UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN BOOKSTACKS Digitized by the Internet Archive in 2011 with funding from University of Illinois Urbana-Champaign http://www.archive.org/details/macroeconomicsof91164brem Faculty Working Paper 91-0164 330 B385 1991:164 COPY 2 The Macroeconomics of the Price Mechanism The Ubrarv o1 1^« MOV 1 b W Hans Brents Department of Ecotiftmics Lectures to Be Given at the Charles University of Prague Winter 1991/1992 Bureau of Economic and Business Research College of Commerce and Business Administration University of Illinois at L'rbana-Champaign BEBR FACGLPr' WORKING PAPER NO. 91-0164 College of Commerce and Business Administration University of Illinois at Grbana-Champaign September 1991 The Macroeconomics of the Price Mechanism Hans Brems Department of Economics University of Illinois 1 206 South Sixth Street Champaign, IL 61820 Sana Brema Leoturea on the Price Mechaniantj Char lea Univeraity of Prague Winter 1991/1992 MACROECONOMICS 4 PREFACE The price mechanism was not always part of macroeconomic theory. It found no room in seventeenth- century or early twentieth-century demand-side macroeconomics. It found ample room in mid-eighteenth and late twentieth-century supply-side macroeconomics . The present mini course will derive the repeated reversal of demand-side into supply-side macroeconomics as rigorously and as succinctly as possible. But supply-side macroeconomics was as static as demand- side macroeconomics had been. The closing chapters of the mini course will dynamize supply-side macroeconomics . Modem economic theory comes in mathematical form, and no other form will do. The minicourse confines itself to elementary algebra and calculus. A reader needing help will find some in our appendix. Chapters 1 and 3 are new. Chapter 2 is newly written but based on material published in chapter 15 of my Pioneering Economic Theory 1630-1980, A Mathematical Restatement , Baltimore: Johns Hopkins Uni- versity Press, 1986. University of Illinois, September 1991 Hod much modernist stuffs, gone wrong and turn- ed sour and sittyj is circulating in our system! J, M. Keynes, Ec. J. 56, 1946, p, 81 CONTENTS MACROECONOMICS 1. Statics: Keynesian and Modem Macro theory ■ 7 2. Dynamics: Neoclassical Growth 31 3. Dynamics: "New" Neoclassical Growth 44 Appendix: A Mathematical Reminder 79 Index 85 About the Author 104 CHAPTER 1 statics: keynesian and modern macrotheory Abstract Between the last half of the seventeenth century and the mid-eighteenth century macroeconomic theory reversed itself from a demand-side to a supply-side equilibrium. For good measure the reversal repeated itself in the last half of our own century. The paper will derive such a reversal as rigorously and as succinctly as possible. Explicit solutions will be found for the equilibrating variables of a demand-side as well as of a supply-side equilibrium. Sensitivities of solutions to policy instruments will be found eund compeared. 8 I. INTRODUCTION 1. Macroeconomics — The Oldest Part of Our Building Macroeconomics is the oldest part of our building: we have practiced it since the last half of the seventeenth century. Macroeconomics considers an economy producing a single good. Unemployment theory determines the physical output of that good, inflation theory determines its price. Let us take a closer look at their historical origins. 2 . Early Demand-Side Equilibria; Unemployment Theory The concern of the mercantilists was unemployment. Petty (1662 (1899: 30)] estimated it an ten percent and analyzed it within the framework of a demand-side equilibrium. Here physical output was seen as bounded by demand. Supply was no problem: demand would always create its own supply. There was always excess capacity. The rate of interest was determined by the demand for and the supply of money hence could be affected by the money supply. Petty thought that ample money had reduced the rate of interest to six percent. Yarranton [1677 (1854: 38)] believed that the use of paper money would reduce it to 9 four percent. Petty [1662 (1899: 29-31)] also recommended public works "of much labour, and little art." In short: monetary or fiscal policy could raise physical output and employment. Capitalism left to itself might be incapable of utilizing its own resources. Government action was the remedy. Within less than a century such a demand-side equilibrium was to reverse itself. 3. Early Supply-Side Equilibria: Inflation Theory Hume's concern was inflation, and he analyzed it within the frcimework of a supply-side equilibrium. Here physical output was seen as bounded by supply. Demand was no problem: supply would always create its own demand. There was never excess capacity. The rate of interest was determined by saving and investment. As a result, Hume [1752 (1875: 321-322)] and Turgot [1769-1770 (1922: 74-76)] agreed, doubling the money supply would not reduce the rate of interest. Hume realized that doubling the money supply of a not fully monetized economy could widen the scope for division of labor hence expand the goods supply. But doubling the money supply of a fully monetized economy, Hume [1752 (1875; 333)] insisted, would merely double prices. Monetary stimuli would simply generate inflation and fiscal stimuli simply 10 crowding-out. Capitalism was entirely capable of utilizing its own resources. Government action, however well meant , was the problem.^ 4. Purpose What interests us is the reversal — all the more so since it occurred twice in three centuries: it repeated itself in our own century. This time the demand-side equilibria of Keynes (1936) and Hansen (1941) reversed themselves into the supply-side equilibria of Friedman (1968), Lucas (1972), and Sargent (1973). Can we derive the reversal of a demand-side equilibrium, whether Mercantilist or Keynesian, into a supply-side equilibrium, whether vintage Hume or modern? The purpose of the present paper is to show how little it takes to do so — and to do it as rigorously and as succinctly as possible. We shall use the following notation. 5. Variables C s physical consumption D = demand for money E = excess demand in goods market I = physical investment L = labor employed 11 R = teuc revenue r = rate of interest w = money wage rate X = physical output Y = money national income y = money disposable income 6. Parameters A = autonomous consumption a = joint factor productivity a, 13 s exponents of a production function B = autonomous investment b = inducement to invest c s marginal propensity to consume F = available labor force f = inducement to hold speculative money G = physical government purchase of goods J = autonomous demand for money j = propensity to hold transaction money X = "natural" employment rate M = supply of money 12 S = physical capital stock T = tax rate The price P of goods will be a parsuneter in a demand-side equilibrium but a variable in a supply-side equilibrium. II. DEMAND-SIDE EQUILIBRIUM 1. Demand-Side Equilibrium; Solution A Keynes-Hansen demand-side equilibrium encompassed two markets, a goods market and a money market, and had two equilibrating variables, physical output and the rate of interest. There was no production function. Price was a parameter shutting off the price mechanism. The equilibrium was a partial one having neither enough markets nor enough equilibrating variables. We write it as follows. Ignore capital consumption allowances and define national income as the market value of physical output: Y • PX ( ^ ) 13 Let tax revenue bej R = TY (2) where < T < 1. Define disposable income as national income minus tax revenue: y • Y - R (3) Let consumption be a function of disposable real income: C = A ■«■ cy/P (*) where A > and < c < 1 . Let investment be a function of the rate of interest: I = B - br (5) where B > and b > 0. Let real demand for money be a function of the rate of interest as well as of physical output: 14 D/P = J - fl * jX (6) where J > 0, f > 0, and j > 0. Two equilibrating variables, i.e., physical output and the rate of interest will clear the goods and money markets: X = C -^ I -^ G (7) M=D (8) Solve the system (1) through (8) for physical output and the rate of interest: "~ y {A + B * G) f ■>■ h(M/P - J) /gv bj ^ [1 - c(l - T)]f _ {A -^ B * G)j - [1 - C(l - D] (M/P - J) MO) bj * [1 - c(l - T)]f 15 2. Demand-Side Equilibrium; Policy Conclusions How sensitive are our demand-side equilibria (9) and (10) to fiscal and monetary policy? Fiscal-policy instruments are government purchases G and the tajc rate T. So take the partial derivatives of (9) and (10) with respect to G: -^ = ^ > (11) dG bj + [1 - c(l - r)]f il = i > (12) dG bj + [1 - c(l - T)] f So if physical government purchase G is up, so is physical output (9) and the rate of interest (10). The higher rate of interest will discourage investment. Consequently there is some crowding-out. Next ta)ce the partial derivatives of (9) and (10) with respect to T. On the latter use (6) with (8) inserted: 16 i^ = £^ < (13) dT jbj + [1 - c(l - D]f ^ = S2JL < (14) dT bj + [1 - c(l - D]f So if the tax rate T is down, both physical output (9) and the rate of interest (10) are up. Again there is some crowding-out. The monetary-policy instrument is the money supply M. So take the partial derivatives of (9) and (10) with respect to M: dX _ b/P dM bj -^ [1 - c(l - T)]f > (15) dr ^ _ [1 - cil - T)]/P dM ~ bj * [1 - c{l - T)] f < (16) So if the money supply is up, physical output (9) is up but the rate of interest (10) is down. Now let us reverse our equilibrium. 17 III. SUPPLY-SIDE EQUILIBRIUM 1. The Natural Supply of Goods Modern supply-side equilibria added the missing market and the missing equilibrium variable. The missing market was the labor market. Here firms are demanding labor and are facing diminishing returns to it. Let their production function be of Cobb-Douglas form: X = aL'S^ (l'^) where 0 0. Purely competitive firms optimize employment by equating the real wage rate with the physical marginal productivity of labor: if = 1^ = aaL-^S^ (18) P dL Raise both sides to the power -1/B and find demand for labor 18 Facing such a demand function, how does labor respond? Friedman's answer (1968) was his "natural" rate of unemployment to which current labor-market literature adds institutional color: Lindbeck and Snower (1986) and Blanchard and Summers (1988) distinguish between "insiders," who are employed hence decision-making, and "outsiders," who are unemployed hence disenfranchised. Let insiders accept the "natural" employment rate X where < X < 1. In other words, if L > XF insiders . will insist on a higher real wage rate. If L=XF <20) they will be happy with the existing one. If L < XF they will settle for a lower one. The real wage rate insiders will be happy with, given their natural rate X of employment, might be called the "natural" one. Find it by inserting (20) into (18): ^ = aa{XF)-^S^ (21) P 19 At the frozen capital stock S, then, labor can have a R percent higher natural real wage rate by accepting a one percent lower natural rate X of employment. May the actual real wage rate differ from the "natural" one (6)? According to New Classicals like Lucas (1972), Sargent (1973), and Sargent-Wallace (1975), with rational expectations agents act as if they knew the structure of the model as well as any systematic monetary policy applied to it. Only random hence unanticipated variations of the money supply can generate deviations of actual from natural. For excimple let a random hence unanticipated expansion of the money supply encourage demand. Let goods prices respond more readily than does the money wage rate and let employers perceive the response sooner than does labor. At first, then, a real wage rate lower than (21) will be perceived by employers but not yet by labor. As a result, actual employment will exceed the natural one (20). Vice versa, let a random hence unanticipated contraction of the money supply discourage demand. At first, then, a real wage rate higher than (21) will be perceived by employers but not yet by labor. As a result, actual employment will fall short of the natural one (20). But, as Friedman (1968) insisted, eventually labor will perceive and respond: new rounds of collective bargaining will restore the equality between the actual and the natural real wage rate, hence the equality between the actual and the natural employment. Labor has no money illusion. 20 At the frozen capital stock S the supply of goods corresponding to the natural rate X of employment may be called the "natural" supplyc^ Find it by inserting (20) into (17): X = a{XF)'S^ (22) 2. Supply-Side Equilibrium; Solution At this point do we have an overdetermined system? We have two alternative physical outputs X. The first is the physical output (9) matching demand for it. The second is the most profitable physical output (22) at which the real wage rate matches the physical marginal productivity of labor. May the two differ? As long as price P remains frozen they may. If they do, there will be positive or negative excess demand defined as the differences between them: ^. {A^B^G)f*b(M/P-J) _3(;^^).50 (23) jbj + [1 - c(i - r)]f Now unfreeze price P, thus allowing excess demand to affect it: let a positive excess demand raise price and a negative excess demand lower it. But there is a feedback: price, in turn, will affect excess 21 demand o Excess demand (23) is a function of price P because demand (9) is, whereas supply (22) is not. Specifically, excess demand (23) is a declining function of price P. To see that it is, take the partial derivative -^ = - k Ji < (24) dp bj ■<■ [1 - c(l - T)]f p2 A higher price, then, will lower a positive excess demand and keep lowering it until it has vanished. A lower price will raise a negative excess demand and keep raising it until it has vanished. In short, there ought to be a price at which the market will clear. To find it set (23) equal to zero and solve for P: P = bM/H, where (25) H - a(A.F)«SP{i)j + [1 - c(l - D] f} - {A * B ^ G) f -^ bJ Corresponding to any value (25) of P there will be a corresponding value of the money wage rate w satisfying (21) and a corresponding value of the rate of interest found by inserting (25) into (10) and solving for r: 22 ^ ^ A * B * G - a(XF)«gP[l - c(l - D] (26) b Policy conclusions drawn from such supply-side equilibria will reverse the policy conclusions drawn from our demand-side equilibria (9) and (10). Let us draw them. 3. Supply-Side Equilibrium; Policy Conclusions How sensitive are the new supply-side equilibria (22), (25), and (26) to fiscal and monetary policy? Fiscal-policy instruments are government purchases G and the tax rate T. So take the partial derivatives of (22), (25), and (26) with respect to G: -^ = (27) dG #=f^>0 (28) dG H 23 ll = 1 > (29) dG b So if physical government purchase G is up, so is price (25) and the rate of interest (26), but physical output (22) is unaffected. The higher rate of interest will discourage investment — but more than it did in the demand-side equilibrium: since physical output (22) is unaffected in the supply-side equilibrium, investment must be down by as much as government purchase is up. The crowding-out is complete. Next take the partial derivatives of (22), (25), and (26) with respect to T: 1^ = (30) dT ^ . - cfX I < (31) dT H 1^ = - c ^ < (32) dT b So if the tax rate T is down, both price (25) and the rate of interest (26) are up, but physical output (22) is unaffected. 24 The monetary-policy instrument is the money supply M. So take the partial derivatives of (22), (25), and (26) with respect to M: 1^ = (33) dM 1^ = ^ > (34) dM H 1^ = (35) dM So if the money supply is up, price (25) is up in proportion, but physical output (22) and the rate of interest (26) are unaffected — as Hume (1752) had said they would be. 25 IV. SUMMARY AND CONCLUSION A demand-side equilibrium encompassed two markets, a goods market and a money market, and had two equilibrating variables, physical output and the rate of interest. There was no production function. Price was a parameter shutting off the price mechanism. At that price industry would always produce a physical output matching demand. There was unemployment simply because that demand was insufficient. We have seen such a demand-side equilibrium (9) as a partial one having neither enough markets nor enough equilibrating variables. A supply-side equilibrium adds the missing market, i.e., a labor market. Here firms demand labor and are facing diminishing returns to it. Consequently their demand for labor (19) is a function of the real wage rate. There is unemployment simply because that real wage rate is too high: facing the demand for labor (19), unions choose a natural rate of employment < A. < 1. The labor market doesn't clear! The natural rate X, in turn, determines a unique natural supply of goods (22). Such a supply-side equilibrium also adds the missing equilibrating variable, i.e., the price of goods. Resuming its place in macroeconomics, a price mechanism clears the goods market. Demand (9) 26 and natural supply (22) coincide, reversing both fiscal-policy and monetary-policy conclusions. In a demand-side equilibrium larger government purchases or a tax cut had raised physical output and the rate of interest: crowding-out was incomplete. In a supply-side equilibrium larger government purchases or a tax cut raise price and the rate of interest but leave physical output unaffected: crowding-out is complete. In a demand-side equilibrium a larger money supply raised physical output and lowered the rate of interest: there was crowding-in. As Hume had observed, in a supply-side equilibrium a larger money supply raises price proportionately but leaves physical output and the rate of interest unaffected: there is neither crowding-out nor crowding-in. Our supply-side equilibrium was as static as our demand-side equilibrium had been: nothing moved, capital stock remained frozen. To unfreeze capital stock we need a dynamic framework, and we begin with the simplest one we know, the original neoclassical growth model. J-HB.2-5 27 FOOTNOTES further documentation in Brems (1986: 19-24). ^Further documentation in Brems (1986: 33-37). ^Hume, to be sure, knew neither unions nor insiders. But if reflecting the equality sign of our < X < 1, i.e., full employment, eighteenth-century institutions would still generate a unique natural supply of goods (22). 28 REFERENCES Blanchard, Oli^Jer/ J., and Summers, Lawrence H., "Hysteresis and the .i European Unemployment Problem," in Cross, Rod (ed.)» Unemployment . Hysteresis and the Natural Rate Hypothesis , Oxford, 1988. Brems, Hans, Pioneering Economic Theory. 1630-1980 — A Mathematical Restatement , Baltimore, 1986. Friedman, Milton, "The Role of Monetary Policy," Amer. Econ. Rev. . March 1968, 58, 1-17. Hansen, Alvin H., Fiscal Policy and Business Cycles , New York, 1941. Hume, David, "Of Interest" and "Of the Balance of Trade," Political Discourses , Edinburgh, 1752, reprinted in Essays — Moral . Political, and Literary , I, London, 1875. 29 Keynes, John Maynard, The General Theory of Employment. Interest, and Money , London, 1936. Lindbeck, Assar, and Snower, Dennis J., "Wage Setting, Unemployment, and Insider-Outsider Relations," Amer. Econ. Rev« , May 1986, 76 , 235-239. Lucas, Robert E. , Jr., "Expectations and the Neutrality of Money," J. Econ. Theory . Apr. 1972, 4, 103-124. Petty, William, A Treatise of Taxes and Contributions . London, 1662; reprinted in C. H. Hull (ed.), The Economic Writings of Sir William Petty . Cambridge, 1899. Sargent, Thomas J., "Rational Expectations, the Real Rate of Interest, and the Natural Rate of Unemployment," Brookings Papers on Economic Activity , 1973, 429-472. Sargent, Thomas J., and Wallace, Neil, "'Rational' Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," J. Polit. Econ. . Apr. 1975, 83, 241-254. 30 Turgot, Anne Robert Jacques, "Reflexions sur la formation et la distribution des richesses, Ephemerides du citoven . Nov. 1769-Jan. 1770, reprinted in E. Daire (ed.), Oeuvres de Turgot , Paris, 1844, 1-71, translated as Reflections on the Formation and the Distribution of Riches , New York 1922. Translated again as "Reflections on the Formation and Distribution of Wealth," in P. D. Groenewegen, The Economics of A. R. J. Turgot . The Hague, 1977, 43-95. Yarranton, Andrew, England's Improvement by Sea and Land. To Outdo the Dutch without Fighting. To Pay Debts without Moneys. To Set at Work all the Poor of England with the Growth of Our Own Lands . . ., London, 1677; quoted from P. D. Dove, Account of Andrew Yarranton . Edinburgh, 1854. 31 Copyright Johns Hopkins University Press CHAPTER 2 DYNAMICS: NEOCLASSICAL GROWTH Abstract Supply-side macroeconomics was as static as demand-side macroeconomics had been. As an introduction to dynamics the present chapter will restate Solow's neoclassical growth model. Out of very few and simple assumptions the model derived a wealth of conclusions none of which was seriously at odds with historical reality: (1) stationary distributive shares , (2) convergence to steady-state growth of output, (3) identical steady-state growth rates of output and capital stock, (4) stationary rate of return to capital, and (5) identical steady-state growth rates of the real wage rate eufid labor productivity. 32 INTRODUCTION 1. Statics and Dynamics A static model determines the levels of its variables at a particular time. Its ec[uations contain variables referring to that time but no derivatives with respect to times no motion can occur. A dynamic system determines the time paths of its variables and contains derivatives with respect to time: it allows us to see the economy as what it is, i.e., a growing one. 2. The So low Model ^ Solow (1956) built the simplest possible model of growth. There was one good with two uses, consumption and investment. An immortal capital stock of that good was the result of accumulated savings under an autonomously given propensity to consume. Solow did not know that halfway through the Second World War Tinbergen [1942 (1959)] had published a similar model with econometric estimates of its parcuneters for four countries. But he had done it in German behind enemy lines. 33 II. THE SOLOW MODEL 1. Variables C = physical consumption g = proportionate rate of growth of variable v I 5 physical investment L = labor employed P = price of good S = physical capital stock a = physical marginal productivity of capital stock w = money wage rate X = physical output 2. Parameters a s joint factor productivity a = elasticity of physical output with respect to labor employed J3 = elasticity of physical output with respect to physical capital stock c = propensity to consume F = available labor force g^ = proportionate rate of growth of parameter v 34 The symbol t is time. All parameters are stationary except a and F whose growth rates are stationary » 3. Definitions Define the proportionate rate of growth of variable v as dlog.v cf ■ — 2- ^^ dt Define investment as 4. Goods-Market Clearance Equilibrium requires output to equal demand for it; (1) I'9sS (2) jsr = c + I <3) 35 5. Income and Product Accounting; Product Exhaustion Let entrepreneurs apply a Cobb-Douglas production function ' X = aL'S^ (4) where < a < 1; 0 0. Let profit maximization under pure competition equalize real wage rate and physical marginal productivity of labor: ^ = ^-.a^ (5) P dL L Define physical marginal productivity of capital stock as "■i'Pi '^' Multiply (5) by L and (6) by S, write real wage and profits bills, and find stationary distributive shares: 36 LvflP = aX (7) So = ^X , (8) Add (7) and (8) and find the slices adding up to the pie: Lw/P + Sa = X (5) Assume full employment: L = F (10) 6. Consumption Let consumption be C=cX (11) where < c < 1. 37 IIIc SOLUTIONS 1. Convergence to Steady-State Growth To solve the system, insert (10) into the production function (4), take the growth rate (1) of the latter, and find 9x = 9a * "■9f * ^9s <^2) Here, g and g, are parameters but g- a variable. Use (11), (3), (1), and (2) in that order to express it as gr^ = (1 - c)X/S (13) Take the rate of growth (1) of (13), use (12), and express the proportionate rate of acceleration of physical capital stock as 9gs = 9x - 9s = o-{9a/«- ^ 9f - 9s) <^^) In (14) there are three possibilities: if g^ > <3ja. + g^, then ggs < 0- i^ 38 9s = 9J0L ^ gp (15) then g g = 0. Finally, if g^ < g /a + q^, then g ^ > 0. Consequently, if greater than (15) g^ is falling; if ec[ual to (15) g- is stationary; and if less than (15) g^ is rising. We conclude that g_ must either equal (15) from the outset or, if it does not, converge to that value. Insert equation (15) into (12) and find the growth rate of physical output 9.= 9s <16) Take the rate of growth (1) of (6), use (16), and find the growth rate of the physical marginal productivity of capital stock (17) Take the rate of growth (1) of (5), use (10), (15), and (16), and find the growth rate of the real wage rate and of labor productivity 9w/P = 9x/L = 9a/ f^ <^®> 39 2. Twice the Propensity to Save; Twice the Capital Coefficient If the propensity to save 1 - c were twice as high, how would a neoclassical model adjust? Rearrange (13) and write it as S/X = (1 - c)/gs (13) where q^ stands for the solution (15). An economy otherwise equal but with twice the propensity to save 1 - c will at any time have twice the capital coefficient S/X. 3. The Real Wage Rate and the Wicksell Effect To solve for the real wage rate insert (4) into (5): w/P = aX/L = aa(5/L)P (1^) Rearrange (13) and divide it by L; S/L= (1 - c) {X/L)/gs (20) Insert (20) into (19) and find the solution for the real wage rate 40 t//P = aa^/«[(l - c)/gsf'* (21) Here is the Wicksell Effect. An economy otherwise equal but with twice the propensity to save 1 - c will, according to (21), have a 2^''" times higher real wage rate w/P. Wicksell himself [1901 (1934: 164)] expressed his effect: "The capitalist saver is, thus, fundamentally, the friend of IcUaour." 4. Conclusions The solutions of the neoclassical growth model possessed five important properties: (1) stationary distributive shares; (2) convergence to steady-state growth of output; (3) identical steady-state growth rates of output and capital stock; (4) a stationary rate of return to capital; and (5) identical steady-state growth rates of the real wage rate and labor productivity. Empirical work by Christensen, Cummings, and Jorgenson (1980), Denison (1967), (1974), Kendrick et al. (1976), Kravis (1959), Kuznets (1971), and Phelps Brown (1973) has found none of the five properties to be seriously at odds with historical reality. The present chapter has restated the bare bones of the neoclassical growth model. There was only one kind of capital, physical 41 capital: no knowledge capital , no human capital. There was no money, no government, hence no policy handles. Our last chapter will try to allow for such things. J-HB.5-15 42 REFERENCES L. R. Christensen, D. Cummings, and D. W. Jorgenson, "Economic Growth 1947-1973: An International Comparison," in J. W. Kendrick and Bo Nfo Vaccara (eds.)f New Developments in Productivity Measurement and Analysis . Chicago and London, 1980. E. F. Denison, Why Growth Rates Differ; Postwar Experience in Nine Western Countries , Washington, D.C., 1967. , Accounting for United States Economic Growth. 1929-1969 , Washington, D.C., 1974. J. W. Kendrick, assisted by Y. Lethem and J. Rowley, The Formation and Stocks of Total Capital , New York, 1976. I. B. Kravis, "Relative Income Shares in Fact and Theory," Amer. Econ. Rev. . Dec. 1959, 49, 917-949. 43 S. Kuznets, Economic Growth of Nations; Total Output and Production Structure , Cambridge, Mass., 1971. E. H. Phelps Brown, "Levels and Movements of Industrial Productivity and Real Wages Internationally Compared, 1860-1970," Econ. J. , Mar. 1973, 83/ 58-71. R. M. Solow, "A Contribution to the Theory of Economic Growth," Quart . J. Econ. . Feb. 1956, 70, 65-94. , Growth Theory — An Exposition , New York and Oxford, 1970. J. Tinbergen, "Zur Theorie der langfristigen Wirtschaftsentwicklung, " Weltw. Archiv , May 1942, 55, 511-549, translated in L. H. Klaassen, L. M. Koyck, and H. J. Witteveen (eds.), Jan Tinbergen , Selected Papers , Amsterdam 1959. K. Wicksell, Forelasninqar i nationalekonomi , I, Lund, 1901, translated as Lectures on Political Economy , I by E. Classen and edited by Lionel Robbins, London, 1934. 44 CHAPTER 3 dynamics: "new" neocussical growth Abstract An augmented Solow growth model has three forms of capital stock In it. First a human capital stock of accumulated flows of education. Second a knowledge capital stock of accumulated flows of R & D. Third a conventional capital stock of accumulated flows of physical investment. The paper solves such a model for its levels as well as for its growth rates and discusses the sensitivities of the solutions to monetary and fiscal policy. 45 INTRODUCTION The original Solow (1956) model had only two factors, labor and physical capital stock. Joint factor ("total factor" or "multif actor" ) productivity was growing, but its rate of growth was an unexplained residual. The model was a standing invitation to explain the residual. Recent literature accepted the invitation. Griliches (1973), (1979), (1988) and Lichtenberg-Siegel (1991) saw a knowledge capital stock of accumulated R&D. Its conceptual and econometric problems were discussed by Griliches (1979: 100). A capital stock of knowledge would be a stock of "results . . . embodied in people, blueprints, patents, books, and oral tradition." An aggregation of such items would be "quite presumptuous" but perhaps not be all that different from a stock of "'physical' capital which aggregates buildings, planes, computers, and shovels." Kendrick (1976) saw one-half of the 1969 U.S. capital stock as a human capital stock of accumulated 46 education. The most recent estimate of its productivity is Mankiw-Romer-Weil ( 1990 ) . Let a Solow model thus augmented produce a single good but make four alternative uses of it. The good may be consumed, it may be invested in knowledge or physical capital stock, or it may be purchased by government and via education be invested in human capital stock. Let's imagine strong cases: let all education be public; let all R&D and physical capital be private; and let all capital stocks be immortal. The purpose of the paper is to solve such a model for its levels as well as for its growth rates and to discuss the sensitivities of the solutions to the supplies of labor and saving and to monetary and fiscal policy. 47 II. THE MODEL 1. Variables A = capital coefficient of knowledge plus physical capital B = capital coefficient of hvunan capital b = tax base C = physical consumption D = demand for money < E = flow of education G = government purchase of goods g = proportionate rate of growth H = stock of human capital I = flow of physical investment J = flow of R & D investment K = stock of knowledge capital k s present gross worth of another unit of knowledge capital K = marginal productivity of knowledge capital stock L = labor employed 48 P = price of good R = tax revenue r = before-tax nominal rate of interest p = aftertax real rate of interest S = stock of physical capital 8 s present gross worth of another unit of physical capital o = marginal productivity of physical capital stock V = money salary rate w = money wage rate X = physical output y = disposable money income 2. Parameters a = joint factor productivity a, R, Y/ 5 = exponents of a Cobb-Douglas production function c = propensity to consume disposable real income F = available labor force f = fraction of government purchase allocated to education X = "natural" employment rate 49 M = supply of money m = reciprocal of the velocity of money n = number of firms in economy T = tax rate All parameters are stationary except a, F, and M whose growth rates are stationary. 3. Definitions Define the proportionate rate of growth of variable v as 9y dlog^v (1) dt Under immortal capital stocks, investment in education adds to human capital stock, investment in R & D adds to knowledge capital stock, and physical investment adds to conventional capital stock: 50 E ' g^ (2) J - g^ ( 3 ) I ' gsS (4) 4. Firm Output Regardless of its use let the single good be produced by n identical firms each applying the Cobb-Douglas function where a, R, y, and 5 are positive proper fractions summing to 1, where a is joint factor productivity, and where the subscript i refers to the ith firm. 51 5. Firm Demand for Labor Let labor be hired at the money wage rate w. The ith firm will maximize its aftertax profits by equating the real wage rate with the physical marginal productivity of labor hired: w/P = dX-/dL-. Differentiate, rearrange, and write firm demand for labor L^ = aXj{w/P) (6) 6. Firm Demand for Services of Human Capital Let services of human capital be hired at the money salary rate v. The ith firm will maximize its aftertax profits by equating the real salary rate with the physical marginal productivity of services hired: v/P = 3X-/3H-. Differentiate, rearrange, and write firm demand for services Hi = PA-i/(v/P) (7) 52 7. Firm Demand for Knowledge and Physical Capital Stocks The physical marginal productivities of knowledge and physical capital stocks are K. - i^ = Y :^ (8) •'■^''t, ''' Their marginal-value productivities will then be k-P and o.P, respectively. Such marginal-value productivities of immortal capital stocks will be marginal net returns taxed at rate T. Let nominal interest expense be tax-deductible, then money may be borrowed at an aftertax nominal rate of interest (1 - T)r. Discount future cash flows at that rate. Define present gross worths k- and s- of another unit of knowledge or physical capital 53 stock as the present worth at time t of all its future aftertax marginal-value productivities. k^ix) ■ /"(I - r)Kj(t)P(t)e-dt ;i(T) ■/*"(! - r)Oi(t)P(C)e-dt In (20) we shall see that k. and a- are stationary. But let price be growing at the rate g-: K^iC) = Ki(T) Oiit) = Oj (t) Pit) = P{x)e^''^''"'^ Insert these, define the aftertax real rate of interest as p - (1 - Dr - STp (10) 54 and take the integrals ki = (1 - T)KiP/p Si = (1 - Do^P/p Present net worth of another unit of capital stock is its present gross worth minus its price. In our one-good economy that price is P, so ki - P = [il - Dkj/p - 1]P Si - P = [(1 - Do^/p - l]P Optimal capital stock is the size of stock at which the present net worth of another unit is zero: (1 - T)K^ = p (11) 55 (1 - Do^ = p (12) To find that size insert (8) and (9) into (11) and (12), respectively, and find firm demand for knowledge and physical capital stock K^ = yil - T)Xi/p (13) Si = 6(1 - r)Xjp (14) 8. Agar eoat ion Dare we adopt "the analytically convenient setting of 'representative agent models'" criticized by Gordon (1990: 1136)? Let's do it. Facing the same factor prices our n firms will behave alike. Multiply their identical output (5) and factor demand (6), (7), (13), and (14) by n, define X = nX-, L = nL-, H = nH-, K = nK-, and S = nSj, and write aggregate physical output and factor demand: 56 X = aL'H^lCS'^ <^5) L = aX/(w/P) (16) H = ^X/ {v/P) (17) K = Yd - T)X/p (18) 5 = 5(1 - T)Jf/p (19) Use (15) to define aggregate physical marginal productivities dx X nXi K"^=Y — "Y = K, o - 1^ = ft ^ - fi i^ = a.. 57 so we may remove the i's from (11) and (12). From (18), (19), and (51) we see that so K, K., o, and o. are all stationary. 9. Unions Facing the aggregate demand for labor (16), how do unions respond? Friedman's answer (1968) was his "natural" rate of unemployment to which current labor-market literature adds institutional color by distinguishing between "insiders," who are employed hence decision-making, and "outsiders," who are unemployed hence disenfranchised. Let insiders accept the natural employment rate \ where < X < 1. The rate X is natural in the sense that if L > Xf insiders will insist on a higher real wage rate. If 58 L=XF (21) they will be happy with the existing one. If L < XF they will settle for a lower one. 10. Income and Product Account ing; Product Exhaustion With their i's removed insert (11) and (12) into (18) and (19), respectively, and write our factor demands (16) through (19) as distributive shares: Lw/P = aX (22) Hv/P = px (23) KK = yX (24) So = 6X (25) Add them and find the slices adding up to the pie: 59 Lw/P + Hv/P * Kk ^ So = X (26) 11. Government; An Inflationary Distortion Into (11) and (12) with their i's removed insert the definition (10). Insert the result into (26) and write aggregate physical output as Lw/P + Hv/P ^ {K ^ S)[i - gp/ {1 - T)] = X (27) The Internal Revenue Service will tax nominal income, so multiply (27) by P, and will tax the full nominal interest income (K + S)Pr. The tax base is then b ' Lw ^ Hv * (K -^ S) Pr = PX * {K -^ S) Pg^l (1 - T) ( 28 ) So the tax base will exceed the value PX of aggregate physical output. The excess (K + S)Pgp/(l - T) is an IRS inflationary distortion. Tax revenue is tax base times tax rate: 60 R = bT (29) where < T < 1. As a first approximation let government finance a deficit by increasing the money supply. The government budget constraint then collapses into GP - R = gJ4 ( 30 ) As another first approximation [Friedman (1959)] let the demand for money be in proportion to the value PX of aggregate physical output but be no function of the rate of interest: D = mPX (31) where m > 0. Let the money market clear: M=D (32) Into (30) insert (28), (29), (31), and (32) and see how the IRS inflationary distortion helps financing government purchase; 61 G = g,^ + rjf f (it: f S)gpT/(l - T) (33) Let the government allocate the fraction f to education: E^fG (34) Into (2) insert (34) and find human capital stock H= fG/g„ (35) 12 . Consumption Define aggregate disposable money income as y ' PX - R (36) Let consumption be the fraction c of disposable real income: C = cy/P (37) 62 where < c < 1. Into (37) insert (28), (29), and (36) and see how the IRS inflationary distortion discourages consumption: C = c[{l - T)X - (K ->■ S) gpT/ (1 - T) ] ( 38 ) 13. Goods-Market Clearance The single good of our one-good economy was consumed, purchased by government, or invested in physical or knowledge capital. Let the goods market clear: A-=C+G+J + J- (39) We may now solve our system for its levels as well as for its growth rates. 63 III. SOLUTIONS 1. Levels The goods market is cleared by the aftertax real rate of interest. Solve for it by inserting (3), (4), (18), (19), (20), (33), and (38) into (39) and dividing X away: p = (Y + 6) (1 - T) lA. where (40) (1 - c) (1 - D - g^ (1 - c)gpr/(l - T) + gr^ (41) What is the economic meaning of A? Insert (40) into (18) and ( 19 ) : 64 K= — X_ AX (42) Y + * AX (43) Y + 6 K * S = AX (44) So A is simply the capital coefficient of knowledge plus physical capital. Insert (44) and (33) into (35): H = BX, where (45) B - f[g^ + r + AgpT/ {1 - T) ]/g„ (46) So B is simply the capital coefficient of human capital. Finally insert (21), (42), (43), and (45) into (15) and solve for aggregate physical output 65 X= a^/^FJ-^-^p/— ^pA/«BP/- (47) Let the market for services of human capital be clearing at whatever human capital stock has accumulated. Then solve for the real salary rate by inserting (45) into (17): v/P = p/B (48) Solve for the real wage rate by inserting (21) and (47) into (16): ^ = aa^'-i Y .r^'/ ^ j'^"^(Y-a)/«B(»/. (49) Solve for price by inserting (31) into (32) P = M/ (mX) (50) 66 2. Steady-State Growth All parameters were said to be stationary except a, F, and M whose growth rates were stationary. In that case differentiate the natural logarithms of our levels (40), (42), (43), (45), (47), (48), (49), and (50) with respect to time and find their steady-state rates of growth: g, = (51) 9h = 9k = 9s ^ 9x = 9al^ * 9f <^2) g./P=0 (53) 9./p = 9joi <54) 9p = 9s - {9a/ «■ * 9p) <55) 67 3. Growth Accounting Has our augmented Solow model explained or at least reduced Solow's unexplained residual? Let's compare the growth accounting of an original and an augmented Solow model. For that we need estimates of a, R, y, and 6. Griliches (1988: 14-15) used a production function whose inputs were labor, knowledge capital stock, and physical capital stock. He summarized findings by himself and others by saying that "the estimated elasticity of output with respect to R & D capital tends to lie between .06 and 0.1." Let's use y = 1/12. Mankiw-Romer-Weil (1990) used a production function whose inputs were labor, human capital stock, and physical capital stock. Exponents of each input of 1/3 were "consistent with our empirical results." Let's use a=R=y+5= 1/3, implying 5 = 1/4. We summarize: a = 1/3 13 = 1/3 Y = 1/12 5 = 1/4 68 Now for our comparison. Collapse our augmented four-factor Solow model into the original two-factor model by classifying human capital as part of labor and knowledge capital as part of capital. Such classification will give us a production function X = aL" * ^S^ * * hence a growth account g^^ = g + (a + fl)g, + (Y ■•■ 5)g_. Let g, = 0.01. Then a residual growth rate g = 0.0133... will make output grow at the same rate as capital stock, i.e., g^. = g_ = 0.03. Of that rate, residual growth g^ is 44 percent. By contrast, the augmented four-factor Solow model has a production function X = aL**H®K^S* hence a growth account gj^ = g^ + ag, + Rg^^ + vg^ "•■ 5g-. Now a residual growth rate g = 0.0066... will, in accordance with (52), make output grow at the same rate as all capital stock, i.e., g^^ = g^^ = gj^ = g^ = 0.03. Of that rate, residual growth g is merely 22 percent. The residual has been cut in half! But with its new a and g our four-factor model still yields the same rate of growth (54) of the real wage rate: ^H/P ~ 0*02 — found by Phelps Brown (1972). 69 IV. SENSITIVITIES OF LEVELS 1. Sensitivities to the Supply of Labor Measure the supply of labor by the natural rate of employment < X < 1. Are our levels sensitive to it? Specifically, does labor or anybody else benefit from lowering it? At the frozen capital stock of a Sargent-Wallace (1975) model labor could have a higher real wage rate at a lower natural rate X of employment. But our unfrozen capital stocks (42), (43), and (45) are all in direct proportion to physical output (47) hence to X. A lower X, then, simply reduces the economy to a lower scale at which factor proportions remain the same. The real wage rate depends upon factor proportions hence remains the same: the natural rate X is absent from the solution (49). So labor doesn't benefit from the lower X; nobody benefits. The economy is simply accumulating proportionately less capital stock and producing proportionately less output. The economy is impoverishing itself. 70 2. Sensitivities to the Supply of Saving Measure the supply of saving by the propensity 1 - c to save disposable real income. Are our levels sensitive to it? The clue is the capital coefficient A of knowledge plus physical capital. To see that dh/d{l - c) > write (41) as gpT/ a - T) * g^/d - c) Here if 1 - c is up, numerator is up, denominator down, and A up. As a result (40), (48), and (50) are down: the aftertax real rate of interest p, the real salary rate v/P, and price P are down. But (42), (43), (45), (46), (47), and (49) are up: all capital stocks K, S, and H, physical output X, and the real wage rate w/P are up. There is a Wicksell Effect 1 71 3. Sensitivities to Monetary and Fiscal Policy Our monetary-policy instrument is the rate of growth g^^ of the money supply. Our fiscal-policy instrument is the tax rate T. Are our levels sensitive to such instruments? The clues are the capital coefficients A and B. In (41) with (55) inserted dA/dg^^ < 0: if g^^ is up, numerator is down, denominator is up, and A down. dA/dl < 0: if T is up, again numerator is down, denominator up, and A down. A was the capital coefficient of knowledge plus physical capital, both assumed to be private. In short: the "private" capital coefficient is always down if g^^ or T is up. In (46) the signs of dE/dq^^ and dB/dl are not unequivocal. But our appendix finds them to be positive in realistic ranges of g^ and T. B was the capital coefficient of human capital, and all education was assumed to be public. In short: in realistic ranges the "public" capital coefficient is up if g^ or T is up. Such crowding-out is accomplished via an interest mechanism. Write (40) as 72 ^ '^ 1 - c - g^/{\ - T) and see that if g^^ or T is up, numerator is up, denominator down, and p up. Private knowledge and physical capital is being crowded out because its cost p is up. May such crowding-out be complete? It may. If g^ or T is up far enough to make (41) reach zero, (40) becomes undefined but has the limit limp = oo A ^ This is Tobin's (1986) "debacle." Allocation of physical output cunong capital stocks, then, was sensitive to monetary and fiscal policy. Is the size of physical output also sensitive? The elasticity of physical output (47) with respect to A is (y + 5) /a and with respect to B Si/a. Both capital coefficients A and B are sensitive to g^^ and T. So 73 allocation as well as size of physical output are sensitive to g„ or T. We have come a long way since Sargent -Wallace (1975) policy irrelevance. Their capital stock was frozen. Ours — in all three of its forms — is variable. J-HB.4-15 74 APPENDIX The partial derivative of (41) with respect to g^. is dA ^ _ m * A{1 - c)r/(l - T) dg^ (1 - c)gpT/{l - T) * g^ (56) which is always negative. Use it to find the partial derivative of (46) with respect to g„: dB ^9m = f m Ags - gp^ 1 - T (1 - c)gpT/{l - T) ■<■ gs I9h (57) which is easily positive for realistic values of A, g^, gp, and m. Only when g^ becomes very large, hence A very small, will (57) turn negative. In a realistic range, then, B is up if <^^ is up. 75 The partial derivative of (41) with respect to T is dA dT (1 - c) 1 + Agp/ (1 - T) (1 - c)gpT/ n - T) * gs (58) which is always negative. Use it to find the partial derivative of (46) with respect to T: dB dT = f 1 + gp Ag^/ il - T) - (1 - c) T 1 - T (1 - c)gpT/{l - T) * gs /9„ (59) which is easily positive for realistic values of A, g^, 1 - c, and T. Only when T becomes very large, hence A very small, will (59) turn negative. In a realistic range, then, B is up if T is up. 76 REFERENCES Friedman, Milton, "The Demand for Money: Some Theoretical and Empirical Results," J. Polit. Econ. , Aug. 1959, 67, 327-351, , "The Role of Monetary Policy, " Amer. Econ. Rev. , Mar. 1968, 58, 1-17. Gordon, Robert J., "What Is New-Keynesian Economics?" J. Econ. Lit. . Sep. 1990, 28, 1115-1171. Griliches, Zvi, "Research Expenditures and Growth Accounting," in Willieims, B. R. (ed. ) Science and Technology in Economic Growth , London: MacMillan, 1973; reprinted in Griliches, Zvi, Technology. Education, and Productivity , Oxford: Blackwell, 1988. 77 ., "Issues in Assessing the Contribution of Research and Development to Productivity Growth," Bell Jour. Econ. . Spring 1979, 10, 92-116. , "Productivity Puzzles and R&D: Another Nonexplanation, " Jour. Econ. Perspectives , Fall 1988, 2, 9-21. Kendrick, John W. , The Formation and Stocks of Total Capital , New York: Columbia, 1976. Lichtenberg, Frank R. , and Siegel, Donald, "The Impact of R & D Investment on Productivity — New Evidence Using Linked R & D-LRD Data," Econ. Inquiry , April 1991, 29, 203-228. Mankiw, N. Gregory, Romer, David, and Well, David N. , "A Contribution to the Empirics of Economic Growth," 1990, Quart. J. Econ. . forthcoming. 78 Phelps Brown, E. H., "Levels and Movements of Industrial Productivity and Real Wages Internationally Compared, 1860-1970," Econ. J. . Mar. 1973, 83, 58-71, Sargent, Thomas J., and Wallace, Neil, "'Rational' Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," J. Polit. Econ. . Apr. 1975, 83, 241-254. Solow, Robert M. , "A Contribution to the Theory of Economic Growth," Quart. J. Econ. . Feb. 1956, 20/ 65-94. Tobin, JcUT^es, "The Monetary-Fiscal Mix: Long-Run Implications," Amer. Econ. Rev. . May 1986, 76, 213-218. 79 APPENDIX: A MATHEMATICAL REMINDER 80 A MATHEMATICAL REMINDER Let a and C be constants, u, v, x, and y variables, f and (j) functional forms, t time, and e Euler's number, the base of natu- ral logarithms. 1. Rules of Differentiation df(u) df(u) du Chain Rule: dx du dx da Constant Rule: — = dx de Euler s Rule: = ae dx du Inverse Rule: dx dx/du dx , Power Rule: = ax dx 81 Product Rule: d(uv) dv du = u — + V — dx dx dx Proportion Rule: d(ax) dx = a Quotient Rule: d(u/v) v(du/dx) - u(dv/dx) dx Sum or Difference Rule: i(u ± v) du dv dx dx dx 2. Rule of Integration The indefinite integral /f(x)dx of the integrand f(x) will equal 4)(x) + C, where C is the constant of integration, if d<|)(x) dx = f(x) From Euler's Rule of differentiation it then follows that 82 ax e /e^dx = — + C 3. Partial Derivatives Consider a function of more than one variable, say, u = f(x, y) The partial derivatives of that function are 8u du — H — treating y as a constant 9x dx 8u du — E — treating x as a constant dy dy 4. The Total Differential For increments dx and dy the total differential of u = f(x, y) is 3u 3u du = — dx + — dy 3x 3y 83 5. Natural Logarithms and Rates of Growth X V Let u = e and v = e , then their natural logarithms are log u = x e and log V = y. To such natural logarithms the following rules apply: Power Rule: u = (e ) = e , hence log (u ) = alog u e e XV X "^ V Product Rule: uv = e e = e -^ , hence log (uv) = log u + log v e e e X V X "■ V Quotient Rule: u/v = e /e = e , hence log (u/v) = log u - log v We have defined the rate of growth g of a variable as the derivative of its natural logarithm with respect to time. Consequently dlog (u ) dlog u _ e e _ g a. = = a = ag ^" > dt dt ^ dlog (uv) dlog u dlog V _ ^e _ ^e °e _ ^<-> ^ dt ° dt dt ^*" '- dlog (u/v) dlog u dlog V 84 In English: the rate of growth of a power of a variable is the ex- ponent times the rate of growth of that variable. The rate of growth of a product is the sum of the rates of growth of its factors. The rate of growth of a quotient is the difference between the rates of growth of its numerator and its denominator. 85 INDEX MACROECONOMICS 86 INDEX MACROECONOMICS Accounting Growth, 67 Income and product, 35-36, 58-59 Aftertax real rate of interest, 53, 63, 70, 72 Aggregation, 55«-57 Allocation of output among capital stocks, 71-72 Augmented Solow model, 45-75 Blanchard-Summers, 18 87 Brems, 27 Budget constraint, government, 60 Capital coefficients, 64, 71-72 human, 45-46, 49-50, 51, 61, 64, 65, 67, 71 immortal , 32, 46, 49, 52 knowledge, 45-46, 49-50, 52-55, 64, 67, 71 physical 45-46, 49-50, 52-55, 64, 67, 71 Capitalism utilizing own resources capable of, 10 incapable of, 9 Christensen, Cummings, and Jorgensen, 40 Cobb-Douglas form, 17, 35, 50 88 Collective bargaining, 19 Competition, pure, 17, 35, 51 Constant returns to scale, 69 Consumption function, 13, 36, 61-62 Convergence of growth rates, 37-38 Crowding-out, 9-10, 15, 16, 23, 71-72 Debacle, Tobin's, 72 Deficit, 60 Demand creating its own supply, 8 for knowledge and physical capital stock, 55-56 89 for labor, 17-18, 35, 51, 56 for money, 13, 14, 60 for services of human capital, 51, 56 Demand-side equilibria, 8-9, 12-16 Den i son, 40 Deviation of actual from natural , 19 Differentiation, 80-82 Diminishing returns, 17 Discounting future cash flows, 52-55 Disposable income, 13, 61 Distributive shares, 35-36, 40, 58 Dynamics, 32 90 Education, 46, 49-50. 61 Employment. See Natural rate of employment Equilibrium. See Market clearing Excess capacity, 8, 9 demand, 20-21 Factor prices, 39-40, 63, 65 use, 51-55, 55-56 Fiscal policy in demand-side equilibrium, 15-16 "new" neoclassical growth, 71-73 supply-side equilibrium, 22-23 91 Friedman, 10, 18-19, 57, 60 Future cash flow, 52-55 Gordon, R. J. , 55 Government budget constraint, 60 purchases as a parameter, 15, 22-23 purchases as a variable, 60-61 Griliches, 45, 67 Growth accounting. See Accounting rates, 37-38, 66 92 Hansen, 10, 12 Human capital. See Capital Human capital services demand for, 51, 56 supply of, 65 Hume, 9, 24, 27 Immortal capital stock, 32, 46, 49, 52 Immunity of physical output to public policy, 22-24, 26, 73 Income and product accounting. See Accounting distribution, 35-36, 40, 58 national , 12, 35, 58 93 Inflation, 9, 66 Inflationary distortion, 59, 60, 62 Insiders, 18, 57 Integration, 81-82 Investment, 13, 34, 49-50 Joint factor productivity, 33, 45, 50. See also Residual growth rate Kendrick, 40, 45 Keynes, 10, 12 Knowledge capital . See Capital 94 Kravis, 40 Kuznets, 40 Labor demand for, 17-18, 35, 51, 56 market doesn't clear, 18, 25, 57, 69 supply of, 18, 57-58, 69 unions, 18-19, 25, 57, 69 Levels, solutions for, 63-65 Lichtenberg-Siegel , 45 Lindbeck-Snower, 18 Logarithms, natural, 83-84 95 Lucas, 10, 19 Macroeconomics, 8 Mankiw-Romer-Weil , 46, 67 Marginal productivity. See Physical marginal productivity Market clearing, 14, 21, 34, 60, 62 Maximization of present net worth, 52-55 profits, 17, 35, 51 Mercantilists, 8-9 Monetary policy in demand-side equilibrium, 16 "new" neoclassical growth, 71-73 96 supply-side equilibrium, 24 Money demand for, 13, 14, 60 illusion, 19 supply of, 14, 60 Multi factor productivity. See Joint factor productivity National income, 12, 35, 58 Natural logarithms, 83-84 rate of employment, 18-19, 57-58, 69 real wage rate, 18 supply of goods, 20 Neoclassical theory of growth, 31-41, 44-75 97 New Classicals, 19 'New" neoclassical growth, 44-75 Nominal rate of interest, 52, 59 Optimized employment, 17-18, 35, 51, 56 knowledge and physical capital stock, 55-56 services of human capital, 51, 56 Outsiders, 18, 57 Partial derivative, 82 equilibrium, 12, 25 98 Petty, 8-9 Phelps Brown, 40, 68 Physical capital. See Capital Physical marginal productivity of capital stocks, 35, 52, 56 labor, 17, 35, 51 services of human capital, 51 Present gross worth, 52-54 net worth, 52-55 Price as equilibrating variable, 20-21, 65 mechanism. See Price as equilibrating variable of factors. See Factor prices "Private" capital coefficient, 71 99 Product exhaustion, 35-36, 58-59 Production function, 17, 35, 50 Profit maximization, 17, 35, 51 "Public" capital coefficient, 71 Pure competition, 17, 35, 51 R&D, 45, 46, 49-50 Random variation of money supply, 19 Rate of growth, 37-38, 66 interest, aftertax real, 53, 63 interest, nominal, 52, 59 unemployment. See Natural rate of employment 100 Rational expectations, 19 Real rate of interest, aftertax, 53, 63 salary rate, 65 wage rate, 18, 39-40, 65, 69 Representative-agent models, 55 Research and development. See R&D Residual growth rate, 45, 67-68. See also Joint factor productivity Sargent, 10, 19 Sargent-Wallace, 19, 69, 73 Scale. See Constant returns to scale 101 Sensitivities of levels to monetary and fiscal policy, 71-73 supply of labor, 69 supply of saving, 70 Slices adding up to pie, 35-36, 58-59 Solow, 31-41, 45, 46, 68 Solutions for capital coefficients, 64, 71-72 demand-side equilibrium, 14 distributive shares, 35-36, 40, 58 growth rates, 37-38, 66 levels, 63-65 physical output, 65 price, 65 rate of inflation, 66 rate of interest, aftertax real, 53, 63, 70, 72 real salary rate, 65 102 real wage rate, 18, 39-40, 65, 69 supply-side equilibrium, 20-22 Statics, 32 Supply creating its own demand, 9 of goods. See Natural supply of goods of labor, 18, 57-58, 69 of money, 14, 60 of saving, 70 of services of human capital , 65 Supply-side equilibria, 9-10, 17-24 Tax base, 59-60 function, 13, 59-60 103 Tinbergen, 32 Tobin, 72 Total differential, 82 Total factor productivity. See Joint factor productivity Unemployment, causes of, 25 Unions, 18-19, 25, 57-58, 69 Wicksell, 40, 70 Yarranton, 8-9 104 ABOUT THE AUTHOR Hans Brems is professor emeritus of economics at the University of Illinois. Danish-born, he was naturalized in 1958. He has taught at Copenhagen and Berkeley and, as a visiting professor, at Basle, Copenhagen, Gothenburg, Gottingen, Hamburg, Kiel, Lund, Stockholm, Uppsala, and Zurich. He has testified before the Joint Economic Committee of the U.S. Congress. He is a foreign member of the Royal Danish Academy of Sciences and Letters and of the Finnish Society of Sciences. His books include: Product Equilibrium under Monopolistic Competition , Harvard, 1951 Output, Employment, Capital, and Growth , Harper, 1959; Greenwood, Quantitative Economic Theory , Wiley, 1968 Labor, Capital, and Growth, D. C. Heath, 1973 Inflation, Interest, and Growth , D. C. Heath, 1980 Dynamische Makrotheorie, J. C. B. Mohr (Paul Siebeck) , 1980 Fiscal Theory, D. C. Heath, 1983 Pioneering Economic Theory 1630-1980 , Johns Hopkins, 1986 105 END HECKMAN BINDERY INC. JUN95 L , T p\.^ N.MANCHESTER, i„u<.J.T^-PUa>^ INDIANA 46952