Output Effects of Inflation with Fixed Price- and Quantity-Adjustment Costs

Article excerpt

I. INTRODUCTION

There is convincing evidence that fixed costs of price adjustment may be large. Levy et al. (1997) found such costs to be 0.7% of a firm's revenue, and Zbaracki et al. (2004) found them to be 1.22%. In the presence of fixed costs of price adjustment, a monopolistic firm does not adjust its nominal price continuously, with the result that the real price and output generally deviate from their static monopoly level. At low inflation rates, the average output is higher than the static monopoly output if there is positive discounting (Danziger 1988) and depends on higher order derivatives of the profit and demand functions if there is no discounting (Benabou and Konieczny 1994). (1)

Most of the literature assumes that only price adjustments are costly, while output can be continuously adjusted without cost. However, Bresnahan and Ramey (1994) document that there may be large fixed costs of quantity adjustments. Relatedly, many publications show that adjusting labor and capital inputs involves significant fixed costs. (2) Such costs may derive from loss of organizational capital (Baily et al. 2001; Jovanovic and Rousseau 2001), as well as from job protection rules, severance pay, and legal and administrative complications.

In a framework with both price--and quantity-adjustment costs, Andersen (1995) and Andersen and Toulemonde (2004) demonstrate that only intermediate-size shock--but not large or small shocks--may affect output. For a constant inflation rate, Danziger (2001) shows that a firm's permanent production decreases with inflation at low inflation rates if discounting is positive, and Danziger and Kreiner (2002) that output capacity decreases with inflation if the elasticity of demand is constant and there is no discounting (see also Danziger 2003).

The purpose of this article is to provide a simple general characterization of the output effects of a constant inflation rate if both price and quantity adjustments involve fixed costs. It is assumed that quantity adjustments are at least as costly as price adjustments, which implies that a firm's production is held constant at a permanent level. (3) Each firm then keeps its nominal price unchanged in periods of equal length, and the nominal price is adjusted so that the initial real price is the same in each period. Thus, a firm's optimal strategy consists of the initial real price, the duration of the periods with unchanged nominal price, and the permanent level of production.

The article shows that in the absence of discounting, the effect of inflation on the aggregate production depends on how fast firms' marginal real revenue decreases with demand and that this effect is fully determined by the elasticity of the marginal real revenue with respect to demand. Thus, aggregate production decreases with inflation if the elasticity of the marginal real revenue always exceeds minus unity, increases with inflation if the elasticity of the marginal real revenue is always less than minus unity, and is invariant to inflation if the elasticity of the marginal real revenue always equals minus unity.

Several studies have found that the comovement between output and prices is typically negative in the long run (Cooley and Ohanian 1991; Den Haan 2000; Den Haan and Sumner 2004; Fiorito and Kollintzas 1994). Within the framework of the present model, the negative comovement indicates that the empirically relevant situation is when the elasticity of the marginal real revenue always exceeds minus unity. This will be the case, among others, if demand functions exhibit a constant price elasticity less than minus unity (as assumed in Danziger and Kreiner 2002).

II. THE MODEL

Consider an economy with a unit continuum of identical consumers and a unit continuum of monopolistic firms producing differentiated perishable products. Each firm and its product are indexed by i, which is uniformly distributed on (0, 1]. …