A NOTE ON THE DYNAMIC ROLE OF MONOPOLISTIC COMPETITION IN THE MONETARY ECONOMY. abstract

Transcription

1 A NOTE ON THE DYNAMIC ROLE OF MONOPOLISTIC COMPETITION IN THE MONETARY ECONOMY abstract In the new Keynesian economics, monopolistic competition plays an important role. Much static research is base on a istortion cause by monopolistic pricing: the price of goos relative to that of leisure becomes too high, resulting in a shortage of consumption an an excess of leisure. When the theory of monopolistic competition is extene to monetary ynamics in the overlapping generations moel (OLG) (Otaki 2007, 2009), the unemployment (excess leisure) problem is entirely resolve by proper monetary fiscal policy. However, there emerges another istortion. Even in full-employment equilibrium, the socially optimal allocation iverges not only from monopolistic competition, but also from Walrasian equilibrium. The optimal net inflation rate in the moel is zero, because the same quantity of goos is transferre to ol iniviuals as they gave to the previous generation. Since there exists no such coorination motive in a monetary economy, the inflation rate possibly excees zero. Monopolistic power lowers the inflation rate; a nominal wage epens on current an future prices. Consequently, the prices of current goos relative to future goos become higher by virtue of the monopolistic power. This improves lifetime utility because the units of current labor supply can buy more future goos. Thus, monopolistic competition possibly ominates Walrasian equilibrium in the monetary economy.

2 1. Introuction It is well known that monopolistic competition plays an important role in the new Keynesian economics. 1 The eaweight loss of monopoly makes room for government intervention. Thus, results of partial equilibrium analysis can apply to the general equilibrium of preceing research. However when we exten the theory to monetary economic ynamics in the OLG moel (Otaki 2007, 2009), we see that proper monetary policy can resolve the uneremployment problem. Nevertheless, another istortion remains. Even when the economy enjoys full-employment equilibrium, the socially optimal allocation iffers not only from monopolistic competition but also from the Walrasian equilibrium. When population growth is zero, the optimal net inflation rate is zero. The reason is that ol iniviuals receive the same quantity of goos as they onate to the previous generation. Since such coorination is impossible in the monetary economy, where ecision making is separate generation by generation, the equilibrium net inflation rate possibly excees zero. 2 In the ynamic moel, price-making behavior lowers the inflation rate compare with price-taking behavior. Since workers reservation wages epen on current an future price levels, monopolistic pricing heightens the current price relative to the future, an lowers the inflation rate. Thus, monopolistic competition ominates the Walrasian equilibrium in the monetary economy. The paper is organize as follows. Section 2 briefly summarizes the moel of Otaki (2007). Welfare comparison between monopolistic competition an Walrasian equilibrium is treate in Section 3. This section also contains iscussion on the welfare loss intrinsic to the monetary economy. Brief concluing remarks are containe in Section 4. 1 For example see Mankiw (1985, 1988); Blanchar an Kiyotaki (1987); an Stratz (1989). 2 Diamon (1965) alreay shows that the economy fails to attain the Golen Age Paths where the total consumption is maximize because of the lack of intergenerational coorination. The essence of the iscussion here is analogous to Diamon moel. 1

3 2. The Basic Moel 2.1 The Structure of the Moel We briefly sketch the ynamic equilibrium Keynesian moel in Otaki (2007). Consier a stanar two-perio overlapping generations moel with money. There exists a continuum of perishable goos inexe by z [0, 1]. Each goo is monopolistically prouce by firm z. Iniviuals are born at a continuous ensity [0, 1] [0, 1]. They can supply one unit of labor an o so only when they are young. Iniviuals Iniviuals have ientical lifetime utility functions U(Ct+j, 1 Ct+j+1, 2 δ t+j ) (Ct+j) 1 α (Ct+j+1) 2 1 α δ t+j β, (1) [ 1 ] c i 1 t+j(z) 1 η 1 1 η z 1 (2) C i t+j where 0 < α < 1 an 1 < η. c i t+j (z) is the consumption of goo z at the i th stage of life uring perio t + j. β is the isutility of labor. δ t+j is a efinition function that takes a value of one when employe an zero when unemploye. 0 We can obtain the following inirect utility function IU by solving the optimization problem ( δt+j W t+j + Π ) t+j IU(, +1, δ W t+j + Π t+j ) A Pt+j α +1 1 α δ t+j β (3) where A α α (1 α) 1 α, [ 1 0 ] p i t+j(z) 1 η 1 z 1 η. W t+j, Π t+j enote the nominal wage an profits equally istribute to each iniviual. wage W R t+j as Using equation (3), we can calculate the nominal reservation Wt+j R = A 1 Pt+jP α t+j+1 1 α β. (4) Since our main concern is imperfect employment equilibrium where some iniviuals are unemploye, the equilibrium nominal wage W t+j is equal to W R t+j. 2

4 Firms The eman function of goo z uring perio t + j is [ pt+j (z)] η Yt+j c t+j (z) = (5) where Y t+j is the real effective eman efine by Yt+j ( Wt+j α L t+j + Π ) t+j + G t+j + M t+j. (6) L t+j is the current employment level an G t+j enotes the nominal government expeniture. M t+j is the nominal money stock that is carrie over from the previous perio. Thus, the first term on the right-han sie of equation (6) is the aggregate consumption function of the young generation. The secon term is real government consumption, an the thir is aggregate consumption by the ol generation. For simplicity, assume that one unit of labor prouces one unit of goos. Then, the profit maximization problem of firm z is The solution is max Π t+j(z) = max [p t+j(z) Wt+j]c R t+j (z). (7) p t+j (z) p t+j (z) p t+j (z) = Substituting (4) into (8), we obtain = W t+j R, z. (8) 1 η 1 ( A 1 β 1 η 1 ) 1 1 α +1. (9) (9) is the ifference equation that equilibrium price sequence, { } j 0, must satisfy. It is noteworthy that { } j 0 has no relationship with the sequence of nominal money supply, {M t+j } j 0. This implies the nonneutrality of money in the sense that real cash balance, M t+j, can be etermine inepenently of the price level,. In aition, we assume η is large enough an β is sufficiently small that the equilibrium inflation rate, ρ, is no less than unity. Thus ρ +1 = [A(1 η 1 )β 1 ] 1 α 1 (10) 3 1

5 hols. The Government The government finances its fiscal expeniture by seigniorage. That is M t+j+1 M t+j = G t+j, j 0. (11) We specify the money supply rules as follows. 1. The government ajusts M t+1 in accorance with the current fiscal expeniture G t (Rule 1). 2. From perio t + 1 onwar, M t+j+1 is controlle so as to keep the real cash balance equal to m t+1 M t+1. Namely, m t+1 = M t+j, j 1 P t+1 hols (Rule 2). By Rule 1 an equation (11), the current buget constraint of the government is ρm t+1 m t = G t P t g t. (12) Rule 2 an equation (11) require that the real government expeniture from the next perio, g, must satisfy 2.2 Market Equilibrium (ρ 1)m t+1 = G t+j g, j 1. (13) There exist three kins of markets: goos markets, labor markets, an the money market. We confine our attention to the first two markets. Labor markets are in equilibrium when the equilibrium nominal wage is equal to the nominal reservation wage. The equilibrium conition for goos markets is Yt+j = α Y t+j + g t + m t = α Y t+j + ρm t+1. (14) Equation (14) is the Keynesian cross in this moel. Suppose that initial nominal money supply, M t, an the government expeniture, G t, are sufficiently small for an arbitrary fixe equilibrium price sequence that satisfies ( Y ) t+j, (9). Then, the solution of (14), is possibly locate within (0, 1]. Such a case correspons to the stationary imperfect employment equilibrium. 4

6 3. Welfare Analysis In this section we shall firstly show that the allocation by monopolistic competition ominates that by Walrasian equilibrium. Seconly, we shall show that market equilibrium in the monetary economy generally iverges from the socially optimal allocation. In this sense there exists the welfare loss intrinsic to monetary economy. 3.1 Monopolistic Competition vs Walrasian Equilibrium Here we consier two types of fiscal policy. One is the wasteful policy that the government consumes all seigniorage an oes not irectly affect the utility of iniviuals. The other is the first-best policy that the government transfers all seigniorage to the younger generation. The Case for the Wasteful Policy From equations (3), (4), (7), (8), an (10), the utility of each iniviual IU, which is inepenent of whether they are employe or not, is represente as IU (( Y t+j ) ) = η 1 β 1 η 1 ( Y t+j ). (15) Since it is apparent from (15) that the full-employment equilibrium is esirable, we confine our attention to the case that = 1. Then we ( Y ) t+j obtain IU(1) = η 1 β. (16) 1 η 1 The numerator of (16), η 1, represents the utility erive from the monopoly rent. The enominator, 1 η 1, represents the welfare effect of the monopolistic power through the inflation rate. It is straightforwar from (16) that there exists positive surplus by proucing goos when the price elasticity of eman η is finite. In aition, note that labor supply bears no positive surplus, since the equilibrium wage remains at the reservation level. 3 3 To put it another way, the inflation rate in monopolistic competition is lower than that in Walrasian equilibrium. It economizes the fiscal expeniture for sustaining the fullemployment equilibrium in stationary state, (ρ 1)m t+1, an hence increases isposable income. Such income is attribute to the form of monopoly rent. 5

7 The limit case that η is equal to + correspons to the Walrasian equilibrium in which each firm behaves as price taker. In this case there exists no surplus. 4 The reason is that wages go own to the reservation level in equilibrium, an that output prices are equal to the equilibrium nominal wage: i.e., zero-profit conition in Walrasian equilibrium. Thus, the resource allocation of monopolistic competition ominates that of Walrasian equilibrium just as much as the monopoly rent. Such a result is significant for economics: free entry to each ifferentiate goo is not always esirable in the ynamic moel, an some firm shoul monopolistically supply the goo. The Case for the First-Best Policy Next we consier the first-best fiscal policy in the stationary state. The policy satisfies the following two conitions. 1. The government transfers all seigniorage to young iniviuals equally. 2. The amount of transfer, g, is etermine so as to keep the fullemployment equilibrium. The above conitions inuce the following equations 1 = α(1 + g ) + m, (17) g = (ρ 1)m. (18) Equation (17) is the equilibrium conition for the aggregate goos market uner full employment. (18) represents the government s buget constraint. Solving equations, we obtain m = 1 α 1 + α(ρ 1), 1 + g = ρ 1 + α(ρ 1). (19) Substituting (4) an (10) into (3), the lifetime utility of each iniviual, IU(1 + g ), is represente as IU(1 + g ) = η 1 + g β. (20) 1 η 1 4 We o not mean that taking the limit η + changes the form of the utility function. The equilibrium solution when firms are price takers for any fixe η happens to correspon to the case η +. This is convenient for calculation purposes. Only comparison between some finite an infinite η is meaningful. The seeming change of utility cause by varying η oes not possess any economic meaning in itself. 6

8 The first term of the numerator of (20) correspons to the contribution of the monopoly rent, an the secon term represents the utility erive from the seigniorage. The enominator is the inflation factor that affects the utility. Comparing (20) with (16), it is clear that the first-best policy ominates the wasteful case just by the seigniorage g. Equation (20) can be rewritten using (3) an (19) as IU(1 + g ) = A(1 + g ) ρ 1 α β = Differentiating (21) with respect to ρ, we obtain ρ IU(1 + g ) = Aρα 1 (1 ρ) [1 + α(ρ 1)] 2. Aρ α β. (21) 1 + α(ρ 1) We can easily ascertain that IU is a ecreasing function of ρ as far as ρ 1. It is also apparent from (10) that ρ is increasing on η. Accoringly, the lifetime utility IU is a ecreasing function of η. Since Walrasian equilibrium is the case for η +, it has been shown that the allocation by monopolistic competition ominates that by Walrasian equilibrium also in the first-best policy. 3.2 Welfare Loss Intrinsic to the Monetary Economy We here eal with the welfare loss intrinsic to the monetary economy. This problem closely relates to the following question: oes the first-best fiscal policy above attain the highest utility? To analyze the problem, let us consier the socially optimal problem in this moel. Suppose that all young iniviuals are employe an some quantity of goos is transferre to the current oler generation. In aition, every generation is assume to be equally treate. By the symmetry of the moel, it is apparent that all goos shoul be prouce in the same quantities. allocation uring perio t + j is Accoringly, the constraint of resource C 1 t+j + C 2 t+j = 1, j 0. Since Ct+j 2 = C2 t+j+1, the maximization problem becomes max (Ct+j) 1 α (Ct+j+1) 2 1 α β, s.t. C Ct+j 1 t+j 1 + Ct+j+1 2 = 1. (22),C2 t+j+1 7

9 The solution is Ct+j 1 = α, Ct+j+1 2 = 1 α, IU = A β > 0. It is noteworthy that the socially optimal solution is inepenent of the price elasticity of each goo, η. The utility erive from the first-best fiscal policy (21) takes the maximum IU = A β at ρ = 1. Hence resource allocation in the monetary economy iverges from the optimal allocation except for the special case. It is apparent that the monetary economy possesses intrinsic istortion. Furthermore, the istortion is more serious when the elasticity, η, is infinite, i.e., firms behave as price takers. In the social planning problem (22), each consumption level of the oler generation is equally treate. The current younger generation is guarantee that they can receive the same future goos as those they give the current oler generation. This implies that intergenerational coorination becomes possible through the existence of the social planner. Nevertheless, in the monetary economy, ecision making is iversifie generation by generation. There exists no motive to coorinate between generations except for the convention of using money. Iniviuals plan their consumption saving an labor supply ecisions, taking into account the next generation s behavior, which is summarize by the future price level, +1, as given. Therefore, the equilibrium inflation rate, as shown by equation (10), iverges from unity where the current an future prices are equal. When it excees unity, the current consumption becomes larger than the social optimum, an the future consumption is excessively small, as appears in equation (19). Namely, inflation biases the iniviual consumption stream towars the current. This phenomenon is consiere to be an intrinsic eaweight loss to the monetary economy that cannot be resolve by income policies. In the ynamic moel, unlike in static analyses, uneremployment by monopolistic pricing is not a crucial problem if the fiscal policy is properly execute. Inflation is a true social cost incurre by using money, an hence monopolistic competition contributes to economic welfare through the 8

10 reuction of such a cost. 4. Concluing Remarks This note has investigate the ynamic role of monopolistic competition in the monetary economy. The results are as follows. Firstly, monopolistic competition lowers the inflation rate. Such a positive effect ominates the etrimental one that the real wage in terms of current goos is cut own by the monopolistic power. Thus, in the ynamic moel, monopolistic competition attains higher utility than that in Walrasian equilibrium. This result is inepenent of whether the seigniorage is waste by the government or transferre to the younger generation. Seconly, there exists some eaweight loss intrinsic to the monetary economy, which cannot be remeie by macroeconomic policies. If coorination between generations is possible, the marginal transformation rate of goos becomes unity. This is because the younger generation can obtain the same quantity of future goos as they onate to the current ol generation. In other wors, the social planner can set the price of future goos relative to current goos to unity an attain highest utility. In the monetary economy, however, ecision making is iversifie with each generation. Hence the inflation rate is not necessarily unity, except for the special case. Compare with the social optimum, the consumption stream is biase towars the current when the inflation rate is higher than unity. Thus, inflation is the eaweight loss intrinsic to the monetary economy. To sum up, monopolistic competition contributes to economic welfare through the reuction of the inflation rate. The welfare-economic results of ynamic monopolistic competition contrast sharply with those of preceing static analyses. Masayuki Otaki an Yoshihiro Tamai 9

11 References [1] Blanchar, Olivier E., an Nobuhiro Kiyotaki, Monopolistic Competition an the Effects of Aggregate Deman, American Economic Review, 77 (1987), [2] Diamon, Peter A., National Debt in a Neoclassical Growth Moel, American Economic Review, 55 (1965), [3] Mankiw, N. Gregory, Small Menu Costs an Large Business Cycles: A Macroeconomic Moel of Monopoly, Quarterly Journal of Economics, 100 (1985), [4]. Imperfect Competition an the Keynesian Cross, Economics Letters, 26 (1988), [5] Otaki, Masayuki, The Dynamically Extene Keynesian Cross an the Welfare-Improving Fiscal Policy, Economics Letters, 96 (2007), [6]. A Welfare Economic Founation for the Full-Employment Policy, Economics Letters, 102 (2009), 1-3. [7] Starz, Richar, Monopolistic Competition as a Founation for Keynesian Macroeconomic Moels, Quarterly Journal of Economics, 104 (1989),