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Optimal Fiscal and Monetary Policy, and Economic Growth Optimal Fiscal and Monetary Policy and Economic Growth Author(s): Duncan K. Foley, Karl Shell and Miguel Sidrauski Source: Journal of Political Economy, Vol. 77, No. 4, Part 2: Symposium on the Theory of Economic Growth (Jul. - Aug., 1969), pp. 698-719 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1829327 Accessed: 21-05-2015 18:36 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of Political Economy. http://www.jstor.org This content downloaded from 132.236.27.111 on Thu, 21 May 2015 18:36:03 UTC All use subject to JSTOR Terms and Conditions Optimal Fiscal and Monetary Policy and Economic Growth Duncan K. Foley,Karl Shell, and Miguel Sidrauski MassachusettsInstitute of Technology 1. Introduction Therehave been two broad strategicapproaches to the studyof economic growth.The first,exemplified by Solow's paper(1956), attemptsto explain how an enterpriseeconomy will grow, given its technology and the market behaviorof its consumers.The second approach,exemplified by Ramsey (1928), attemptsto determinean optimaldevelopment strategy for a fully plannedeconomy, given its technologicalconstraints. These approachesfail to capturea centralpolicy problem of a modern mixed'"economy in whichthe governmentcan influenceinvestment and saving,but only indirectly, by manipulatingcertain basic variableslike the deficitand the moneysupply. Our paper representsan attemptto begin the analysisof thisproblem.1 The veryterm "mixed economy" impliesthat there are two centersof decision makingand that the preferencesof the consumersand of the governmentare distinguishable.2It is notat all clearwhere the preferences of the governmentcome from,or even whethergovernments have con- sistentpreferences of the kindwe willtalk about. But a constanttheme of policyliterature is thatgovernment intervention in theeconomy is effective and can be judged as good or bad forthe economy without direct reference to consumerpreferences. This is particularlytrue of policyprescriptions for economic growth.It seems to us that postulatinga social welfare We are indebted to Peter A. Diamond, Edmund S. Phelps, Robert M. Solow, and James Tobin for their helpful comments. Shell gratefullyacknowledges the support of the Ford Foundation Faculty Research Fellowship program. 1 In a very simple dynamic model, Nelson (1966) studied the monetaryand fiscal policies consistent with full employment. Using a differentmodel, Phelps (1965a) has studied the effectsof differentmonetary and fiscal policies on the level of invest- ment and the rate of inflation. 2 This distinctionbetween consumer behavior and governmentpreferences is basic to Arrow's work on social investmentcriteria (see Arrow, 1966). 698 This content downloaded from 132.236.27.111 on Thu, 21 May 2015 18:36:03 UTC All use subject to JSTOR Terms and Conditions FISCAL AND MONETARY POLICY 699 functionalfor the governmentis the best way to make rigorousthe pre- scriptionof governmentcontrol in the mixedeconomy. We considera model of a marketeconomy with two producedcom- modities-consumptiongoods and investmentgoods--and threeassets- money,bonds, and capital. From the usual two-sectorproduction model we derivedemands for the productive services of capital and labor,which are suppliedinelastically at any moment,and supplyflows of consumption and investmentgoods, whichdepend onlyon factorendowments and the consumptionprice of capital. We assumethat the demand for consumption is proportionalto netdisposable income which includes government taxes and transfers,made in a lump-sumfashion. Given the consumption-goods priceof capital and the nominalvalue of net governmenttransfers, equi- libriumin the marketfor consumptiongoods can be achieved only at some equilibriumconsumption-goods price of money. Given the consumption-goodsprice of money,the marketsfor stocks determineprices and ratesof returnfor three assets: money,bonds, and capital. We do not attemptto derivedemand functionsfor assets from individualmaximizing behavior, but we believeour formulationis fairly general.Since the marketsfor assets and consumptiongoods mustequili- brate simultaneously,the consumption-goodsprice of capital, the con- sumption-goodsprice of money,and the bond interestrate are jointly determinedin these markets.The price of capital is of particularimpor- tance because it determinesthe flow of outputs of consumptionand investmentgoods. Producersnote the going price of capital, and they supplyas much new investmentas is profitablefor themat that price. The new capital findsa place in portfoliosthrough the accumulationof savingsand, if necessary,through a changein theprice and rateof return to all capital,old and new. The governmenthas alreadyappeared twice. First, its deficitappears as transferincome and influencesthe demand for consumptiongoods. Second, thegovernment can changethe relativesupplies of its own bonds and moneyto theasset marketby makingopen-market purchases or sales. Changes of this kind will affectthe equilibriumprice of capital and will, therefore,affect the economy'sgrowth path. We assumethe government has two goals: maximizationof the integral of discountedutility of per capita consumptionand the managementof aggregatedemand to achieve a stable consumerprice level. We describe the optimal growthpath for consumptionand investmentwhich, for a given welfarefunctional, depends only on the technologyand initial capital-laborratio, since under our assumptionsthese two factsare the only bindingconstraints on possible paths. To achieve this path while maintainingstable consumerprices, the governmentmust manipulate its deficitand open-marketpolicy to induce the privatesector to produce investmentgoods at theoptimal rate at each instant. This content downloaded from 132.236.27.111 on Thu, 21 May 2015 18:36:03 UTC All use subject to JSTOR Terms and Conditions 700 JOURNAL OF POLITICAL ECONOMY If we comparethis model with the conventional optimal growth model, we see thatthe privateasset demandsand consumptionbehavior are like additionalconstraints from the government's point of view.They are facts withwhich the government must operate in orderto achieveits goals. Optimalityimplies a specificpath for the governmentpolicy variables -particularlythe deficit(and thusthe stockof governmentdebt) and the compositionof thedebt. The mixedeconomy with optimal monetary and fiscalpolicy tends to a unique capital-laborratio and a unique per capita governmentindebtedness which are independentof initialendowments. For the special case in whichthe instantaneousutility function of per capita consumptionhas constant marginal utility,we show that the deficitincreases with the capital stockalong the optimalpath. We are also able to establishpropositions concerning the relationbe- tweenlong-run optimal values forthe per capita capital stockand the per capita debtfor economies which have differentsocial ratesof discountand differentprivate saving propensities.It is possible in our model for an economywith a lowersocial rate of discountand thusa higherlong-run capital-laborratio to have a largerlong-run per capita governmentdebt. We draw a finalconclusion which bears on the idea of the "burden of thedebt." In thismodel the initial stock of debt has no effectat all on the optimal growthpath of consumptionand investment.The economy's growthpossibilities are constrainedonly by its technologyand its initial endowmentsof capital and labor. There is no burdento the debt per se, althoughthe accumulation of thedebt may have been partlyat theexpense of capital accumulation. This paper representsonly the beginningsof a satisfactorytheory of growthpolicy in an indirectlycontrolled market economy. In particular, we expectthat this analysis can be extendedto modelswhich differ some- what in theirdescriptions of marketbehavior; for example,to models withmore general consumption functions. 2. Production Our productionmodel is the simpletwo-sector constant returns-to-scale model of Uzawa (1963). The heavy curve in Figure 1 is the production possibilityfrontier (PPF) correspondingto a capital-laborratio k. Produc- tion will take place at the point at which the PPF has slope -pk, wherepk is theprice of capital relativeto consumptiongoods. Inspectionof thefigure shows that, wherey, and Yc are per capita output of investmentand consumption, yj = yI(k,pk), and Yc = yc(k,Pk), (2.1) withk and Pk uniquelydetermining yj and Yc- Also, a- > 0, and Ad- < 0. (2.2) ~Pk bPk This content downloaded from 132.236.27.111 on Thu, 21 May 2015 18:36:03 UTC All use subject to JSTOR Terms and Conditions FISCAL AND MONETARY POLICY 701 Y C Y(2,Pk) yC(k 'Pk) Teyc~k~pk) - -slope (-Pk) y(k,)Pk) I yI(k'Pk)/Pk FIG. I Three other comparativestatics propositionswill be needed in our analysis.For a fulldiscussion of thesepropositions, see Rybczynski(1 955) or Uzawa (1963). We assume that productionof consumptiongoods is always morecapital-intensive than productionof investmentgoods. This impliesthat -y, < 0 and -yk > O. (2.3)
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