in 1954, grain farms in 1959, 
 and beef farms in 1959 — exhibited increasing returns to scale that were 
 significant at the 0.05 level of probability. The hypothesis of constant 
 returns to scale was not rejected for the remaining eight groups of farms. 
 
 Because the groups of farms with significant increasing returns to 
 scale occurred in three diff"erent types of farms and in two time periods, 
 constant returns to scale were assumed for all groups of farms and for 
 estimates of the marginal value products from the constrained function 
 used in the distributive shares analysis. The major effect of this assump- 
 
12 
 
 Bulletin No. 720 
 
 [August, 
 
 tion on the three groups of farms with increasing returns to scale was a 
 reduction in the estimated elasticity of production of the labor input. 
 Caution should be used in the interpretation of the respective labor pro- 
 ductivities and labor shares for these three groups of farms. 
 
 Tables 1 through 4 present estimates derived from the constrained 
 functions for the grain, hog, beef, and dairy farms, respectively. Each 
 table contains the geometric means of the output and factors of produc- 
 tion, the estimated elasticity of production for each factor, the correspond- 
 ing marginal value product of each factor, and the resulting marginal 
 factor share of the total product. Appendix Tables 3 through 6 present 
 corresponding results from the unconstrained functions. 
 
 Table 1. — Constrained Estimates of Factor Productivities and Factor Shares 
 on Illinois Grain Farms, 1949, 1954, and 1959" 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpO 
 
 1949 
 
 N = 149 
 
 R2 = .9207 
 
 
 
 Y 
 
 $17,248 
 
 
 
 
 Xi 
 
 65,233 
 
 .4519** 
 
 $ .1195 
 
 $ 7,795 
 
 X2 
 
 2,954 
 
 .0531 
 
 .3100** 
 
 916 
 
 Xs 
 
 957 
 
 .0033 
 
 .0597* 
 
 57 
 
 X4 
 
 3,788 
 
 .2478* 
 
 1.1282 
 
 4,274 
 
 X6 
 
 751 
 
 .0998* 
 
 2.2912** 
 
 1,721 
 
 Xe 
 
 791 
 
 .1441** 
 
 3.1437** 
 
 2,485 
 
 Sum 
 
 
 1.0000 
 
 
 17,248 
 
 1954 
 
 N = 151 
 
 R2 = .8899 
 
 
 
 Y 
 
 S18,538 
 
 
 
 
 Xi 
 
 91,894 
 
 .4429** 
 
 $ .0893 
 
 $ 8,210 
 
 Xa 
 
 3,275 
 
 .1472** 
 
 .8330 
 
 2,729 
 
 Xs 
 
 1,273 
 
 -.0117 
 
 -.1701** 
 
 -217 
 
 X4 
 
 5,003 
 
 .0913 
 
 .3383** 
 
 1,693 
 
 Xs 
 
 2,608 
 
 .3016** 
 
 2.1440** 
 
 5,591 
 
 Xe 
 
 1,010 
 
 .2087 
 
 .5266 
 
 532 
 
 Sum 
 
 
 1.0000 
 
 
 18,538 
 
 1959 
 
 N = 194 
 
 R2 = .9026 
 
 
 
 Y 
 
 S 22,094 
 
 
 
 
 Xi 
 
 135,973 
 
 .2463** 
 
 S .0400 
 
 S 5,442 
 
 X2 
 
 3,740 
 
 .1549** 
 
 .9149 
 
 3,422 
 
 Xs 
 
 1,716 
 
 -.0175 
 
 -.2248** 
 
 -387 
 
 X4 
 
 6,242 
 
 .2434** 
 
 .8617 
 
 5,378 
 
 Xs 
 
 3,200 
 
 .2356** 
 
 1.6263** 
 
 5,205 
 
 Xe 
 
 1,137 
 
 .1373** 
 
 2.6686** 
 
 3,034 
 
 Sum 
 
 
 1.0000* 
 
 
 22,094 
 
 a The estimating equation was constrained to force the sum of the regression coefficients to 
 equal one. 
 
 * Null hypothesis rejected at the 0.05 level of probabihty. The null hypotheses are: (1) 
 
 bi = 0, where i = 1 to 6; (2) 2 bi = 1; and (3) mvpi = $1 where i = 2 to 6. 
 ** Null hypothesis rejected at the 0.01 level of probability. 
 
1966] 
 
 Resource Productivity and Income Distribution 
 
 13 
 
 Some general observations of the estimates shown in Tables 1 through 
 4 may be useful to provide a background for the examination of the 
 major hypotheses of the study. This discussion is not intended to be a 
 complete analysis of the adjustments required to achieve an optimal 
 allocation of resources on the farms. Its purpose is to call attention to 
 some of the basic underlying relationships of resource productivity that 
 influence the distributive shares analysis of the aggregate factors — real 
 estate, labor, and capital. 
 
 First, the estimated marginal value products of labor, land improve- 
 ments, and machinery inputs were less than their dollar cost on all types 
 of farms and in all periods, except for the machinery input on grain farms 
 in 1949. This indicates that too many units of these inputs were being 
 
 Table 2. Constrained Estimates of Factor Productivities and Factor Shares 
 on Illinois Hog Farms, 1949, 1954, and 1959^ 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1949 
 
 N = 151 
 
 R2 = .8337 
 
 
 
 Y 
 
 $16,515 
 
 
 
 
 Xi 
 
 41,362 
 
 .2459** 
 
 $ .0982 
 
 $ 4,061 
 
 X2 
 
 3,231 
 
 .0718 
 
 .3669** 
 
 1,186 
 
 Xs 
 
 1,364 
 
 .0068 
 
 .0820t 
 
 112 
 
 X4 
 
 3,451 
 
 .1682* 
 
 .8049 
 
 2,778 
 
 X5 
 
 392 
 
 .0384 
 
 1.6163 
 
 633 
 
 Xe 
 
 1,483 
 
 .4690** 
 
 5.2229** 
 
 7,745 
 
 Sum 
 
 
 1.0000 
 
 
 16,515 
 
 1954 
 
 N - 150 
 
 R2 = .8874 
 
 
 
 Y 
 
 $18,033 
 
 
 
 
 Xi 
 
 67,207 
 
 .4014** 
 
 $ .1077 
 
 $ 7,238 
 
 X2 
 
 3,556 
 
 .0432 
 
 .2192** 
 
 779 
 
 X3 
 
 1,912 
 
 -.05271 
 
 -.4966** 
 
 -948 
 
 X4 
 
 4,887 
 
 .1293* 
 
 .4772* 
 
 2,332 
 
 X5 
 
 1,542 
 
 .1300** 
 
 1.5208 
 
 2,344 
 
 Xe 
 
 2,129 
 
 .3487** 
 
 2.9532** 
 
 6,288 
 
 Sum 
 
 
 1.0000** 
 
 
 18,033 
 
 1959 
 
 N = 162 
 
 R2 = .8517 
 
 
 
 Y 
 
 $19,834 
 
 
 
 
 Xi 
 
 83,660 
 
 .2818** 
 
 $ .0668 
 
 $ 5,588 
 
 X2 
 
 3,777 
 
 .1207** 
 
 .6337 
 
 2,394 
 
 X3 
 
 2,272 
 
 .0395 
 
 .3443** 
 
 783 
 
 X4 
 
 5,784 
 
 .1501* 
 
 .5146* 
 
 2,975 
 
 X5 
 
 1,614 
 
 .1187** 
 
 1.4582 
 
 2,354 
 
 Xe 
 
 2,427 
 
 .2894** 
 
 2.3648** 
 
 5,740 
 
 Sum 
 
 
 1.0000 
 
 
 19,834 
 
 a The estimating equation was constrained to force the sum of the regression coefficients to 
 equal one. 
 
 * Null hypothesis rejected at the 0.05 level of probability. The null hypotheses are the same 
 as those listed under Table 1. 
 
 ** Null hypothesis rejected at the 0.01 level of probability. 
 
 t Null hypothesis rejected at the 0.10 level of probability. 
 
14 
 
 Bulletin No. 720 
 
 [August, 
 
 Table 3. 
 
 Constrained Estimates of Factor Productivities and Factor Shares 
 on Illinois Beef Farms, 1949, 1954, and 1959^ 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1949 
 
 N =64 
 
 R2 = .8376 
 
 
 
 Y 
 
 $23,825 
 
 
 
 
 Xi 
 
 57,467 
 
 .2596** 
 
 $ .1076 
 
 % 6,185 
 
 Xz 
 
 4,137 
 
 .0963 
 
 .5545 
 
 2,294 
 
 X3 
 
 2,000 
 
 .0794 
 
 .9457 
 
 1,892 
 
 X4 
 
 4,389 
 
 .1408 
 
 .7646 
 
 3,355 
 
 Xe 
 
 507 
 
 .0356 
 
 1.6712 
 
 848 
 
 Xe 
 
 2,283 
 
 .3883** 
 
 4.0522** 
 
 9,251 
 
 Sum 
 
 
 1.0000 
 
 
 23,825 
 
 1954 
 
 N = 126 
 
 R2 = .7557 
 
 
 
 Y 
 
 $18,072 
 
 
 
 
 Xi 
 
 79,154 
 
 .3290** 
 
 $ .0751 
 
 $ 5,946 
 
 X2 
 
 3,837 
 
 .0288 
 
 .1355* 
 
 520 
 
 X3 
 
 2,450 
 
 .0333 
 
 .2456* 
 
 602 
 
 X4 
 
 5,370 
 
 .2212* 
 
 .7444 
 
 3,997 
 
 X6 
 
 1,748 
 
 .0609 
 
 .6296 
 
 1,101 
 
 Xe 
 
 2,489 
 
 .3268** 
 
 2.3729* 
 
 5,906 
 
 Sum 
 
 
 1.0000 
 
 
 18,072 
 
 1959 
 
 N =99 
 
 R2 = .6785 
 
 
 
 Y 
 
 $ 24,458 
 
 
 
 
 Xi 
 
 113,706 
 
 .3670** 
 
 $ .0789 
 
 S 8,975 
 
 X2 
 
 4,251 
 
 .0202 
 
 .1161 
 
 494 
 
 Xs 
 
 2,872 
 
 .0483 
 
 .4109 
 
 1,181 
 
 X4 
 
 6,812 
 
 -.1098 
 
 -.3941t 
 
 -2,685 
 
 Xs 
 
 2,161 
 
 .2388** 
 
 2.7027t 
 
 5,841 
 
 Xe 
 
 3,500 
 
 .4355** 
 
 3.0434t 
 
 10,652 
 
 Sum 
 
 
 1.0000* 
 
 
 24,458 
 
 a The estimating equation was constrained to force the sum of the regression coefficients to 
 equal one. 
 
 * Null hypothesis rejected at the 0.05 level of probability. The null hypotheses are the same 
 as those listed under Table L 
 
 ** Null hypothesis rejected at the 0.01 level of probability. 
 
 t Null hypothesis rejected at the 0.10 level of probability. 
 
 used in relation to the other inputs employed. A test of the hypothesis 
 that the marginal value products of the inputs were equal to $1.00 re- 
 vealed that the marginal value product could range from approxi- 
 mately 50 cents to $1.50 before they were significantly different from 
 $1.00. 
 
 A second general observation to be noted is the high marginal value 
 products estimated for the crop and livestock inputs on all types of farms 
 and in nearly all periods. A high marginal value product for crop inputs 
 may be the result of the difficulty of financing inputs that are nonasset- 
 creating, such as fertilizer purchases.^ This would be particularly true 
 
 ^ G. B. Baker and G. D. Irwin, "Effects of Borrowing From Gommercial 
 Lenders on Farm Organization," 111. Agr. Exp. Sta. Bui. 671, pp. 21-22. 1961. 
 
1966] 
 
 Resource Productivity and Income Distribution 
 
 15 
 
 if the financial difficulty contributes more heavily to an inadequate 
 fertilization program on farms with low total value of production. It 
 would tend to raise the estimated elasticity of production of the crop 
 input and, as a result, the marginal value product of the crop input 
 would also be raised. 
 
 With this brief discussion of the basic input-output relationships of 
 the selected groups of farms in this study, attention is now turned to the 
 major hypotheses of the study. 
 
 Interpretation of Results 
 
 An examination of the marginal value products of land in Tables 1 
 through 4 reveals a moderate decline in the rate of return on current 
 land value of about 3 percentage points among hog and beef farms from 
 1949 to 1959 and a decline of 1 percentage point among dairy farms 
 from 1954 to 1959. Among grain farms the decline in the rate of return 
 on land was more accentuated, dropping from 12 percent in 1949 to 4 
 percent in 1959. These trends can be clearly seen in Figure 2. A least- 
 squares trend line fitted to these data indicates that the rate of return on 
 current land value has declined 2.2 percentage points each five years 
 
 Table 4. 
 
 -Constrained Estimates of Factor Productivities and Factor Shares 
 on Illinois Dairy Farms, 1954, and 1959'' 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, hi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1954 
 
 N =87 
 
 R2 = .7630 
 
 
 
 Y 
 
 S 9,633 
 
 
 
 
 Xi 
 
 27,183 
 
 .2372** 
 
 $ .0841 
 
 $ 2,285 
 
 X2 
 
 3,095 
 
 .2206* 
 
 .6866 
 
 2,125 
 
 Xs 
 
 916 
 
 .0071 
 
 .0742 
 
 68 
 
 X4 
 
 3,604 
 
 .1160 
 
 .3100* 
 
 1,118 
 
 X5 
 
 1,368 
 
 .2374** 
 
 1.6718 
 
 2,287 
 
 Xe 
 
 861 
 
 .1817* 
 
 2.0334 
 
 1,750 
 
 Sum 
 
 
 1.0000 
 
 
 9,633 
 
 1959 
 
 N = 119 
 
 R2 = .8149 
 
 
 
 Y 
 
 $16,280 
 
 
 
 
 Xi 
 
 43,725 
 
 .I960** 
 
 $ .0730 
 
 $ 3,192 
 
 X2 
 
 3,955 
 
 .1289t 
 
 .5307 
 
 2,099 
 
 Xs 
 
 1,486 
 
 .0875* 
 
 .9586 
 
 1,424 
 
 X4 
 
 5,544 
 
 .2482** 
 
 .7289 
 
 4,041 
 
 Xs 
 
 1,589 
 
 .1260* 
 
 1.2911 
 
 2,051 
 
 Xe 
 
 1,463 
 
 .2133** 
 
 2.3738t 
 
 3,473 
 
 Sum 
 
 
 1.0000 
 
 
 16,280 
 
 ^ The estimating equation was constrained to force the sum of the regression coefficients to 
 equal one. 
 
 * Null hypothesis rejected at the 0.05 level of probability. The null hypotheses are the same 
 as those listed under Table 1. 
 
 ** Null hypothesis rejected at the 0.01 level of probability. 
 t Null hypothesis rejected at the 0.10 level of probability. 
 
Bulletin No. 720 
 
 [August, 
 
 2% 
 
 HOG FARMS 
 
 / 
 
 DAIRY FARMS 
 
 RATE OF RETURN 
 FROM FARM LAND 
 
 1949 1954 
 
 Figure 2. — Trends in rates of return on current land value. 
 
 1959 
 
 during the decade. This decline in the marginal value product of land 
 during the decade indicates that a larger portion of the income among 
 all four types of farms was capitalized into land value at the end of the 
 decade than at the beginning. 
 
 Evidence to support or refute the hypothesis that the market value of 
 farm land exceeds its imputed value, based on the contribution of land to 
 the product of the firm, was obtained by comparing the estimated 
 marginal value product of land with an assumed market rate of return 
 that would be expected by landowners on the investment in land. 
 
 Because land is a residual claimant and receives a return according to 
 its ability to substitute for other inputs that carry a cost of production, 
 rising land values would be expected to reflect increases in the pro- 
 ductivity of land. If land values had risen according to the increase in 
 land productivity, the marginal value product of land would be constant 
 over time. Or, if there was a difference between the estimated pro- 
 ductivity of land and the market evaluation of land productivity in the 
 first period of the study, a change in the marginal value product toward 
 the expected market rate would be anticipated in the succeeding periods.^ 
 
 The mortgage interest rate is frequently used as an indicator of a 
 
 ^ Direct comparisons of changes in land productivity and in land value for 
 these groups of farms are presented in Roger W. Strohbehn, op. cit., pp. 86-90. 
 
1966] Resource Productivity and Income Distribution 17 
 
 landowner's expected rate of return on the investment in land. This rate 
 is not completely valid as an indicator, because it underestimates the 
 "true" rate of return expected on land as a factor of production. The 
 mortgage rate can be viewed as the opportunity cost of money tied up in 
 land when it is valued at current market value. This opportunity cost is 
 less than the "true" expected return since it is determined under condi- 
 tions of relative certainty as evidenced by the conservative appraisal 
 procedures followed in ascertaining the loan value of the land, the down 
 payment required, and possession of title of the land by the lender as a 
 safeguard against the uncertainty associated with farm income and loan 
 repayment. The landowner also considers the mortgage rate as an under- 
 estimate of the "true" expected return, because crop yields and prices 
 are subject to uncertainty and some return is necessary to compensate 
 for accepting the monetary hazards of operating under such conditions. 
 
 If the landowner expects a management return on land, this would 
 also raise the expected return on land. In addition, if the landowner 
 expects the land to generate the saving necessary to acquire debt-free 
 ownership of the land, a sinking fund factor should be included in the 
 expected return on land for the equity buildup. The sinking fund allot- 
 ment can be viewed as an annual franchise or license payment that an 
 operator makes by choosing to own land as a means of assuring himself 
 an entrepreneurial position in agriculture each year. Since this "right to 
 farm" is attached directly to the land, the owner-operator can recover 
 his franchise payments by selling his land after his farming career has 
 ended. 
 
 Whether the landowner expects a return on land that covers a land 
 management return, a sinking fund allotment, and a return for accepting 
 the challenge of uncertainty, is open for debate. These additional ex- 
 pected returns were included in the analysis because to omit them 
 requires the assumptions of ( 1 ) perfect knowledge to nullify any manage- 
 ment function; (2) equity in land to be derived entirely from labor and 
 other nonland income; and (3) certainty that current yields and prices 
 will continue in the future. None of these assumptions appears to be in 
 harmony with the existing conditions and the traditional method of land 
 acquisition by farm operators. 
 
 The "true" expected rate of return on land was assumed to include 
 (1) the opportunity cost of money invested in land, valued at current 
 market prices, as indicated by the mortgage rate of interest; (2) a man- 
 agement return on land equivalent to the typical charge of a professional 
 farm manager, computed as a percentage of the marginal share to land — 
 7 percent on grain farms and 8 percent on livestock farms; (3) an equity 
 charge to permit the land to be repurchased during the operating career 
 
18 
 
 Bulletin No. 720 
 
 [August J 
 
 of each generation, as indicated by the 40-year sinking fund rate; and 
 (4) a charge for uncertainty of 1 percent on the current value of land. 
 Comparisons of the marginal value products of land and the expected 
 market rate of return in Table 5 reveal that grain, hog, and dairy farms 
 in 1959 had marginal value products of land that were less than the ex- 
 pected rate of return. However, only on the grain farms was the marginal 
 value product significantly less than the expected market rate of return. 
 On the dairy farms in 1959 and on all types of farms in 1949 and 1954 
 the marginal value product of land was larger than the expected rate of 
 return, being significantly larger on grain farms in 1949 and hog farms in 
 1954. These comparisons indicate that the proportion of farm income 
 being capitalized into land value increased over time and that by 1959 
 the market had elevated land prices to a level that exceeded the pro- 
 ductivity value of land. 
 
 Table 5. — Comparisons Between Marginal Value Products of Land and Expected 
 Market Rates of Return on Selected Types of Illinois Farms, 1949, 1954, and 1959 
 
 rr J Marginal 
 
 Type and ^^f^^ 
 
 P^^^°^ product^ 
 
 GRAIN 
 
 1949 $ .1195 
 
 (.0123) 
 
 1954 0893 
 
 (.0106) 
 
 1959 0400 
 
 (.0059) 
 
 HOG 
 
 1949 0982 
 
 (.0207) 
 
 1954 1077 
 
 (.0141) 
 
 1959 0668 
 
 (.0114) 
 
 BEEF 
 
 1949 1076 
 
 (.0366) 
 
 1954 0751 
 
 (.0199) 
 
 1959 0789 
 
 (.0284) 
 
 DAIRY 
 
 1949 No data available 
 
 1954 0841 
 
 (.0276) 
 1959 0730 
 
 (.0228) 
 
 a Standard errors are in parentheses. 
 * Significant difference at the 0.05 level of probability. 
 ** Significant difference at the 0.01 level of probability. 
 
 Expected 
 
 market rate 
 
 of return 
 
 t ratio 
 
 $.0727 
 
 3.805** 
 
 .0717 
 
 1.660 
 
 .0703 
 
 5.136** 
 
 .0722 
 
 1.256 
 
 .0740 
 
 2 . 390* 
 
 .0728 
 
 .526 
 
 .0730 
 
 .945 
 
 .0714 
 
 .186 
 
 .0738 
 
 .180 
 
 .0721 
 
 .435 
 
 .0733 
 
 .013 
 
1966] 
 
 Resource Productivity and Income Distribution 
 
 19 
 
 Return to real estate 
 
 The treatment of land and land improvements as a single market unit 
 of real estate in a distributive shares analysis enables land, as a residual 
 claimant, to receive the gain or loss associated with the investment in land 
 
 Table 6. — Comparisons (in Dollars) Between the Expected Market Return and the Marginal Share 
 to Real Estate on Selected Types of Illinois Farms, 1949, 1954, and 1959 
 
 1949 
 
 Return Gumula- 
 
 to tive 
 
 real differ- 
 
 estate* ence^ 
 
 1954 
 
 Return Cumula- 
 to tive 
 
 real differ- 
 
 estate** ence'^ 
 
 1959 
 
 Return Gumula- 
 to tive 
 
 real differ- 
 
 estate'* ence'' 
 
 GRAIN 
 
 Marginal share return $ 7,852 $ 7,993 S 5,055 
 
 (1,201) (1,427) (1,194) 
 
 Expected market return: 
 
 Mortgage interest 2,935 S4,917** 4,255 S3, 738** 6,662 S-1, 607 
 
 Land improvement expense . . 957 3,960** 1,273 2,465 1,716 -3,323** 
 
 Management return 550 3,410** 559 1,906 354 -3,677** 
 
 Sinking fund allotment 610 2,800* 836 1,070 1,156 -4,833** 
 
 Charge for uncertainty 652 2,148 919 151 1,360 -6,193** 
 
 HOG 
 
 Marginal share return 4,173 6,290 6,371 
 
 (1,497) (1,434) (1,518) 
 
 Expected market return: 
 
 Mortgage interest 1,861 2,312 3,112 3,178* 4,099 2,272 
 
 Land improvement expense . . 1,364 948 1,912 1,266 2,274 -2 
 
 Management return 334 614 504 706 509 -511 
 
 Sinking fund allotment 387 227 611 151 711 -1,222 
 
 Charge for uncertainty 414 -187 672 -521 837 -2,059 
 
 BEEF 
 
 Marginal share return 8,077 6,548 10,156 
 
 (3,650) (2,468) (5,268) 
 
 Expected market return: 
 
 Mortgage interest 2,586 5,491 3,665 2,883 5,571 4,585 
 
 Land improvement expense . . 2,000 3,491 2,450 433 2,872 1,713 
 
 Management return 646 2,845 523 -90 812 901 
 
 Sinking fund allotment 537 2,308 720 -810 967 -66 
 
 Charge for uncertainty 575 1,733 792 - 1 , 602 1,137 - 1 , 203 
 
 DAIRY 
 
 Marginal share return No data available 2,353 4,616 
 
 (1,309) (1,699) 
 
 Expected market return: 
 
 Mortgage interest 1 ,259 1 ,094 2,142 2,474 
 
 Land improvements 916 178 1 ,486 988 
 
 Management return 189 —11 370 618 
 
 Sinking fund allotment 247 -258 372 246 
 
 Charge for uncertainty 272 -530 437 - 191 
 
 » Standard error in parentheses. 
 
 ^ Marginal share to real estate minus cumulative sum of expected return to real estate. 
 * Significant difference at the 0.05 level of probability. 
 ** Significant difference at the 0.01 level of probability. 
 
20 Bulletin No. 720 [August, 
 
 improvements. The factor share to real estate, either market or marginal, 
 is simply the sum of the land share plus the land improvement share. 
 
 If the estimated marginal shares to real estate are taken as the best 
 estimate of the actual productivity of real estate, and similarly, if the 
 hypothetical expected market return to real estate is assumed to accu- 
 rately reflect the landowners expected return, then these two estimates 
 may be compared for an additional test of the hypothesis relating to land 
 values. Such comparisons in Table 6 indicate that the marginal share 
 was less than the total expected return for all groups of farms in 1959; 
 hog, beef, and dairy farms in 1954; and hog farms in 1949. Furthermore, 
 the difference between the marginal share and the expected return be- 
 came less advantageous for the landowner between 1949 and 1959. 
 
 This again indicates that a growing portion of farm income was being 
 capitalized into land value during the decade and that the market value 
 of land was tending to diverge from its productivity value. For the eight 
 groups of farms on which the expected return exceeded the marginal 
 share, more farm income had been capitalized into land value than could 
 be justified on the basis of the contribution of real estate to the total 
 product of the farm. 
 
 Evidence from the sample data in support of the hypothesis that the 
 market value of farm land exceeds its imputed productivity value was 
 statistically significant only in the case of grain farms in 1959. However, 
 the analysis does indicate that an increasing proportion of farm income 
 was capitalized into land value during the decade from 1949 to 1959. 
 The analysis also indicates that the marginal share to real estate decreased 
 relative to the expected market rate of return during the decade to the 
 disadvantage of the landowner. Thus the whole analysis does lend 
 support, although not conclusively, to the hypothesis that the market 
 value of land has exceeded its productivity value. 
 
 Return to operator 
 
 Evidence to support or refute the hypothesis that farmers tend to 
 capitalize part of their labor and management return into land value was 
 obtained by comparing the proportion of the total value of production 
 accruing to the farm operator, as determined by a marginal share com- 
 putation, with a corresponding residual "market" share. If farmers had 
 capitalized part of their labor and management into land value, the 
 operator's marginal share would be greater than his residual "market" 
 share. 
 
 The marginal share accruing to the operator was comprised of a 
 
1966] Resource Productivity AND Income Distribution 21 
 
 marginal return to the labor of the operator, plus a management or entre- 
 preneurial return on the nonreal estate capital inputs. This share is 
 shown algebraically as : 
 
 (6) Oms = (X2mvp2 — X2h) + (X4mvp4 + Xsmvps + Xemvpe 
 
 — X4 — X5 — Xe) 
 
 Definitions of the terms in this equation are: 
 Oms = Operator's marginal share; 
 X2 = geometric mean of the labor input; 
 
 X4 = geometric mean of the machinery and equipment input; 
 X5 = geometric mean of the crop input; 
 Xe = geometric mean of the livestock input; 
 h = fraction of nonoperator labor in the labor input; and 
 mvpi = marginal value product of the respective inputs. 
 
 The first term of the right-hand side of equation (6) represents the 
 marginal return (loss) to operator labor after hired and nonoperator 
 family labor had been paid at full market cost. The second term repre- 
 sents an entrepreneurial risk and management return (loss) to the op- 
 erator on the nonreal estate capital inputs. Computing the marginal 
 share to the operator by this method reflects a distribution of the value 
 of production of the farm among the inputs in such a way that nonreal 
 estate inputs were paid their market costs, including an opportunity cost, 
 while the real estate and operator inputs were paid according to their 
 marginal productivities. This distribution utilizes marginal productivity 
 with the modification that the assumption of perfect knowledge is dropped 
 and the operator accepts the entrepreneurial task of resource allocation 
 under the expectation of receiving a return for undertaking the risk and 
 uncertainty associated with it. 
 
 The residual "market" return to the operator for his labor and 
 managerial skills was computed by subtracting all real estate and nonreal 
 estate operating expenses, including nonoperator labor, from the total 
 value of production. The annual market cost of real estate was deter- 
 mined as the sum of the annual land improvement expense, plus the 
 mortgage interest payment computed on the total current land value. 
 The residual income to the operator must cover any expected equity 
 accumulation in land, plus a return for the uncertainty involved in the 
 farming operation. 
 
 The marginal share to the operator was low in the 1954 period in 
 relation to 1949 and 1959 for all types of farms except beef farms, which 
 had low marginal shares to the operator in both 1954 and 1959. This can 
 
22 
 
 Bulletin No. 720 
 
 [August f 
 
 Table 7. 
 
 — Marginal and Residual Market Share Returns to Operator Inputs 
 on Selected Types of Illinois Farms, 1949, 1954, and 1959 
 
 Type and 
 period 
 
 Value of Percentage share to operator 
 production Marginal Residual market 
 
 GRAIN 
 
 1949 SI 7, 248 
 
 1954 18,538 
 
 1959 22,094 
 
 HOG 
 
 1949 16,515 
 
 1954 18,033 
 
 1959 19,834 
 
 BEEF 
 
 1949 23,825 
 
 1954 18,072 
 
 1959 24,458 
 
 DAIRY 
 
 1949 No data available 
 
 1954 9,633 
 
 1959 16,280 
 
 15.9 
 
 3.0 
 
 22.8 
 
 32.7 
 
 8.7 
 
 11.2 
 
 25.5 
 
 .2 
 
 -.3 
 
 1.7 
 7.8 
 
 38.8 
 
 16.3 
 
 7.7 
 
 38.4 
 15.8 
 11.2 
 
 40.2 
 2.6 
 6.7 
 
 3.5 
 13.9 
 
 be seen by studying figures in Table 7. The low marginal share to the 
 operators on hog farms in 1954 and beef farms in 1954 and 1959 was 
 largely caused by the method of computing the labor component of the 
 operator's share. Operator labor was required to bear the entire burden 
 of the low marginal value product of total labor. Hog farms in 1954 and 
 beef farms in 1954 and 1959 had negative operator labor earnings. (See 
 Appendix Table 7.) Grain and dairy farms in 1954 had low marginal 
 shares to the operator because of the negative return in the entrepreneurial 
 risk component of the operator's share (Appendix Table 7). Low yields 
 of corn and soybeans in 1954 may have been a contributing factor to the 
 low operator share in that period. In the remainder of the analysis, 
 attention will be directed to the first and last periods of the study. 
 
 Comparisons between the operator's marginal and residual market 
 shares in 1949 reveal that the market share on all types of farms was 
 substantially larger than the marginal share. Operators in this period 
 received a market share of approximately two-fifths of the value of pro- 
 duction — a quantity that was greater than their marginal contribution 
 to the farm business. This income transfer to the operators presented a 
 situation of relative prosperity for the farmers in this period, as contrasted 
 with the later periods. Between 1949 and 1959, resource adjustments 
 had taken place that increased the amount of nonreal estate capital and 
 acreage per farm, while land values had increased by 71 percent. These 
 changes resulted in a sharp decline in the operator's market share. 
 
1966] Resource Productivity and Income Distribution 23 
 
 On grain farms in 1959, the residual market share to the operator was 
 only one-third as large as the marginal share. This is a clear indication 
 that part of the operator's labor and management earnings on these farms 
 had been capitalized into land value. On hog farms the evidence in 
 support of the hypothesis is not quite so strong. The marginal and re- 
 sidual market shares were identical in 1959. This means that the entire 
 marginal share to land had been capitalized into land value, forcing the 
 landowner-operator share to absorb any sinking fund allotment to acquire 
 land and leaving nothing to the landowner as a land management return 
 or a return to cover uncertainty of income to real estate inputs. 
 
 If these three items are considered as reasonable expected returns by 
 the landowner-operator, then it appears that the land market had capital- 
 ized part of the owner-operator's expected earnings into land value. 
 
 In the case of beef farms in 1959, the operator's negative marginal 
 share makes it difficult to support or refute the basic hypothesis. This 
 group of farms had significant increasing returns to scale in the un- 
 constrained model. The fairly high marginal value product to total labor 
 in the unconstrained model was sharply reduced by the assumption of 
 constant returns to scale in the constrained model. Hence, caution should 
 be used in evaluating operator earnings on beef farms in 1959. Perhaps 
 it will be sufficient to point out that the residual market share of 6.7 
 percent provided a return of only $1,633 as an indication of low operator 
 earnings on these beef farms. 
 
 Among the dairy farms there was only slight evidence to support the 
 basic hypothesis, since the operator's residual market share was larger 
 than the marginal share in 1959 — 13.9 percent and 7.8 percent, respec- 
 tively. If land is expected to generate its own savings, provide a return 
 for real estate management, and allow for uncertainty, then the difTer- 
 ence of 6.1 percent noted above was 1.2 percent below the necessary 
 amount to cover these items. This means that land was very close to 
 being appropriately priced on these dairy farms and that operators were 
 only about $200 short of receiving their marginal product. 
 
 It should be remembered that the farms used in this analysis repre- 
 sented farms of above-average size in land and capital use and the oper- 
 ators on these farms had above average management ability. If a random 
 sample had been drawn of all farms within a specified type, the results 
 of this distributive shares analysis would probably indicate a smaller 
 operator's residual market share relative to the marginal share than was 
 found in the analysis of data from the Farm Bureau Farm Management 
 Service records. This implies a larger income transfer from operators to 
 real estate would be expected for the entire population of farms within 
 each type than was observed in the sample groups of this analysis. 
 
24 Bulletin No. 720 [August, 
 
 Capital accumulation for land purchase 
 
 One consequence of the steady decline in the agricuhural parity ratio 
 and the rising trend in land values from 1949 to 1959 is the increased 
 difficulty that confronts farmers as they try to accumulate savings from 
 their labor and management earnings for the purchase of land. This is 
 illustrated in the following example. Two tenure situations are presented 
 for identical farmers (operating with resources and productivities indi- 
 cated in the production function analysis) for grain, hog and beef farms. 
 Farmers in both situations are assumed to have started farming in 1949. 
 
 Farmers under alternative A bought their 1949 land on a 100-percent 
 loan and additional land in 1959 to bring their total acreage up to the 
 average for that period. Farmers under alternative B, however, rented 
 their land until 1959, at which time they purchased the total acreage per 
 farm for that period. As a down payment, they used a savings fund 
 equal to a 10-year annuity of the annual sinking fund allotment that 
 would have been required to amortize the 100-percent loan of alternative 
 A. In other words, under alternative A a farmer bought land when he 
 started farming and put his savings in land, whereas under alternative B 
 a farmer put an equivalent amount of savings in an annuity fund and 
 used it to purchase land 10 years later. The residual market income to 
 farmers under alternatives A and B for 1959 and their net worth in land 
 at the end of the 1959 production year are compared in Table 8. 
 
 The residual market income to the operators under alternative A for 
 grain, hog, and beef farms was $3,423, $3,314, and $3,195, respectively. 
 These are to be compared with corresponding residual market income to 
 operators under alternative B of $986, $1,769, and $1,046 for grain, hog, 
 and beef farms, respectively. Farmers operating under alternative A 
 would be able to meet their amortization payment with a modest sacrifice 
 from family living. However, farmers under alternative B would find it 
 difficult to maintain an adequate level of living while purchasing land at 
 1959 land values. In addition, capital gains that occurred during the 
 decade were realized only by farmers under alternative A. This served 
 to increase the net worth in land of alternative A farmers so that it was 
 approximately six times larger than the net worth of farmers under 
 alternative B. 
 
 Capital gains and farm income 
 
 In addition to the conventional "production" income discussed in the 
 preceding analysis, the contribution of nonconventional income from 
 capital gains to the welfare of the resource owners should also be recog- 
 
1966] Resource Productivity and Income Distribution 25 
 
 nized. The importance of capital gains as a source of income has been 
 discussed in the literature with increasing frequency.^ Real capital gains 
 arise from an interaction of such forces as expectations about the future 
 flow of income from an asset, net credit position of resource owners, 
 changes in the purchasing power of money, and changes in the discount 
 rate that is used to convert future income into a present value. 
 
 To the extent that farm families own assets that have increased in 
 value (primarily real estate), they may be able to capture this capital 
 gain when they sell the asset and thus consider the increase in value as a 
 component of their income. Capital gains are unrealized income until 
 the asset is sold. However, if the farm families substitute the expected 
 annual capital gain on real estate for their savings, they may be able to 
 increase their current consumption by spending the amount that would 
 have been set aside in some form of savings.^ Because capital gains are 
 influenced by such elusive and transitory factors as buyers' confidence in 
 the real estate market and anticipation of an increase in the stream of 
 income to real estate, capital gains cannot be considered as a perfect 
 substitute for savings as a means of raising current disposable income. 
 
 The role of capital gains in the welfare of farm families is an impor- 
 tant and complex factor. The complexities of capital gains are not un- 
 related to the problem of determining the distributive shares of conven- 
 tional income, but they do represent a set of additional considerations. 
 The thorough analysis of these considerations is beyond the scope of this 
 study. 
 
 The inclusion of anticipated capital gains in an analysis of farm in- 
 come and resource valuation introduces speculative considerations that 
 are beyond the realm of marginal analysis. For the purposes of this study, 
 perhaps it will be sufficient to recognize that capital gains have occurred 
 during the decade under study to the benefit of the landowners. This had 
 the eff'ect of raising the annual rate of return on their investment in real 
 estate by an additional percentage ranging from 5.3 percent to 8.9 per- 
 cent, depending on the amount of equity the owners held in their real 
 
 ^ D. E. Hathaway, "Agriculture and the Business Cycle," pp. 51-76, Policy 
 for Commercial Agriculture, Joint Economic Committee, 85th Cong., U.S. Govern- 
 ment Printing Office, Washington, D.C. 1957. E. W. Grove, "Farm Capital Gains 
 — A Supplement to Farm Income?" Agricultural Economics Research, pp. 37-42 
 12:2. April, 1960. D. M. Hoover, "The Measurement and Importance of Real 
 Capital Gains in the United States Agriculture, 1940 Through 1959," Jour, of 
 Farm Economics, 44:929-940. November, 1962. D. H. Boyne, Changes in the 
 Real Wealth Position of Farm Operators, 1940-1960, Mich. Agr. Exp. Sta. Tech. 
 Bui. 294. 1964. 
 
 ' D. H. Boyne, op. cit., p. 30. 
 
26 Bulletin No. 720 [August, 
 
 Table 8. — Allocation of 1959 Value of Production Under Two Alternatives 
 
 With Respect to Purchase or Rental of Land at the Beginning of the 
 
 Farming Career in 1949 on Selected Types of Illinois Farms 
 
 Grain Hog Beef 
 
 Value of production S22,094 S19,834 $24,458 
 
 Nonreal estate expense 12,005 11 ,254 14,381 
 
 Land improvement expense 1 ,716 2,274 2,872 
 
 Alternative A 
 
 Mortgage payment on 100% loan on 1949 
 
 land value 2,935 1,861 2,586 
 
 Mortgage payment on 100% loan on land added 
 
 in 1959 at 1959 value 1,197 634 756 
 
 Sinking fund allotment on 1949 land 610 387 537 
 
 Sinking fund allotment on land added in 1959 208 ' 110 131 
 
 Residual income to operator 3,423 3,314 3,195 
 
 Alternative B 
 
 Mortgage payment on loan of 1959 land value, 
 
 minus 10-year annuity of 1949 sinking fund 
 
 allotment 6,295 3,866 5,248 
 
 Sinking fund allotment on above loan 1 ,092 671 911 
 
 Residual income to operator 986 1 ,769 1 ,046 
 
 Ten-year annuity of sinking fund 7,496 4,755 6,599 
 
 Capital gain on 1949 land 46,315 29,367 40,802 
 
 Net worth in land under alternative A 54,629 34,619 48,069 
 
 Net worth in land under alternative B 8,588 5,426 7,510 
 
 estate.^ Estimates of capital gains that accrued to individuals who owned 
 land in 1949 were presented in Table 8 for grain, hog, and beef farms. 
 A long-term continuation in the rate of capital gains observed during the 
 period from 1949 to 1959 is unlikely, however, since it appears that the 
 market underestimated land productivity in 1949. 
 
 Real estate for agricultural uses derives its value primarily through its 
 contribution in the production of commodities demanded by society. 
 Capital gains on real estate in any given time period depend heavily on 
 the ability (or lack of ability) of the real estate market to estimate this 
 contribution. 
 
 Evidence in this study indicates that the market underestimated the 
 productivity value of real estate in 1949. By 1959 the market had ad- 
 justed itself to approximate the productivity value of real estate on dairy 
 farms in southern Illinois, but it overestimated the productivity value on 
 grain farms in east-central Illinois and on hog and beef farms in west- 
 central Illinois. Thus, the landowners represented in this study who 
 
 ^ Real estate values in Illinois increased an average of 7.1 percent annually 
 during the decade under study, while the purchasing power of the dollar declined 
 by 1.8 percent annually (measured by the consumer price index). Thus, the 
 range in real capital gain extends from 5.3 percent for owners with 100 percent 
 equity to 8.9 percent for owners with zero equity in their real estate. 
 
1966] Resource Productivity and Income Distribution 27 
 
 acquired real estate in 1949 obtained part of their capital gains at the 
 expense of the previous owner because of imperfections in the real estate 
 market in 1949. Owners of grain, hog, and beef farms obtained a portion 
 of their capital gain from the previous owner and a portion from the 
 future landowners, because present owners would extract a quantity of 
 money from the future owners for the anticipated future increases in real 
 estate productivity. 
 
 It should be pointed out that from a theoretical standpoint, tech- 
 nology that substitutes capital for land or that increases output for an 
 inelastic market will have the eflfect of reducing the total acres required 
 for agricultural production. Hence, if the market was free to establish 
 a new equilibrium position, capital losses would be expected from new 
 technology of this type. 
 
 Summary and Implications 
 
 An application of efficiency criteria to the problem of determining the 
 distributive shares, specifies that resources are to be paid according to 
 their marginal value products. If the firm is operating at a level of pro- 
 duction characterized by constant returns to scale, as tends to be the case 
 under perfect competition, a marginal share distribution among the re- 
 sources will just exhaust the total product of the firm. One test of the 
 effectiveness of a tenure system is its ability to enable each resource to 
 receive its marginal factor share of the total product. 
 
 The analysis of the functional distribution among the factors of pro- 
 duction has shown that the marginal share to operator labor was low on 
 each type of farm and in each time period. A partial explanation for this 
 is that the adoption of labor-saving technology renders part of the existing 
 labor redundant, resulting in a low marginal product to labor until re- 
 source adjustments can be made. Since operator labor is fixed to the firm, 
 the operator seeks adjustments that will make full utilization of his time 
 and equipment by spreading his labor over more acres. It is at this junc- 
 ture that the immobility feature of operator labor exerts pressure on the 
 tenure system as an institution to associate factor costs and returns. 
 
 Competition among farm operators for the limited supply of land may 
 encourage them to bid up the price of land (rental or purchase) in an 
 efifort to acquire the additional land needed for efficient use of machinery 
 and equipment in combination with the available labor. As the competi- 
 tion for land becomes more intense, the price of land may exceed the 
 value of land based on its marginal productivity contribution to the total 
 product of the farm. If a farmer has limited alternatives for employment 
 outside of agriculture or places a high premium on operating a farm, he 
 
28 Bulletin No. 720 [August, 
 
 is likely to accept a low return to his own personal efforts and bid up the 
 price of land in an effort to acquire the necessary land that will assure 
 himself a position in farming. This is particularly so if the farmer is in 
 a high-equity position that enables him to achieve a reasonable level of 
 income for family living while purchasing additional land. Actions such 
 as this represent an income transfer from operator labor to land and 
 result in a dissociation of costs and returns. 
 
 Although the analysis in this study was not designed to determine the 
 reasons behind the rise in land values, the analysis does indicate that 
 the trends in land value and the trends in land productivity during the 
 decade from 1949 and 1959 have not been moving in harmony. To the 
 extent that the interaction of the immobility feature of operator labor and 
 the economic necessity of farm expansion has been a major force in the 
 land market, it does appear that operators on grain and hog farms in 
 Illinois had capitalized part of their labor and management earnings 
 into land value by 1959. On beef and dairy farms the marginal share to 
 the operator was low in relation to income of nonfarm workers, but the 
 land market had not succeeded in capitalizing part of this return into 
 land value. 
 
 The dissociation of costs and returns on the grain and hog farms may 
 be an indication that the struggle for owner-operatorship may be a can- 
 cerous development that could destroy the owner-operator tenure sys- 
 tem itself. If buyers of land at current high prices discover that they 
 cannot meet both the interest payment and the sinking fund components 
 of their amortization payments, land ownership will shift to lending agen- 
 cies. Under conventional lending arrangements, farm operators will have 
 a type of leasehold possession of the real estate through a contract of per- 
 petual debt, with a fixed commitment in place of a negotiable rental con- 
 tract. If such circumstances evolve in agriculture, the lack of equity 
 accumulation by the operator means that the operator would be unable 
 to share in any capital gains that accrue to land. However, the operator's 
 fixed commitment to the perpetual debt acts as a buffer to the lender 
 against possible capital losses that may occur as a result of lower product 
 prices and reduced farm earnings. Thus the operator would be denied 
 participation in capital gains, but would be required to forestall capital 
 losses to the lender at the expense of the farm family's level of living. 
 
 Evidence from this study indicates that achievement of the tradi- 
 tional goal of owner-operatorship of the real estate inputs of the farm 
 business may be jeopardized by the trend of rising land values and a lower 
 residual market share to the operator. Accumulating savings from the 
 
1966] Resource Productivity and Income Distribution 29 
 
 operator's residual market share for the purchase of land in 1959 would 
 be very difficult if the general production and price relationships of 1959 
 continue in the future. An operator who began his farming career as a 
 tenant in 1949 and purchased land in 1959 would have a residual op- 
 erator labor income from the 1959 production of $986, $1,769, and 
 $1,046 on grain, hog, and beef farms, respectively. 
 
 The low marginal shares to the operators that were observed in this 
 study indicate that if the traditional tenure goal of owner-operated farms 
 is to continue, the expected return to land must cover the cost of land 
 acquisition. This implies that the discount rate used to calculate a present 
 value of land from the expected annual marginal contribution of land 
 should include a sinking fund rate. This would not violate the effi- 
 ciency condition of equating factor costs and returns for an effective ten- 
 ure system, but instead simply recognizes that under a tenure system of 
 owner-operated farms, land must provide a return that covers its purchase 
 price in any given year. The operator would thus be relieved of relying 
 on his low marginal return to his personal efforts as the source of savings 
 for the purchase of land. 
 
 Viewing the return to land and the consequent valuation of land from 
 this standpoint places land in the same category as other resources in that 
 the return to a resource is expected to cover its purchase price for periodic 
 replacement. The only difference is that in the case of land the owner 
 is acquiring an equity in a resource that has negligible depreciation over 
 time when properly managed and, therefore, provides a saving fund to 
 the owner-operator. 
 
 The difficulty of accumulating sufficient savings from the operator's 
 labor and management earnings during his operating career for the ac- 
 quisition of land he operates, indicates the need for a reevaluation of 
 public land tenure policies. One such review could be oriented toward 
 whether the goal of owner-operatorship is still relevant for a large seg- 
 ment of agriculture, and if so, what policy changes are needed to facilitate 
 the achievement of this goal under the present conditions of high per farm 
 capital requirements. On the other hand, if this goal has ceased to have 
 wide public support, the review could be focused on what tenure policy 
 changes are needed that are consistent with the goal of a wide distribution 
 of private entrepreneurship of farm businesses and equitable returns to 
 efficient producers. This implifes that other policies should be directed 
 toward the problems of inefficient producers with respect to resource 
 adjustments, retraining and mobility of operator labor, and income 
 supports. 
 
30 Bulletin No. 720 [August, 
 
 Literature Cited 
 
 BakeRj C. B. and Irwin, G. D., EfTects of Borrowing From Commercial 
 
 Lenders on Farm Organization, 111. Agr. Exp. Sta. Bui. 671. 1961. 
 BoYNE, D. H., Changes in the Real Wealth Position of Farm Operators, 
 
 1940-1960, Mich. Agr. Exp. Sta. Tech. Bui. 294. 1964. 
 Brandow, G. E., Interrelations Among Demands for Farm Products and 
 
 Implications for Control of Market Supply, Pa. State Univ. Bui. 680. 
 
 1961. 
 Grove, E. W., "Farm Capital Gains — A Supplement to Farm Income?" 
 
 Agricultural Economics Research, 12:2. April, 1960. 
 Hathaway, D. E., "Agriculture and the Business Cycle," Policy for Com- 
 mercial Agriculture, Joint Economic Committee, 85th Congress, U.S. 
 
 Government Printing Office, Washington, D.C. 1957. 
 Hoover, D. M., "The Measurement and Importance of Real Capital 
 
 Gains in United States Agriculture, 1940 through 1959," Jour. Farm 
 
 Econ., 44:929-940. November, 1962. 
 Illinois Farm Bureau Farm Management Service, Farm Business 
 
 Analysis Report on Illinois Farms for 1959, Univ. 111. Dept. Agr. Econ. 
 
 July, 1960. 
 Mueller, Allan G., "Comparison of Farm Management Service Farms 
 
 and a Random Sample of Farms in Western Illinois," Jour. Farm 
 
 Econ., 36:285-292. May, 1954. 
 Ross^ R. C, and Case^ H. C. M., Types of Farming in Illinois, 111. Agr. 
 
 Exp. Sta. Bui. 601. April, 1956. 
 Strohbehn, R. W., Income Distribution on Selected Types of Illinois 
 
 Farms and Implications for Tenure Adjustments, unpublished Ph.D. 
 
 thesis, Univ. 111. 1965. 
 TiNTNER, G., Econometrics, John Wiley and Sons, New York. 1952. 
 
 APPENDIX 
 
 Appendix Table 1. — Interest Rates Used to Represent Opportunity Costs 
 of Capital Used by Farm Businesses, by Years 
 
 Year and opportunity cost rates 
 
 Input 1949 1954 1959 
 
 (f) p (j) p </) p 
 
 Hired and family labor S.029 $.031 $.034 
 
 Land improvements 029 $.045 .031 $.0463 .034 $.049 
 
 Machinery and equipment. . . .021 .045 .024 .0463 .027 .049 
 
 Crop inputs 033 .045 .036 .0463 .039 .049 
 
 Livestock inputs 029 .058 .031 .0620 .034 .068 
 
1966] 
 
 Resource Productivity and Income Distribution 
 
 31 
 
 Appendix Table 2. — Monthly Wage Rates Used to Value Unpaid Labor, 
 by Areas and Years'" 
 
 y East-central and 
 
 ^^^ western livestock areas 
 
 1948 $175 
 
 1949 175 
 
 1950 175 
 
 1953 175 
 
 1954 175 
 
 1955 185 
 
 1958 200 
 
 1959 215 
 
 1960 215 
 
 a Source: Illinois Agricultural Statistics, Annual Summary, 1951 
 
 General livestock area 
 
 $160 
 160 
 160 
 
 160 
 160 
 170 
 
 185 
 200 
 200 
 
 1956, and 1962. 
 
 Appendix Table 3. — Estimated Factor Productivities and Factor Shares on Illinois 
 Grain Farms, 1949, 1954, and 1959 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1949 
 
 N = 149 
 
 R2 = .9207 
 
 
 
 Y 
 
 $17,248 
 
 
 
 
 Xi 
 
 65,233 
 
 .4513** 
 
 $ .1193 
 
 $ 7,784 
 
 X2 
 
 2,954 
 
 .0568 
 
 .3316* 
 
 980 
 
 X3 
 
 957 
 
 .0037 
 
 .0667* 
 
 64 
 
 X4 
 
 3,788 
 
 .2494** 
 
 1.1356 
 
 4,302 
 
 X5 
 
 751 
 
 .0993** 
 
 2.2806** 
 
 1,713 
 
 Xe 
 
 791 
 
 .1441** 
 
 3.1421** 
 
 2,485 
 
 Sum 
 
 
 1.0046 
 
 
 17,328 
 
 1954 
 
 N = 151 
 
 R2 = .8899 
 
 
 
 Y 
 
 $18,538 
 
 
 
 
 Xi 
 
 91,894 
 
 .4429** 
 
 $ .0893 
 
 $ 8,206 
 
 X2 
 
 3,275 
 
 .1467* 
 
 .8304 
 
 2,720 
 
 Xs 
 
 1,273 
 
 -.0117 
 
 -.1704** 
 
 -217 
 
 X4 
 
 5,003 
 
 .0909 
 
 .3368** 
 
 1,685 
 
 Xb 
 
 2,608 
 
 .3017** 
 
 2.1446** 
 
 5,593 
 
 Xe 
 
 1,010 
 
 .0288 
 
 .5286 
 
 534 
 
 Sum 
 
 
 .9993 
 
 
 18,521 
 
 1959 
 
 N = 194 
 
 R2 = .9053 
 
 
 
 Y 
 
 $ 22,094 
 
 
 
 
 Xi 
 
 135,973 
 
 .2444** 
 
 $ .0397 
 
 $ 5,398 
 
 X2 
 
 3,740 
 
 .2145** 
 
 1.2672 
 
 4,739 
 
 Xs 
 
 1,716 
 
 -.0114 
 
 -.1468** 
 
 -252 
 
 X4 
 
 6,242 
 
 .2723** 
 
 .9638 
 
 6,016 
 
 X6 
 
 3,200 
 
 .2317** 
 
 1.5997** 
 
 5,119 
 
 Xe 
 
 1,137 
 
 .1205** 
 
 2.3415** 
 
 2,662 
 
 Sum 
 
 
 1.0720* 
 
 
 23,682 
 
 * Null hypothesis rejected at the 0.05 level of probability. The null hypotheses are: (1) 
 
 6 
 
 0, where i = 1 to 6; (2) 2 bi = 1; and (3) mvpi = $1, where i = 2 to 6. 
 i-i 
 
 * Null hypothesis rejected at the 0.01 level of probability. 
 
32 
 
 Bulletin No. 720 
 
 [August J 
 
 Appendix Table 4. — Estimated Factor Productivities and Factor Shares 
 on Illinois Hog Farms, 1949, 1954, and 1959 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1949 
 
 N = 151 
 
 R2 = .8354 
 
 
 
 Y 
 
 $16,515 
 
 
 
 
 Xi 
 
 41,362 
 
 .2528** 
 
 $ .1009 
 
 $ 4,174 
 
 X2 
 
 3,231 
 
 .1174 
 
 .6001 
 
 1,939 
 
 X3 
 
 1,364 
 
 .0162 
 
 .1961t 
 
 267 
 
 X4 
 
 3,451 
 
 .1818** 
 
 .8700 
 
 3,002 
 
 X5 
 
 392 
 
 .0346 
 
 1.4577 
 
 571 
 
 Xe 
 
 1,483 
 
 .4557** 
 
 5.0748** 
 
 7,526 
 
 Sum 
 
 
 1.0585 
 
 
 17,479 
 
 1954 
 
 N = 150 
 
 R2 = .8937 
 
 
 
 Y 
 
 $18,033 
 
 
 
 
 Xi 
 
 67,207 
 
 .4174** 
 
 $ .1120 
 
 $ 7,527 
 
 X2 
 
 3,556 
 
 .1117* 
 
 .5664 
 
 2,014 
 
 X3 
 
 1,912 
 
 -.0404 
 
 -.3810** 
 
 -728 
 
 X4 
 
 4,887 
 
 .1780** 
 
 .6568 
 
 3,210 
 
 Xs 
 
 1,542 
 
 .1230** 
 
 1.4384 
 
 2,218 
 
 Xe 
 
 2,129 
 
 .3194** 
 
 2.7054** 
 
 5,760 
 
 Sum 
 
 
 1.1091** 
 
 
 20,001 
 
 1959 
 
 N = 162 
 
 R2 = .8517 
 
 
 
 Y 
 
 $19,834 
 
 
 
 
 Xi 
 
 83,660 
 
 .2816** 
 
 $ .0668 
 
 $ 5,588 
 
 X2 
 
 3,777 
 
 .1201* 
 
 .6307 
 
 2,382 
 
 X3 
 
 2,274 
 
 .0395 
 
 .3445** 
 
 783 
 
 X4 
 
 5,784 
 
 .1499* 
 
 .5140* 
 
 2,973 
 
 X5 
 
 1,614 
 
 .1187** 
 
 1.4587 
 
 2,354 
 
 Xe 
 
 2,427 
 
 .2894** 
 
 2.3650** 
 
 5,740 
 
 Sum 
 
 
 .9992 
 
 
 19,820 
 
 * Null hypothesis rejected at the 0.05 level of probability. The null hypotheses are the same 
 as in Appendix Table 3. 
 
 ** Null hypothesis rejected at the 0.01 level of probability. 
 t Null hypothesis rejected at the 0.10 level of probability. 
 
 Appendix Table 5. — Estimated Factor Productivities and Factor Shares 
 on Illinois Beef Farms, 1949, 1954, and 1959 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1949 
 
 N =64 
 
 R2 = .8395 
 
 
 
 Y 
 
 $23,825 
 
 
 
 
 Xi 
 
 57,467 
 
 .2723** 
 
 $ .1129 
 
 $ 6,488 
 
 X2 
 
 4,137 
 
 .1420 
 
 .8178 
 
 3,383 
 
 X3 
 
 2,000 
 
 .0716 
 
 .8529 
 
 1,706 
 
 X4 
 
 4,389 
 
 .1515t 
 
 .8224 
 
 3,610 
 
 X5 
 
 507 
 
 .0336 
 
 1.5789 
 
 801 
 
 Xe 
 
 2,283 
 
 .3894** 
 
 4.0637** 
 
 9,277 
 
 Sum 
 
 
 1.0604 
 
 
 25,264 
 
1966] 
 
 Resource Productivity and Income Distribution 
 
 33 
 
 Appendix Table 5. — Continued 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1954 
 
 N = 126 
 
 R2 = .7570 
 
 
 
 Y 
 
 $18,072 
 
 
 
 
 Xi 
 
 79,154 
 
 .3474** 
 
 $ .0793 
 
 $ 6,277 
 
 X2 
 
 3,837 
 
 .0432 
 
 .2035* 
 
 781 
 
 Xs 
 
 2,450 
 
 .0360 
 
 .2655* 
 
 650 
 
 X4 
 
 5,370 
 
 .2550* 
 
 .8582 
 
 4,609 
 
 X5 
 
 1,748 
 
 .0577 
 
 .5965 
 
 1,043 
 
 Xe 
 
 2,489 
 
 .3096** 
 
 2.2479t 
 
 5,595 
 
 Sum 
 
 
 1.0489 
 
 
 18,955 
 
 1959 
 
 N =99 
 
 R2 = .6951 
 
 
 
 Y 
 
 $ 24,458 
 
 
 
 
 Xi 
 
 113,706 
 
 .3834** 
 
 $ .0825 
 
 $ 9,377 
 
 X2 
 
 4,251 
 
 .1664 
 
 .9574 
 
 4,070 
 
 Xa 
 
 2,872 
 
 .0780 
 
 .6642 
 
 1,908 
 
 X4 
 
 6,812 
 
 .0456 
 
 .1637 
 
 1,115 
 
 X5 
 
 2,161 
 
 .2204** 
 
 2.4945t 
 
 5,391 
 
 Xe 
 
 3,500 
 
 .3451* 
 
 2.4116 
 
 8,440 
 
 Sum 
 
 
 1.2389* 
 
 
 30,301 
 
 * Null hypothesis rejected at the 0.05 level of probability. The null hypotheses are the same 
 in Appendix Table 3. 
 ** Null hypothesis rejected at the 0.01 level of probability, 
 t Null hypothesis rejected at the 0.10 level of probability. 
 
 Appendix Table 6. — Estimated Factor Productivities and Factor Shares 
 on Illinois Dairy Farms, 1954, and 1959 
 
 
 Geometric 
 
 Elasticity of 
 
 Marginal value 
 
 Marginal factor 
 
 
 mean 
 
 production, bi 
 
 product 
 
 share (Xi) (mvpi) 
 
 1954 
 
 N =87 
 
 R2 = .7729 
 
 
 
 Y 
 
 $ 9,633 
 
 
 
 
 Xi 
 
 27,183 
 
 2382** 
 
 S .0844 
 
 $ 2,294 
 
 X2 
 
 3,095 
 
 .3143** 
 
 .9782 
 
 3,028 
 
 X3 
 
 916 
 
 -.0055 
 
 -.0578t 
 
 -53 
 
 X4 
 
 3,604 
 
 .1496 
 
 . 3999* 
 
 1,441 
 
 Xs 
 
 1,368 
 
 .2466** 
 
 1.7365 
 
 2,376 
 
 Xe 
 
 861 
 
 .1976* 
 
 2.2108 
 
 1,903 
 
 Sum 
 
 
 1.1408 
 
 
 10,989 
 
 1959 
 
 N = 119 
 
 R2 = .8182 
 
 
 
 Y 
 
 $16,280 
 
 
 
 
 Xi 
 
 43,725 
 
 .2054** 
 
 $ .0765 
 
 $ 3,345 
 
 X2 
 
 3,955 
 
 .1804* 
 
 .7426 
 
 2,937 
 
 X3 
 
 1,486 
 
 .0888* 
 
 .0729 
 
 1,446 
 
 X4 
 
 5,544 
 
 .2674** 
 
 .7852 
 
 4,353 
 
 X6 
 
 1,589 
 
 .1182* 
 
 1.2110 
 
 1,924 
 
 Xe 
 
 1,463 
 
 .2169** 
 
 2.4136t 
 
 3,531 
 
 Sum 
 
 
 1.0771 
 
 
 17,536 
 
 * Null hypothesis rejected at the 0.05 level of probability, 
 in Appendix Table 3. 
 ** Null hypothesis rejected at the 0.01 level of probability, 
 t Null hypothesis rejected at the 0.10 level of probability. 
 
 The null hypotheses are the same 
 
34 
 
 Bulletin No. 720 
 
 [August y 
 
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1966] 
 
 Resource Productivity and Income Distribution 
 
 35 
 
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