Price Dispersion, Inflation, and Welfare*

Abstract

Several empirical studies have documented a positive relationship between the rate of inflation and the dispersion of consumer prices. We examine this relationship and the welfare costs of inflation in a monetary economy in which ex ante identical buyers search among prices posted by identical sellers. Under certain conditions, stationary monetary equilibria of our economy necessarily exhibit dispersion of real prices. If the degree of buyers' incomplete information about posted prices is fixed exogenously, both price dispersion and the average real price are increasing in the inflation rate. Money creation lowers welfare by increasing the market power of sellers and exacerbating the effects of the inflation tax. As the rate of inflation approaches the Friedman rule, price dispersion and welfare costs both vanish. If households choose the number of prices to observe, then the Friedman rule is not optimal. Rather, up to some point increased inflation lowers the average real price and raises welfare by inducing search and eroding sellers' market power.

Optimal fiscal and monetary policy when money is essential

“…1 This optimal deviation from the Friedman Rule is not because the inflation tax acts as a substitute instrument for a missing tax, as is sometimes 1 In a different context, one that abstracts from public finance considerations, Rocheteau and Wright (2005) show that a positive nominal interest rate may be optimal because it can correct inefficiencies along the extensive margin of bilateral trading by influencing the relative number of traders on each side of the market. In other micro-founded models of money that also abstract from public finance considerations, Shi (1997), Bhattacharya, Haslag, and Martin (2005), and Head and Kumar (2005) also find that deviations from the Friedman Rule can be optimal.…”

Relative price variability and inflation: New evidence

“…Results for the Euro area presented by Nautz and Scharff (2012), indicate that inflation significantly increases RPV only if inflation is either very low or very high in the range of their sample values. 3 More recently, conformable with recent monetary search and Calvo-type model predictions (see Head andKumar, 2005 andChoi, 2010), evidence has been provided of a U-shaped relationship between inflation and RPV by Choi (2010) for the US and Japan, Choi and Kim (2010) for the US, Canada and Japan, Becker (2011) for a panel of European countries, and Fielding and Mizen (2008) for the US. 4 Moreover, in a more recent study of the effect of inflation targeting (IT) on the inflation-RPV nexus, Choi et al (2011) analyzed a data set of twenty industrial and developing countries consisting of 12 targeters and eight non-targeters, including Turkey, during the so-called great moderation period.…”

“…Contrary to these aforementioned studies, during highly inflationary episodes, the association between inflation and inflation variability is significantly lower. However, Bick and Nautz (2008) found that for the US, both positive and negative effects of inflation on RPV are observed in the sense that in-1 Whereas menu cost or Lucas-type confusion models predict linear and positive associations between inflation and RPV, recent monetary search and Calvo-type models (see Head and Kumar (2005) and Choi (2010)) predict an inflation-RPV nexus with a U-shape form 2 See Van Hoomissen (1988), Lach and Tsiddon (1992), Parsley (1996), and Lastrapes (2006), among others.…”

Money, price dispersion and welfare

“…Also, the marginal effect of i on utility throughz is negligible, and so a marginal change in i affects utility entirely through its effects on q * (z) and y. 11 The second-order partial derivative of net utility with respect to i is negative under the maintained assumptions L > 0 and B < 0. Thus, the optimal choice of i is interior.…”

“…Because a buyer makes take-it-or-leave-it offers, his average surplus per match is the utility of the average level of quality-weighted consumption per match minus the average cost of production. 11 …”