Theoretical Economics Letters, 2011, 1, 122128 doi:10.4236/tel.2011.13026 Published Online November 2011 (http://www.SciRP.org/journal/tel) Copyright © 2011 SciRes. TEL A Pure Theory of Aggregate Price Determination Masayuki Otaki Institute of Social Science, University of Tokyo, Tokyo, Japan Email: ohtaki@iss.utokyo.ac.jp Received September 6, 2011; revised October 18, 2011; accepted October 26, 20 1 1 Abstract This article considers aggregate price determination related to the neutrality of money. When the true cost of living can be defined as a function of prices in an overlapping generations (OLG) model, the marginal cost of a firm depends solely on the current and future prices. Thus, the sequence of equilibrium price becomes in dependent of the quantity of money. Hence, money becomes nonneutral. However, when people hold the extraneous belief that prices increases proportionately with money, this belief becomes selffulfilling as long as the increment of money and true cost of living are low enough to guarantee full employment. Keywords: Marginal Cost, True Cost of Living, Neutrality of Money, Credibility of Money, Rational Extraneous Belief 1. Introduction As Keynes [1] po ints out, a disparity exists between ma croeconomics and microeconomics on the mechanism of price determination. In microeconomics, prices are gov erned by marginal costs. However, macroeconomics em phasizes the role of money in the process of aggregate price determination. How are these perspectives related to each other? The present paper explores this disparity between microeconomics and macroeconomics. The disparity is closely connected to the neutrality of money. Otaki [2,3] has already shown, by using the standard deterministic twoperiod overlapping genera tions (OLG) model of production economy, that the equilibrium sequence of the aggregate price can b e inde pendent of the quantity of money. However, Lucas [4] proves that the quantity theory of money holds. These seemingly contradictory results suggest the fol lowing theoretical hypothesis: The assumption that prices are determined by marginal costs means that equi librium production/employment level is an interior solu tion. That is, the economy is at the imperfect employ ment. This interior solution emerges from to the lack of pur chasing power of money. By some plausible assumption, the true cost of living becomes a function of the current and future prices independent of quantities. Hence, the nominal reservation wage also depends on these factors. Thus, when the equilibrium current price is equal to the marginal cost, the equilibrium price sequence becomes independent of the quantity of money. If the quantity of money is sufficiently smaller than the equilibrium price level determined beforehand, some individuals are un employed, and the interior equilibrium emerges without any price stickiness. In other words, although most new Keynesian econo mists seem to believe that a pricestickiness assumption or restriction concerning price realignment is unavoid able in obtaining the nonneutrality of money (e.g., Calvo [5], Mankiw an d Reis [6], Woodford [7 ], and Galì [8], money is nonneutral without such frictions in the OLG model. The boundary solution, namely, the quantity theory of money, can be achieved by the following two conditions. First, people hold the extraneous belief that the price level varies proportionately with the quantity of money. For example, Lucas [4] specifies the equilibrium price function as =(pmz) to support the quantity th eory of money under perfect information. This assumption cor responds to the extraneous belief in this article. Second, the increased rate of money, that is, the inflation rate, is sufficiently modest to reduce the true cost of living, and every individual wishes to work. Under these conditions, for an arbitrarily given money supply, the current price level flexibly adjusts the pur chasing power of money to attain the fullemployment equilibrium. Thus, onetoone correspondence is estab lished between the cu rrent price level and the quantity o f money. Namely, the quantity th eory of money holds, and money becomes neutral.
123 M. OTAKI Consequently, money is intrinsically nonneutral and affects the employment and output level without any price friction, as Keynes [1] tacitly considers. The quan tity theory of money is upheld by the extraneous belief that money is only a measure of value and possesses no substantial value. This paper is organized follows. Section 2 describes the basic model and explains the nonneutrality of money under perfect competition. Section 3 provides the neces sarysufficient condition for supporting the quantity the ory of money. It also discusses the difference between the Keynesian and monetarist views on money. Section 4 explains how the methods of injecting money affect the conclusion. Section 5 provides the concluding remarks. 2. The Basic Model 2.1. Optimization Problems of Economic Agents 2.1.1. Individuals We consider a standard twoperiod OLG model with money and one perishable good under certainty. Indi viduals are born with continuum density between in each period, and live for two periods: youth and old age. They can supply unit labor at their discretion when they are young. Their disutility is denoted as [0,1] . The lifetime utility function of each individual is U 121 121 ,, , tt tttt Uc cuc c, (1) where 1t and 21t are the current and future con sumptions of generation respectively. t cc t is a defini tion function that takes the value of unity when the indi vidual works and zero when he/she does not work. ( )u is wellbehaved homothetic function that repre sents the lifetime utility derived from consumption. As Shephard [9] proves, iff the utility fun ction is homothetic, the true unit cost of living becomes a function of prices independent of the consumption quantity. Although the separability between the consumption stream and leisure seems restrictive, the assumption can be justified by Di ewert’s [10] dis cussion. “Although this (homothetic) assumption is generally not justified when we consider the consumer’s overall cost of living index, it can be ju stified in the context of a subaggregate if we assume that the consumer has a separable subaggregator function, () q q, which is line arly homogenous. In this case, is no longer inter preted as the entire consumption vector, but refers only to a subaggregate such as ‘food’ or ‘clothing’ or some more narrowly defined aggregate.” From the economic perspective, Diewert [10] suggests that aggregation should be performed among similar goods. In this sense, in Equation (1), we assume that consumption and leisure have quite different properties as compared to the current and future consumption.1 The budget constraint that each individual faces is 112 ,, tttttttt pcMWp cM 1 (2) where t is the price of the good; t p is the nominal wage; and t is the nominal money demand of gen eration to prepare for future consumption. The profits of the firm can also become the income. However, we assume that all the markets (goods, money, and labor) are in perfect competition. Hence, we can neglect the profits as a source of income. t An individual maximizes Equation (1) on 121 ,,, tt tt cc M subject to Equation (2). Since U is homothetic, the true cost of living fun ction , which is the expenditure function to attain a u tility le ve l , exists such that u 11 ,,= , tt tt pp ufupp , (3) where ( ) is a linear homogenous function. It also increases with and . We can calculate the nominal reservation wage t p1t p t W by using the true cost of living function Equation (3) as 1 =, R tt Wf pp . t (4) In addition, the aggregate current consumption func tion of the young generation becomes t C 1 = ttt t p Cc wl p , (5) where is the employment level located within the interval . t l(0,1) 2.1.2. Firms Next, we proceed to the optimization problem of a rep resentative firm. The only production factor is labor. For simplicity, the representative firm faces the constant re turn product i o n fu nct i o n 1The assumption that each individual can supply only one unit of labo seems to be rather restrictive. However, the distinction between how many individuals a firm employs and how many hours of work it offers to each individual causes, at least theoretically, a difficultdynamic roble , when there is some fixed training costs for employing an individual. Fukao and Otaki [11] have already solved this problem by applying a real business cycle model. Nevertheless, since the purpose of this paper is to show the existence of unemployment due to the shortage of effective demand, we neglect the adjustment of hours worked per individual and normalize the working time as unity. =, s tt l (6) where t denotes the output level. Since the firm acts as a price taker, the profits become zero in the equilib rium. Hence, using Equation (4), we obtain the following important di f ference equatio n: Copyright © 2011 SciRes. TEL
M. OTAKI 124 ** 1 *1 * == 1=1,. R tt ttt t t pWp fpp p fp ** , (7) Thus, we obtain Lemma 1. If equilibrium emplo yment is located within , that is, the equilibrium price is determined by the marginal cost, the equilibrium price sequ ence, (0,1) * 0 tj p, can be determined independently of the sequence of the quantity of money 0 tj M. Furthermore, the equi librium inflation rate, *1 * tj K tj p p , is constant over time. In addition, to avoid the multiplicity of equilibrium in the goods market, we define the credibility of money as follows. Definition 1. We say that money is credible when the rational expectation concerning the future value of money * 0 1 tj p is not perturbed by the change of the sequence of nominal money supply . This can be represented as follows: 0 {} tjj M *=0, ,,0. tj tk dp jkt dM Credibility of money implies that all individuals be lieve in the intrinsic value of money (the inverse of the future price level), which is not affected by the quantity of money. In other words, young individuals are ready to accept all forms of additional money at the prevailing price of the good. As long as money is credible, the ini tial price t is historically determined by the rational expectation of the previous young generation. Thus, the price t is endogenously fixed. In other words, the price become sticky not because of frictions concerning the revision of price (menu cost, Calvo rule, etc.) but because of the belief in the stability of the value of money.2 p p 2.1.3. The government Finally, we must specify the money supply rule. New money 1tt M t G is injected through the government expenditure . Thereafter, money is supplied to keep the real cash balance * 0 tj tj M p equal to the initial level * t t mp . Therefore, using Lemma 1, the real gov ernment expenditure tj is expressed by 1 * * , = =1 1, t tt tj tj tj K M Mif p G gpmifj 0, 1. j (8) Note that either t or t is the only exogenous variable in our model. In addition, for simplicity, all the goods that the government purchases are assumed to be wasted. G 2.2. Market Equilibrium There are three kinds of markets in the model: goods market, labor market, and money market. Following Walras’ Law, we confine our attention to the first two markets. When the labor market is in interior equilibrium, , the equilibrium nominal wage is equal to the nominal reservation wage 0< <1 t l t W. To clarify the discussion, let us define the neutrality of money. Definition 2. Money is called neutral iff the nominal money supply tj M never affects the equilibrium real GDP * tj y . Note that 0 tj M contains all the possi ble paths that are not confined to Equation (8). From Lemma 1 and Definition 1, it is clear that iff the goods market is located at an interior equilib rium, money is not neutral. Thus, have Theorem 1. Money is nonneutral iff the goods market is in any interior equilibrium. Proof. The aggregate demand for the good d t is de fined by 1 * =. t dKs t tt t M yc ygp (9) The third term of Equation (9) is the aggregate expendi ture of the old generation. Substituting Equation s (5), (6), (8), and the zeroprofit condition of the firm into Equa tion (9) and using Lemma 1, we obtain =. dKs tt yc ym 2Farmer [12, 13] also exhibits the price stickiness without frictions. He assumes that money socially facilitates the exchange. Owing to the expansion of opportunities for the exchange, increase in the nominal money supply initially stimulates the output, leaving the price intact. However, thereafter, the congestion in markets raises the price gradu ally and reduces the consumption. Ultimately, money is neutral in the stationary state even in his models. Since *== ds yy , the equilibrium condition of the goods market is ** = K yc ym . (10) Consequently, if money is credible and is suffi m Copyright © 2011 SciRes. TEL
125 M. OTAKI ciently small, an interior equilibrium exists in the sense that some individuals are unemployed and * 0< <1y holds. It is evident from (10) that money is nonneutral in any interior equilibrium. Conversely, if the economy is located at the boundary equilibrium , where prices cease to be equal to marginal costs, by definition, money becomes neutral. Hence, whenever money is nonneutral, the economy is in some interior equilibrium. *=1y When the prices are determined by the marginal cost, the HicksSamuelson 45° line analysis is justified under perfect competition and rational expectations without any exogenous price stickiness. If the expansionary monetaryfiscal policy is implemented, the employment and output increase. Thus, money is nonneutral. The fiscal multiplier is 1 1K c , as shown by Kahn [14] and Keynes [1]. Note that the induced effective demand theory, which is summarized by Equation (10), corresponds to the longrun stationary equilibrium without any price friction. This correspondence implies that the friction or sticki ness concerning prices is not a necessary condition for the nonneutrality of money. Furthermore, the properties of the basic model clearly differ from the new Keynesian economics, in that money is nonneutral even in the long run and the theory extended in Keynes [1] can be inter preted as the economics of the stationary state. 3. Sustaining the Quanti ty Theory of Money The previous section proves that money is intrinsically nonneutral, and an expansionary fiscalmonetary policy stimulates employment and output. This section deals with the necessary/sufficient condition for sustaining the quantity theory of money in the basic model. 3.1. Two Different Briefs on the Value of Money The basic model supports the Keynesian view that im perfect unemployment equilibrium emerges from the lack of effective demand without any price friction. Equation (7) and the concept of credibility play crucial roles in this assertion. Nevertheless, even if money is credible, the value of money is determined by its own future (rational) expec tation. Equation (7) also implies that if individuals expect money to become more valuable in the future independ ent of nominal money supply, it is soon transmitted to its current value appreciation (deflation) and vice versa. Such fragility of the base of the credibility of money is rooted in the fact that money does not provide any utility by itself. These properties of money resemble those of the fiat money we actually use. To sum up, when prices are determined by marginal costs, the value of money is determined not by its quantity but by its credibility. This is considered to be the Keynesian view on money. In other words, the fact that the price of a good is in sensitive or sticky to a monetary shock does not indicate the significant existence of various frictions on the revi sion of price but the high credibility of money. However, the monetarist view regards money only as a measure of value; hence, individuals believe that an in crease in the quantity of money brings about a propor tional price increase and has no effect on the employ ment and output level under rational expectations. In comparison with the Keynesian view, which con siders that people believe in the intrinsic value of money, the monetarist view entirely lacks the of credibility of money aspect. Friedman and Schwartz [15] consider that money can be circulated solely on the basis of the confi dence of others’ will. Although the two concepts of credibility of money and confidence of others’ will, appear to resemble each other, the situation where the confidence of others’ will be comes indispensable to sustain the monetary economy, by itself, reveals that the credibility of money is entirely lost and that the role of money has become quite restrict tive. This is because estimating the will of numerous and anonymous others is far more difficult than assuming that each individual simply believes in the intrinsic value of money. Furthermore, even if the confidence exists, another problem persists. That is, how much money do young individuals re quire in exchange for a unit of goods when the credibility collapses? Thus, once the credibility of money is lost, money ceases to have absolute substance and is re duced to the relative measure of value. In such cases, it is plausible for each individual to expect that prices are determined by the quantity of money. Such a phenomeno n occurs in the following two polar cases. In the first case, the economy is located at the full employment equilibrium. Here, any additional money does not produce any output. Accordingly, prices in crease proportionately with money. Keynes [1] calls this inflation as true inflation. The second is the polar case of hyperinflation, in which money completely loses credibility and is used only as a measure of value. Note that the seminal empirical work of Cagan [16], concerning the quantity theory of money, confines the data to the period of hyperinflation in six European countries immediately after World Wars I and II. (Greece is an exception. The data used for Greece belong to the Copyright © 2011 SciRes. TEL
M. OTAKI 126 World War II period). Accordin g to Ca gan [16], “Even a substantial fall in real income, which gener ally has not occurred in hyperinflations, would be small compared with the typical rise in prices. Relations be tween monetary factors can be studied, therefore, in what almost amounts to isolation from the real sector of the economy.” However, credibility of money was highly damaged soon after the World Wars. There are two persuasive reasons for this. First, the potential production capacity of the economy was at its lowest. In addition, govern ments were forced to monetize huge amounts of debt issued for military expenditure. Such aspects of hyperin flation are similar to those of true inflation. The second reason, which is more important than the first, concerns the incentive of labor supply. When indi viduals hold the extraneous belief that prices increase proportionately with the quantity of money, the rate of increase of nominal money supply is equal to the equi librium inflation rate. Once the inflation rate is higher than some threshold, the equilibrium nominal reservation wages begin to exceed the price of the current good. This is because the true cost of living index be comes extremely high owing to the acceleration of infla tion. Consequently, individuals begin to lose their incen tive to work. The credibility of money is entirely lost in this polar case. Contrary to Cagan [16], hyperinflation can be regarded as the pathology of the monetary econ omy. On the basis of the above discussion, in the next sub section, we shall show how the basic model is trans formed into a model that justifies the quantity theory of money. 3.2. Rational Extraneous Belief and the Monetary Policy To transform the basic model into a monetarist model, we need to assume the following. Assumption 1. Every individual believes that money is not credible and holds an extraneous belief that the price of a good is proportional to the quantity of money. That is, each individual considers that the equilibrium price function takes the following form: 1 =, tjtj tj pMM ,,j (11) where is some positive constant. Under Assumption 1, we can prove the following theorem: Theorem 2. A rational extraneous belief equilibrium exists under full employment. That is, there exist * p, * , and 1 *tj f tj M M that satisfy Equation (11) and for an arbitrarily given *=1yt . Proof. To attain the fullemployment equilibrium, the price of the good must exceed the equilibrium reserve tion wage. From Equation (7), the equilibrium price * t p should satisfy ** 1 * 1 * >> 1> 1, ** , fR fff tt ttt f tf t pW ppp p fp . f (12) Since each individual agrees with Equation (11), by sub stituting it into Equation (12), we obtain *. f 1> 1,f (13) Because is a continuous and increasing function on , taking Equation (7) into consideration, * must satisfy * >. f (14) By the continuity of , it is certain that there exists * that satisfies (14). Condition (14) assures full employment. Next, we de termine ** , ff p in order to be consistent with Equa tion (11). Note that . Then, using Equations (10) and (11), we obtain *=1y ** ** 1= ff f cc =1 f . (15) By Equations (11) and (15), we finally determine the equilibrium price function as ** tj = f tj f M p . (16) This equation completes the proof. We now deal with the case of hyperinflation. To avoid the unboundedness of the current equilibrium price, we make the following assumption: Assumption 2. There are some individuals whose dis utility of labor is zero. Their Lebesgue measure is , 0< 1 . Under this assumption, we obtain the following theo rem concerning hyperinflation. Theorem 3. A rational extraneous belief equilibrium exists where the employment and output level is at its lowest . That is, there exist , , and *h p*h *h that satisfy Equation (11) and ** ==yl . (17) Furthermore, the equilibrium inflation rate *h is the highest in comparison with the economies described by Theorems 1 and 2. Proof. From (7), the following inequality is the nec essary and sufficient condition that the employment and Copyright © 2011 SciRes. TEL
127 M. OTAKI output level is at its lowest : *1 ** < 1<1, =1, <. hR t tt t hKh p pW fp f (18) By the continuity of , there exists *h that satisfies Equation (18) . Next, we prove the existence of . Using (10), *h *** * = =1 hhh h c.c Finally, by Equation (11), we obtain the equilibrium price function as ** = tj h tj h M p . * . (19) By Equations (14) and (18), the equ ilibrium inflation rate is shown as * << Kh (20) This completes the proof. 4. The Injection Methods of Money In the previous section, we assume that money is sup plied through the government expenditure and is equally distributed to each individual. However, this differs from the rule in Lucas [4]. Lucas [4] assumes that new money is injected into the economy as interest on the existing money. In this section, we consider how such a differ ence in money supply rule affects the conclusions in Theorems 1, 2, and 3.3 Let us denote the gross rate of interest of money dur ing period as tt . Hence, the money supply rule obeys 11 = tt . t xM (21) In addition, we assume that Assumption 1 holds, and all individuals expect the equilibrium price as in Equation (11). Then, the budget constraint of each employed indi vidual becomes 112 1 12 1 , . ttttt ttt t ttt tt pcMWp cx M p ccw px 1 . t t (22) From Equation (11), 11 11 =, = ttt t pMp xM (23) Substituting Equation (23) into (22), we obtain 12 =. tt t cc wy (24) While we assume here that the production function s is Equation (6), in this section t is assumed to be hours worked per individual. Thus, the values of 1t lm and 1 , tt x are irrelevant to an individual’s consumption leisure decision, independent of the form of utility func tion. This implies the neutrality of money. Con sequently, we obtain the following theorem. Theorem 4. When every individual holds the extrane ous belief of (11) and money supply obeys rule (21) money is neutral in the sense that and 0 {} tjj x1t do not affect * . Proof. It is enough to show the unique existence of * . Equation (24) can be reinterpreted as the goods market equilibrium condition. Let us denote the optimal consumption decision as ** 12 ,cc. Note that the equilib rium output * is independent of equilibrium prices ** 12 ,pp, so are these variables. Then, by Equations (11) and (24), ** ***** 12 2 * *** 2 = =, =. tj tj M cy cyycy p cy (25) This completes the proof. A monetarist may find Theorem 4 to be very effective at the first glance. Theorem 3 implies that the quantity theory of money is upheld even in the normal economy, at least mathematically. The superneutrality of money is also supported. Nevertheless, some unusual phenomenon will be observed in this economy. That is, even if the economy possesses idling resources and the marginal cost is constant additional money only raises the price level. In other words, the credibility of money is entirely lost in the economy. Equation (11) in Assumption 1 and Equation (21) are crucial factors. The newly issued money subject to (21) refers to a kind of denomination—the change of the unit of money—and hence, it is possible for individuals to lose the credibility of money. As a result, individuals hold an extraneous belief that prices increase proportion ately with the quantity of money. Such a method of in jecting money—continuous denomination that reduces money from the absolute substance to the relative meas ure of value—is scarcely adopted. Therefore, the rele vance of Theorem 4 is much lower than that of Theorem 1. 5. Concluding Remarks 3Otani [17] has already proved that if the moneysupply rule differs from Lucas [4], money becomes nonneutral in the more general framework than ours. However, it is not his concern how the change o nominal money supply affects the macro economy. We have analyzed the mechanism of aggregate price determination, which closely relates to the problem of the neutrality of money. The results obtained are as fol Copyright © 2011 SciRes. TEL
M. OTAKI Copyright © 2011 SciRes. TEL 128 lows. First, when the economy stays within imperfect em ployment equilibrium, the price of the good is deter mined by its marginal cost, independent of the quantity of money. This conversely implies that imperfect em ployment equilibrium emerges from the lack of effective demand (or money). The stickiness of the aggregate price, which the new Keynesian economists emphasize, may not indicate the substantial cost of changing the price, but the high credi bility of money. We have succeeded in proving the ag gregate price stability by introducing the concept of credibility of money by using a model in which prices can change flexibly in accordance with exogenous shocks. Second, we have also succeeded in transforming the basic Keynesian model into a monetarist model in which the quantity theory of money is upheld and money is insignificant. The transformation requires two additional conditions to the basic model. One is the extraneous belief on the equilibrium aggregate price lev el. That is, all individuals believe that the aggregate price level changes propor tionately with the quantity of money. The other is the qualification on the rate of increase of money supply. Under such an extraneous belief, the inflation rate be comes equal to the rate of increase of money supply. Accordingly, if the rate of increase of money supply is sufficiently low, nominal reservation wages will be lower than the current pr ice of the good. Hence, fullemployment equilibrium is attained. Since newly issued money can not bear any output, the extraneous belief becomes self fulfilling. Keynes [1] calls this case true inflation. The other polar case is hyperinflation. When the rate of increase of money supply (the inflation rate) is high enough, nominal reservation wages exceed the current price of the good. In such a case, massive unemployment occurs and the production level falls to its lowest. Thus, the quantity theo ry of money holds. To sum up, the quantity theory of money is valid in the two polar cases where money loses its intrinsic valu e and only operates as a relative measure of value. Al though the money supply rule, that new money is added as interest on the outstanding money, strengthens the monetarist’s view, such a rule is rarely adopted in reality. 6. References [1] J. M. Keynes, “The General Theory of Employment, Interest and Money,” Macmillan, London, 1936. [2] M. Otaki, “The Dynamically Extended KeynesianCross and the WelfareImproving Fiscal Policy,” Economics Letters, Vol. 96, No. 1, 2007, pp. 2327. doi:10.1016/j.econlet.2006.12.005 [3] M. Otaki, “A Welfare Economics Foundation for the Full Employment Policy,” Economics Letters, Vol. 102, No. 1, 2009, pp. 13. doi:10.1016/j.econlet.2008.08.003 [4] R. E. Lucas Jr., “Expectations and the Neutrality of Mo ney,” Journal of Economic Theory, Vol. 4, No. 2, 1972, pp. 103124. [5] G. Calvo, “Staggered Prices in a Utility Maximizing Fra mework,” Journal of Monetary Economics, Vol. 12, No. 3, 1983, pp. 383398. doi:10.1016/03043932(83)900600 [6] N. G. Mankiw and R. Reis, “Sticky Information vs. Sti cky Prices: A Proposal to Replace the New Keynesian Phillips Curve,” Quarterly Journal of Economics, Vol. 100, No. 2, 2002, pp. 529539. doi:10.2307/1885395 [7] M. Woodford, “Interest and Prices: Foundations of a Theory of Monetary Policy,” Princeton University Press, Princeton, 2003. [8] J. Galì, “Monetary Policy, Inflation, and the Business Cy cle: An Introduction to the New Keynesian Framework,” Princeton University Press, Princeton, 2008. [9] R. W. Shephard, “Cost and Production Functions,” 2nd Edition, SpringerVerlag, Berlin, 1981. [10] W. E. Diewert, “Cost of Living Indexes and Exact Index Numbers,” Discussion Paper 0906, Department of Eco nomics, University of British Columbia, Vancouver, 2009. [11] K. Fukao and M. Otaki, “Accumulation of Human Capi tal and the Business Cycle,” Journal of Political Econ omy, Vol. 101, No. 1, 1993, pp. 7299. [12] R. E. A. Farmer, “Sticky Prices,” Economic Journal, Vol. 101, No. 409, 1991, pp. 13691379. doi:10.2307/2234890 [13] R. E. A. Farmer, “Nominal Price Stickiness as a Rational Expectations Equilibrium,” Journal of Economic Dy namics and Control, Vol. 16, No. 2, 1992, pp. 317337. doi:10.1016/01651889(92)90036E [14] R. F. Kahn, “The Relation of Home Investment to Unem ployment,” Economic Journal, Vol. 41, No. 162, 1931, pp. 173198. doi:10.2307/2223697 [15] M. Friedman and A. J. Schwartz, “A Monetary History of the United States18671960,” Princeton University Press, Princeton, 1963. [16] P. Cagan, “The Monetary Dynamics of Hyperinflation,” In: M. Friedman, Ed., Studies in the Quantity Theory of Money, University of Chicago Press, Chicago, 1953, pp. 25117. [17] K. Otani, “Rational Expectations and NonNuetrality of Money,” Weltwirschaftliches, Vol. 121, 1985, pp. 207 216.
