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Title Author Publisher Jtitle Abstract Genre URL Powered by TCPDF (www.tcpdf.org) Multiplier theory and public goods : a macroeconomics of the mixed economies 大山, 道広(Oyama, Michihiro) Keio Economic Society, Keio University Keio economic studies Vol.51, (2015. ) ,p.1- 17 In this paper we reconsider and extend the economic theory of deep depression, initiated by Keynes (1936), taking explicit account of the concept of public goods largely blurred in his general theory and after. To contrive the model of secular stagnation where the interest rate falls to zero and monetary policy is restricted by the zero-bound, we concentrate on "real economy" model featuring the theory of public finance. In so doing, we synthesize the traditional theory of public finance and the Keynesian theory of fiscal policy; and cast new light to their welfare significance. In stead of the Samuelsonian neo-classical synthesis, we propose the neo-Keynesian (or the mixed economy) synthesis that requires optimization of public good provision as well as full employment of labor. Journal Article http://koara.lib.keio.ac.jp/xoonips/modules/xoonips/detail.php?koara_id=AA00260492-201500000001 KEIO ECONOMIC STUDIES 51, 1-17 (2015) h YAM Keio First version Abstract: In pression, goods initiated stagnation finance. nesian by concentrate In so doing, the Samuelsonian economy) (1936), we and account after. To and economic the traditional theory of the contrive monetary model policy we propose optimization of public finance good of secular is restricted the de- of public model theory by the of public and significance. the neo-Keynesian of public of deep concept the featuring light to their welfare synthesis, theory the Key- In stead of (or the mixed as well multiplier,public goods, secular stagnation, public finance,neo-Keynesian synthesis as full of labor. Key words: JEL Classification Number: E12, E22, E24, H30, H40 1. Since the explicit and economy" cast new 2015 provision employment that requires December extend taking theory "real synthesize neo-classical synthesis and rate falls to zero on of fiscal policy; accepted reconsider in his general the interest we theory we Keynes blurred where zero-bound, received Apriion this paper largely University, Tokyo, Japan the collapse of the Bubble ture continued to expand condition leaving the government for more INTRODUCTION in early 1990, the national rate of unemployment deficitincreased the Japan's government than 20 years, but failed to improve and consequently accumulated enormously. icyHntended toincrease the aggregate income This experience expendi- the business at high levels. In the meantime, the balance of the government bond cast doubt to the effectiveness of fiscal poland employment multiplier theory originated in the midst of the great depression in Japan. The Keynesian of 1930s has served as Acknowledgments. The draft of this chapter was firstpresented at the workshop presided by Ryuzo Sato on November 29, 2014. I benefited from instructive comments by Sato on the contributions by Richard Musgrave regarding the concept of public goods, together with constructive discussions from other attendants of the workshop. I am indebted to helpful comments by Masatoshi Tsumagari and an anonymous referee of Keio Economic Studies. 1 Fiscal policy is here defined as a macroeconomic gregate employment by controlling the government policy designed to stabilizenational income public financein the narrow sense limited to the provision of public goods. Copyrightc2015, by the Keio Economic and ag- revenue and expenditure. It should be distinguished from Society 1 2 KEIO the cornerstone ECONOMIC of the fiscal policy in the standard textbook for a long time. It empha- sized multiplier effects of government employment STUDIES symbolizing deficit expenditure the Keynesian policy. The recent experience not as large as believed in the past. Moreover, frequent use of fiscalpolicy undermined the government fiscal discipline giving rise to inefficient resource allocation in Japan as well as in many multiplier theory typically abstracts from goods regarding works the aggregate as an important tradable in the market. introduced when considered public glossed over the distinction he talked of the national product as if it were one good (1959) and Samuelson their interpretation, public goods the dictation of the government of public and private product. Keynes of fiscalpolicy, but somehow At the time of the General by Musgrave other countries. the coexistence output as a composite element of private and public goods and of the stagnation of Japan and other countries, however, revealed that the multiplier effect was The on the national income revolution in the history of macroeconomic differ from Theory, (1954, the concept of public goods 1955) was not known yet. In private goods in that they are provided while private goods are provided supply in the market. This distinction is not really understood through by demand and even now, after more than half a century. Another problem with the multiplier theory is its disregard of welfare economics. tends to undervalue and employment workers the welfare effect of public goods, while overestimating effects arising from for the production surpassing its direct income theory, however, more an expansion increase in welfare though the accompanying by Keynes mines In fact, the use of unemployed of public goods may and employment effects.In terms of the simple Keynesian of the government yield an increase in social welfare deficit expenditure brings about a far through its multiplier effects than its direct meager provision himself is the employment and digging them public works. It the income of public goods. A well-known of workers for burying up again. It would through its multiplier effect even though effects illustration given old bottles in disused coal increase the real income of the community there is no sense in such a project in terms of social welfare. One of the most public expenditure national income controversial problems with the multiplier theory was whether financed by the government deficit would the really create much more than its face value. In order to finance the project, the government must issue the corresponding value of bonds, future. The of the project to taxpayers is, therefore, equivalent, regardless real burden which it has to repay later by taxation in the of whether it is financed by deficit or by taxation. This recognition Barro, is now ignores well known the message as the equivalence of this theorem theorem.2 completely. The due to Ricardo simple In fact, many multiplier theory public work put into practice in Japan by deficit financing during the "lost two decades" collapse of the bubble number failed to revive the slumped of public facilitiessuch as dams economy. Moreover, projects since the they created a and buildings detrimental to environments 2 Ricardo's idea is recorded in his "Essays in the Funding 1979) formalized hisidea clearlyin the words of modern System," in McCulloch economics. and and (1888). Barro (1974, OHYAMA: social welfare. During debt continued MULTIPLIER AND PUBLIC the decades, the government to increase at unprecedented risks attributable to government many THEORY 3 GOODS deficitincreased pace. and its resulting In the 21st century, the sovereign debt financing began to threaten business prospects of follows, we reconsider the effects of fiscalpolicy using a simple real model of countries all over the world. In what macroeconomies. In the absence of the economy may become of innovations and new frontiers,the effective demand insufficient to ensure the full employment interest rates decline to zero like the "liquidity trap" envisioned In Section 2, we consider the simple real economy only private goods This basic model envisioned are traded in the market. Money is useful for the purpose by Hicks (1937) of illuminating as "liquidity trap" where Hicksian liquidity trap within the framework cause of such edy such a depression are assumed the deep depression monetary (1998) of IS-LM to introduce equilibrium. government away. economy policy becomes reintroduced inef- the concept The is deficiency of effective private demand. a situation, it is necessary the without public goods, in which and government fective and fiscal policy does not exist. Krugman even when by Hicks (1937).3 of fundamental In order to rem- fiscal policy conjugating private and public goods. In Section 3, we modify tervenes in the economy the preceding providing taxation. It abides by balanced setup and assume public goods budget in the sense that its payment and transfer is fully financed by taxation. The by the government democratically amount come of income expressed taxation. One becomes of private goods unit of government by the that the national disposable in- constant independently expenditure and associated labor services meaning of of public goods is determined of public goods) is determined It will be shown in terms of private goods of the government private goods in the market. in- by means for public goods or dictatorially, while the amount (including labor services required for production adjustment that the government and transfer payment of the level generates one unit of that the multiplier of government expenditure is exactly unity. In Section 4, we develop a two-good are considered model in which explicitly and distinctly. When crease in the government public as well as private goods the economy expenditure increases employment good, but does not affect the national disposable income. to be useful by a given social utility function, however, fare. Furthermore, if the public good is so designed goods, the fiscal multiplier will be strengthened. further increase in government public goods This means If the public good is defined it clearly increases social wel- to stimulate the demand Once an in- full employment for private is realized, a expenditure, i.e., a further increase in the provision gives rise to "crowding private goods. is underemployed, and the output of the public out," or a corresponding that the opportunity of decrease in the supply of cost of public goods is positive rather than zero. In Section 5, we explore the effects of macroeconomic 3 Ohyama (1987, 2004, 2007) developed a version of the IS-LM to characterize the "liquiditytrap" as its special case. policy under full employment. model with a microeconomic foundation 4 KEIO ECONOMIC STUDIES In this phase, an increase in public expenditure social utilityfunction even though it may be desirable to decrease government public good is illustrated by looking the production employment. not be justifiedin view expenditure. at how At a firstglance, this idea may (1954). The optimal provision of the The purpose the supply of the public good by Samuelson of the given the social indifference curve intersects with frontier of public and private goods. this phase is to optimize introduced may the public good is useful on its own. In other words, seem of public finance in rather than just to preserve full to resemble the neoclassical synthesis But as we argue in Section 5, the government realize full employment and optimize Thus it should be named the neo-Keynesian the supply of the public good (or mixed must at the same time. system) synthesis of employment and public finance. 2. THE PRINCIPLE Let us begin by considering supposed to be a private good OF EFFECTIVE a simplest model in which staple. A unit of rice is supposed for h hours per day for the wage "rice," the most popular using a units of homogeneous a given amount rate wc It is as well as for consump- be named be produced labor. The representative worker is bestowed to work there is only one good. used for production, investment tion and tradable in the market. For simplicity, it may Japanese DEMAND of leisure and is supposed determined by labor contract on the basis of the social convention. Figure 1 depicts the representative worker's indifference curves between wage rate and leisure and the determination vertical line showing at a value between the given labor hour. Contract wage reservation wage, which the employers (1981) and Ohyama (1987) The total number number ND the number the above who of workers how workers, > or N wc We requires at least and unity 1. See McDonald in the US then are the determinants is denoted N. Let us denote by Ns or the supply of workers When on contract wage stock K, which may contract wage may or Ns of workers of involuntary Decades" of social demand = Such a is insufficient in Japan. for national product? In the present demand for national product con- /. Private consumption consumption C = c(wc,r,Y,K) N. for as in the case of the Great rate wc, real rate of interest r, national income be written as an aggregate satisfies falls short of the unemployment. after the Bubble social private demand C and investment the and by not be equilibrated to the demand for national product at fullemployment the government, sists of private consumption Solow under unemployment. here that the demand and the "Lost Two and bargaining by the economy. of workers on the to be negotiated is in the state of full employment, assume the demand setup abstracting from assuming < the supply of national product at full employment Depression depends demanded giving rise to the emergence situation occurs when to absorb of wage in the economy the supply ND. supply of workers the worker or w_ < are willing to be employed, inequality, the economy Figure 2 shows What for models of workers of workers w_, which can pay at most, of contract wage is supposed demand Y and capital function (1) OHYAMA: MULTIPLIER THEORY AND PUBLIC 5 GOODS w 1 w o Figure 1. Standard Labor Hour and Reservation Wage. dc For simplicity, investment the firm's long-term The dc > 0 Cyn market 1 CV demand expectation equilibrium > Y goods given wc, intersectionof E the works among condition as an adjustment K aggregate determination or Eug supported intervention, and market by the = c(wc, <0, disposable c* to be given Y,K) the ― oK >0 exogenously depending on + Dd and income. fails to realize is I (2) the demand equilibrium expenditure and national 45° line, while Figure G#. 5 shows supply income Figure the In the absence full employment 4 Keynes (1936), p. 25. "The point of intersection of the aggregate demand supply function will be called the effectivedemand. = factors. to equilibrate curve government dc ― or unemployment 3 shows demand mechanism Cr other under factor /. Figure of national 0 , / is supposed Y where > of private Ye at the 4 illustrates equilibrium F# of government in this situation. The function and the aggregate 6 KEIO ECONOMIC STUDIES w 1 wc w o YJa N N Figure 2. Supply Curve of Labor. market gap" equilibrium income FG falls short of full employment income, Yf, by "deflationary in case of Figure 3, or by G a G gin case of Figure 5 implying corresponding unemployment. Reverting gap coincides with unemployment to Figure 2, we observe equal to segment tical to the familiar illustration of "Keynesian take full advantage of the newly introduced NeS. the existence of that the deflationary Figure 3 is essentially iden- Cross," whereas general equilibrium Figure model 5 is invoked to covering private and public goods.5 5 The private goods portion, given becomes convex of public This the stock used in the production of public of private capital. In such to the origin and that the aggregate goods may be subject to decreasing a case, the production supply function returns frontier of private and public depends positively to progoods on the relative price goods. modification of aggregate supply is not necessary, functions. however, for our conclusions but is agreeable to the Keynesian concepts OHYAMA: MULTIPLIER THEORY AND PUBLIC 7 GOODS Y Ye O YE YF Y Figure 3. The Principleo f EffectiveD emand. 3 GOVERNMENT Let us now AND introduce government expenditure endogenous variables. spent on government payments FISCAL POLICY government (TWO EQUILIBRIUM) variables on national income that proportion expenditure GENERAL and consider the multiplier effects of changes in and other exogenous Suppose GOOD a of national tax revenue G on public goods and related T is to be and proportion (1 ― a) on transfer R: T = G + R (3) G = aT (4) R = (\-a)T (5) Z = Y-T + R = Y-aT (6) With theintroduction of government, privateconsumption function is modified as C = c(wc,Y -aT,K) (7) Given the reservation wage wc, tax T, privateinvestment / and consumption function, the new market equilibrium conditionis written Y - aT determines equilibrium income = c(wc, Y - ccT, K) + / Ye and disposableincome (8) 8 KEIO ECONOMIC STUDIES z *e Y o Figure 4. The Determination of National Disposable Income. Z(= YE - aT). The effectof an increase in autonomous investment on equilibrium income and dis posable income is shown by Marginal propensity to spend smaller than 1, which much more plier.The dzE 9/ di than 1. This conclusion is nothing spends its tax revenue often spend more to positive and than the familiar investment multito than capitalistson private goods. First suppose that the government This is exactly the case of Keynesian old bottles in disused coal mines expenditure more cz, is assumed multiplier is positive and could be wc, is not quite clear but often supposed expenditure? on useless goods. an increase in government (9) l-cz that the investment about the effect of government of burying 1 out of disposable income, implies effect of a rise in contract wage, be positive as workers How dYE and digging them under balanced parable effect of budget is dYE = up again. The a, (10) dT To be sure, the balanced budget multiplier is equal to unity, or dYE dG = 1 (11) OHYAMA: Needless MULTIPLIER THEORY AND PUBLIC to say, the multiplier effect on the equilibrium dZE 9 GOODS disposable income becomes = 0 (12) 8G PROPOSITION vails 1 (balanced under at (I ―a) balanced of tax revenue, by a but leaves Standard just Here, of tax revenue, the standard smaller These balanced people systems private to social goods in financed noted national and The to work public good collaboration like roads, Here, stock (or social is specified with public harbors, 6 Also see Musgrave goods. 1, per income. parks, as a labor public is defined service used investment national The to poor of the social most security are homo- expenditure expenditure does in T brings not about government goods on not affect affect an equal expenditure and income therefore labor the income and of the public of employed the increase potential increases good and in word expenditure). investment good, the production forces in addition from (1974)).6 of public in public An employment distinguished of Uzawa is investment defense in the government aggregate public to be flow workers workers. effect of government capital in the embankments, (1959), pp. 13-14. Thus, among workers. capital. Public and for the provision capita among common rich is one of as it were. goods good effect payments that consumers in the used on public to provide public from This for public money sharing sharing net government but it does and income-sharing is supposed payment. aggregate income assume increase goods taxation, (income) income we an increase increases, expenditure and government capital = of or, the transfer of tax government The Caesar's through 2 (work work public 1. If a that the fact, however, reform expenditure employment in government to transfer the value larger is goods. is because of public in the face of constant realizes multiplier The to decrease of public sector. to Caesar amounts tend budget. production the aggregate Proposition increase income is set at 1 ― or than distributes simultaneous government in the private expenditure budget or smaller expenditure. In this paper This balanced employment decreases payment national transfer assumption In which that a tax-financed tax increases is returned the payments income. under implicit consumption in Japan. transfer in the While to a obtains. is zero. benefits, aggregate employment goods of our in the production be Ye /a by security discussed used also the disposable equal of unity demand regarding therefore It should equilibrium of government becomes the results increasing recently and pre- transfer unaffected. proportion multiplier aggregate problems geneous increase are on related thereby controversial unemployment the multiplier. payments are often of tax increases income multiplier budget that of government tells us that the balanced that if the tax based conclusions transfer disposable say Suppose the proportion of macroeconomics we becomes multiplier). Given a unit increase equilibrium textbook unity. budget budget. Here, good capital in stock etc. that are publicly merit wants considered there are related to flow public 10 KEIO owned. We ECONOMIC will consider the economic capital stock in more STUDIES significance of public investment For simplicity, 1 unit of public good is supposed good. The workers total number employed of workers N in the government where X the mixed economy where equilibrium G employment Ne through to provide market. contains unemployed The of the equilibrium workers =XE+aG of the public good and vertical axis measures The when (14) < N. frontier between G and X on the simpli- that the labor coefficient a is given and fixed. The curves Ss are the social indifference curves between of the public goods decreases G and X on the assumption given the aggregate consumption Su is the social indifference curve where public goods is given spondingly determined expenditure increases but what that G is equal to the amount undertakes The curve Tt depicts a straight line production The curve Note and the horizontal axis that of the private good. NE fying assumption of (13) of the public good. Figure 5 shows the government expenditure is the sum = X + aG, the private sector supplies private goods the government using a unit of private in national production denotes the output of the private good. in the production to be produced employed and private sectors: N labor employed and public detailin the next section. at Ga and the consumption on Su. As pointed that the marginal utility of the private goods. the government expenditure of the private goods Zo on is corre- out above, an increase in the government the aggregate income and employment in the same proportion, can we say about its welfare effects? An increase in the aggregate income employment would increase the expected the probability of their employment. of public goods would and utility of the potential workers by increasing Moreover, the associated increase in the provision increase the welfare (social utility)by itself. To make clear, let us define the social utility function (the graphical representation this point of which is the social indifference curve) as W PROPOSITION = u(X,G), uG>0. expenditure to increase social welfare along the expansion to the old Keynesian expenditure view, of path EaEb- a bond-financed whereas government the future tax burden it focuses only on the income expenditure a tax-financed increase in results in an equal increase in national income. gued, this view is untenable in that it overlooks increase. Furthermore, The expansion shifts the equilibrium point under unemployment brings about a multiplied increase in national income, government (15) 3 (expansion path in the presence of unemployment). tax-financed government According ux>0, As already ar- of the expenditure effects of the expenditure increase neglecting its welfare effects. In light of (15), an increase in tax-financed government expenditure creates extra income under unemployment. There are some Itis bound public goods and employment without incurring opportunity costs to increase social welfare. that complement and promote private consumption and OHYAMA: investment. MULTIPLIER For example, the provision may increase consumption of public roads vestments AND PUBLIC 11 GOODS of care and nurse services by the government by creating leisure time for housekeepers. and port facilitiesmay in general. Under be important these circumstances, ten as a function of government income THEORY expenditure The maintenance for business opportunities and in- consumption function may be rewrit- as well as on real interest rate r, national and on capital stock: C =c(wc,r, Y-aT, K,aT) (16) and investment function may be similarlymodified as (17) / = i(r,aT,K) where cr < 0 ir < 0. Proposition The balanced expenditure 4 (government expenditure complementing budget multiplier of a government privateexpenditure) expenditure that complements private has a multiplier greater than a under unemployment? After all the prevalence of unemployment the result of unwillingness shortage of public goods stems from deficiency of effective demand, on the part of people to consume in the broad sense including or invest. It may reflect the those that complement private expenditure. 4. In the presence public good FISCAL POLICY of unemployment, by using labor from and maintained, curve Sb passing though This means improving shown however, Eb that the supply no opportunity the full employment is costs. Once frontier Tt from of the without reducing down 5, indifference left to right above is insufficient and there are rooms for social welfare by increasing its supply. The socially optimal equilibrium by E* where indifference curve S* touches from decreased full employment, along Tt. Throughout Figure 6 depicts the case where along of the public good and increase the expansion is how- only if the supply of the process, labor the private sector to the public sector and the equilibrium point from path (or adjustment the output of the public good optimal point F* is smaller than that of Eb. adjustment Tt. Under of the public good is achievable and the social welfare increases EbF*. workers this is no longer the case. In Figure cut production the private good is correspondingly to F* EMPLOYMENT it is possible to carry out the production of the public good ever, an increase in the supply moves FULL the pool of unemployed output of private goods, i.e.,incurring achieved UNDER Eb path) at the socially It is desirable to decrease the production that of the private good along the expansion path (or path) EbF*. 7 Aside from the demand increasing effectsfrom the introduction of public goods considered here, it is also worth taking note of the supply increasing effectsfrom the public goods. In the present model, however, the supply shocks of thiskind do not affectthe short -run adjustment process under unemployment. We shall explore the long-run effects of public investment (increase in the stock of public capital)later in the next section. 12 KEIO ECONOMIC STUDIES G N/a G* GB GA O 7 Figure 5. PROPOSITION expenditure 5 (Expansion Equilibrium. Path under Full Employment). has to be pursued of the production Economy differsfrom along the expansion frontier. To be more precise, ifG* X N 0 Path of the Mixed that ensures the full employment further adjustment EbF* An Expansion ^ Zo * When the government its socially optimal level, a path (or adjustment > Gb, path) the government must increase the its expenditure and the supply of public goods. In contrast, ifG* < Gb, government The social must decrease its expenditure and the supply welfare increases in the process of the adjustment 5 NEO-KEYNESIAN of public process along goods. the EbF*. SYNTHESIS Early in 195O's, Samuelson put forward theidea that once the government succeeds in maintaining fullemployment, labor embodied in the employed workers will be optimally allocatedthrough market mechanism, sis".8 If full employment is maintained allocation of private goods mize will be achieved social welfare. Within theorem of welfare economics and named it the "neo-classicalsynthe- by the government's the simple model by market devoid optimally to maxi- of public goods, the fundamental is established that general equilibrium optimal under the condition of perfect competition 8 See Samuelson (1955), p. 212. fiscal policy, the resource mechanism and in the absence becomes Pareto of externalities. OHYAMA: MULTIPLIER THEORY AND PUBLIC 13 GOODS G G*' G* o z* z*' t v x Figure 6. Productivity Improvement in PrivateGood Production. In the present model the shortage of social public goods in the short run and social capital stock in the long run may short run unemployment and long run stagnation as mentioned ment depress consumption and investment bringing about above. Thus the govern- provision of social public goods in the short run and the social capital stock in the long run may exert positive externalities in the sense that it promotes tion and investment easing short run unemployment and 6 illustrate how the government ployment equilibrium optimal equilibrium Proposition the optimal intervention Ea allocation of national resources along through with market private consump- and long run stagnation. Figures 5 mechanism full employment may be achieved starting from equilibrium Eb by the unem- culminating in the E*. 6 (Neo-Keynesian or mixed-economy synthesis). Suppose that given 14 KEIO resource endowment, production ary state prevails where ECONOMIC STUDIES technology net investment and consumers' and saving stabilizes at the natural level. Also suppose ket for private goods zero and real interest rate that perfect competition prevails in the mar- with no technological externalities. The government anticipate the short-run as well as the long-run foresight. The government to increase employment optimal provision preference, static station- become should is assumed effectsof public investment to with perfect then be able to use expenditure policy appropriately in the short-run and maintain full employment of public goods in the long-run. and achieve This design of economic the policy may 1 named ^J4-1 V * {or ( 4-1 mixed-economy) ' J \synthesis. 4-1 ' y be the neo-Keynesian the So far we have nology and public, however, abstracted formation the present ment. us divide Let latter to improve K. model taking G/. / is supposed Considering these explicit former and ci(Kg) vestment we productivity N(K, Kg) tion of K, supply Figure may Kg since private and public roads, in future optimal inferior event. increase the to T't'. Given goods, in public will decrease the future and output Similarly, and and the private capital constraint Kg stock as since thereby labor government in- improving labor coefficient a) and units as an increasing stock private frontier labor education about and serve as the basis may F*, consumption on the labor asymmetrically the optimal how Tt production of the public 9 For simplicity, we have assumed proposition introducing the government good away as before, a and of the to T't. The point future goods frontier effects public funcof labor increase, position as environ- of labor measured frontier expected with and T't'. future Barring will increase on future and F* in such in that public expand cost of future from and increase shifts as a result good relative will change will normally An the present of contact of its expansive coefficient from the the supply points the production account on Tt. shift of production curves or the of the present 7 depicts investment F*' by in projects increase a parallel upward by investment is shown productivity the social indifference Figure decrease frontier Kg- of private (or lowering in efficiency capital present improving are shown social Similarly, of public The facilities and units bringing equilibria It will effects frontier. investment harbor of stock goods to (14') capital government Gq services a(KG)G function of labor consumption efficiency or have effects of invest- the employment government of public We public capital stock a decreasing supply and dynamic tech- private units. 6 illustrates in efficiency duction production either resources. government and + and to produce rewrite =X future the national of production private stock. the shows in efficiency shape ment, in to be increases into the quality relationship, is supposed certainly G on production of investment of these of public N(K,KG) where account is supposed efficiency to improve essence of technology expenditure The the quality effects of investment It is the the quality government investment investment the dynamic that it improves reconsider government from of resources. but the future the pro- public to F*'. As of an capital good a result, output of the the externalitiesof any kind. It would be easy to extend this tax-cum subsidy scheme to internalize externalities. OHYAMA: MULTIPLIER THEORY AND PUBLIC 15 GOODS G N la G*' G* t o Z*[ Figure 7. private good may growth income public of resources. educational and and many and we initiated attempt run As advanced public in the loss 10 The third arrow of "Abenomics" both public economic effects by countries, and destroy labor beyond of economic consumption the current however, difficulties in misguided tremendous natural supply and investment private, run. it is vitally important expenditure and as the engine in the long witnessed of aggregate CONCLUDING (1936) work stock investment of public to reconsider Keynes and indebtedness frontier. Therefore, implications by other untimely of production the welfare run. government facilities resulting In this paper Production. in general, capital positive in the long to serious Useless private of generating 6. pression in Public Good Investment in the short public and in Japan contraction account run can lead strategy). employment is capable short finance investment and and by accumulating in the Productivity Improvement 7 (growth Investment both X N decrease. PROPOSITION increases Z* public misallocation environment and in efficiency units to take into full in particular. REMARKS and taking extend explicit in the Japanese Economic public investment and deregulatory measures to improve the economic account of the theory of deep concept de- of public policy calls for the growth strategy of useful the opportunities of privateinvestment. 16 KEIO ECONOMIC STUDIES goods largely blurred in his general theory and after. To contrive the model stagnation where zero-bound, the interest rate falls to zero and monetary we concentrate on real economy In so doing, we synthesize of secular policy is restricted by the featuring on the theory of public finance. the traditional theory of public finance and the Keynesian fiscaltheory and cast new light to their welfare significance. (1) As the basic setting, we assume are no market-originated fallen to zero. Using Keynesian a simple involuntary the adjustment equilibrium not through of commodity librium, it is necessary prices. To reduce for the government carrying out public investment. we show that deficient Key- is realized through the of interest rate nor through or remove to intervene Conversely, model can arise there from equilibrium the adjustment there and the interest rate has general equilibrium This underemployment of national income, stationary statein which and investment macroscopic unemployment nesian effective demand. adjustment the Schumpeterian private innovations unemployment by producing the government in the equi- public goods or intervention in this fashion is justified only under the present setup. (2) In line with the Ricardo-Barro to abide by the balanced budget to increase labor employment tional disposable income theorem, (3) If the government (private goods) in the government expenditure (Propositions expenditure The process services continuously. It may librium as in EaEbE* expenditure (5) The of the public good, between the public good of the public good necessary may whether must and the private good be determined in view indifference curve and the production to consume budget (Proposition 4). it is useful or not, incurs opportu- and employment Starting from expenditure without is maintained, the initial will initiallyin- decreasing that of there arises trade-off so that a further increase in the supply not warrant improvement (1954) proposed and equi- are useful, the national welfare unemployment. as full employment tunity cost in terms of the private good. (6) Samuelson path of unemployment to increase the propensity to decrease the supply of the public good the public good be divided on goods In such a case, the multiplier of the gov- of involuntary of the public good the private good, but as soon may increases expenditure equilibrium, an increase in the government crease the production time to accomplish to be desirable in itselfin the sense that it directly to effective demand. nity cost except in the presence unemployment 1 and 2). will be greater than 1 even under balanced production (income) 3). social welfare, but it is often designed or invest thereby adding the na- take some be visualized as an expansion is supposed sector keeping full employment in Figure 5. If the public goods (4) The public good ernment toward the government will increase along the path (Proposition enhances be able is sufficiently large, it will realize full employ- of adjustment into discreet periods during which is supposed should be called the work theoretically in no time. In reality, however, it may full employment. the government so, the government at a constant level . This may sharing effects of the government ment equivalence discipline. Even of national welfare. It may on the way. of some become The optimal supply of welfare criterion and its oppor- Figure 6 illustrates this point using the social frontier (Proposition 5). the so-called neo-classical synthesis to the effect that OHYAMA: once full employment the Pareto optimum government's optimization THEORY the achievement of social welfare through (or the mixed foregoing production technology to the "short run" of the economy by the advocateors should serve as the growth The of public 6). setting where the and therefore the production public as well as private, is not only conducive growth of the economy through its frontier.In fact,it extends the future production of the accumulation the It extends to the of labor is called for (Proposition but also to the "long-run" argued will accomplish above, however, synthesis that calls for optimization and labor resources effects on the production tierby means the market of full employment. analysis is applicable only to the short-run recovery 17 GOODS appropriate provision of the public goods. economy) frontier are given and fixed. 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