سیاست های پولی بهینه به صورت تصادفی با انعطاف ناپذیری اسمی

This paper studies a money-in-the-utility function model with imperfect competition and one-period ahead nominal price setting. Under standard assumptions on preferences, Friedman's rule—setting the money growth rate equal to the household time discount factor—generates an equilibrium that is optimal within the class of deterministic policies. We then provide conditions under which a random monetary policy increases ex ante expected welfare relative to Friedman's rule. The result obtains because random policy can reduce the distortion associated with imperfect competition. Our result exhibits original features relative to existing cases of welfare-improving random monetary policy, such as Polemarchakis and Weiss (J. Econom. Theory 15 (1977) 345).

Optimal monetary policy has been studied extensively when the transactions demand for cash is the sole monetary friction.1 In these environments, the government often should maximize real balances by equating the rate of return between monetary and non-monetary assets. Friedman's rule—setting the money growth rate equal to the household time discount factor—often accomplishes this goal. Much less work addresses this problem when additional frictions, such as nominal price rigidity, are present.2 With imperfect competition and predetermined prices, adding a purely random component to the money growth rate may improve on Friedman's rule from the standpoint of households’ ex ante expected utility. We model imperfectly competitive product markets by assuming that firms engage in monopolistic competition. Nominal rigidity exists because each firm must set its nominal price one period in advance. Money-in-the-utility function (MIUF) is the source of money demand.3 Here is the intuition for why randomness can be welfare improving. Firms choose a price to maximize expected real profits discounted by marginal utility. If marginal utility is sufficiently convex, firms respond to monetary policy risk by lowering their expected markup.4 Reducing the expected markup raises expected household consumption, which offsets the market power distortion. The fall in the expected markup must be sufficiently large to offset the decrease in expected utility caused by introducing consumption variance. Our mechanism is different from another case where random monetary policy is welfare improving. Polemarchakis and Weiss [18] establish that the optimal money growth rate involves infinite variance in the Lucas [12] islands model. In the islands model, imperfect information leads households to respond to information about prices in a distortionary manner. Adding noise to the money growth rate leads households to ignore this information and distortionary activity is not undertaken. A criticism of this form of optimal randomness is that, realistically, governments do not want to destroy the information content of prices. Our mechanism applies to a different class of models and is not subject to this criticism. Our paper is closely related to the work of Blanchard and Kiyotaki [3], who study an economy with MIUF, monopolistic competition and predetermined prices.5 In that paper, holding nominal prices fixed, monetary injections can raise aggregate demand, thereby increasing output and welfare. We expand on Blanchard and Kiyotaki by modelling dynamic nominal price setting and stochastic monetary policy explicitly, whereas they consider a static, deterministic model. In the next section, we describe the model and its associated equilibria. In Section 2, we prove a theorem concerning the optimality of random policy. Section 3 concludes.

Optimal policy may contain a purely random component in a standard imperfect competition-predetermined price model. The result is more likely with greater market power, greater consumer prudence and less consumer risk aversion. If all conditions are met, it begs the policy question: does or should the Federal Open Market Committee set policy with a roulette wheel? Probably not; however, national economies are constantly being hit by small, random shocks to money demand. Whereas this paper considers random money supply disturbances, alternatively random money demand shocks can generate variation if they are not neutralized. If a central bank chooses not to or cannot neutralize every shock, then money demand shocks could act as a natural randomization device. From the standpoint of policy, our results speak to an important operational question: how costly is low, variable inflation? Recently, a number of authors have attempted to characterize the welfare losses associated with low inflation in the US.14 Others advocate policies that, in principle, can insure price stability, such as targeting CPI futures [7] and targeting inflation [17]. This paper raises a new potential benefit of random monetary policy in an economy with predetermined prices. Small, random money injections may allow a central bank to reduce the distortion due to market power.