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Bailey's measure of the welfare costs of inflation as a general-equilibrium measure.

Article Excerpt
SINCE THE SEMINAL work of Bailey (1956), economists have devoted considerable effort to measuring the welfare cost of inflation. Bailey's formula has been derived in a partial-equilibrium setting. It treats real money balances as a consumption good and inflation as a tax on real balances. The welfare cost is computed by measuring the area under the inverse money demand function.

Lucas (2000) has shown that, for small values of the nominal interest rate, Bailey's measure happens to give a good approximation to the general-equilibrium measures that emerge from the Sidrauski and the shopping-time models.

The purpose of this paper is to show that Bailey's formula can actually be obtained in Sidrauski's general-equilibrium framework as the correct measure of the welfare costs of inflation by considering a specific class of utility functions. As stated by Gillman (1995, p. 1): "Evidence suggests that integration under the money demand function appears applicable in general-equilibrium economies." Based on a specific utility, this conjecture is proved here.

This point is important because Bailey's methodology has served as the basis for several well-known measurements of the welfare costs of inflation in the economic literature (e.g., Bailey 1956, Lucas 1981, Fisher 1981, among many others).

Moreover, one can still find many measurements of such welfare costs based on Bailey's formula (e.g., Lucas 2000, Attanasio, Guiso, and Japelli 2002, Serletis and Virk 2006, Craig and Rocbeteau 2006, Ireland 2007), and therefore, all such measurements are subject to the usual criticism that they originate from a partial-equilibrium analysis. (1)

This paper provides a counterexample to this usual proviso that Bailey's measure is to be regarded as no more than a partial-equilibrium measure. For a specific class of utility functions, we show that Bailey's measure provides ah exact measure of the welfare costs of inflation derived from an intertemporal general-equilibrium model of the entire economy, rather than just from a partial-equilibrium analysis of one single market.

1. THE MODEL

To simplify the exposition, we present Sidrauski's model in a continuous-time setting and abstract from growth considerations. Real output is normalized to 1.

We shall write M for money, B for bonds, P for the price index, and c, m, and h, respectively, for real consumption, real money balances, and real lump-sum taxes. The amount rB stands for the nominal interests paid by bonds to the representative consumer.

Given g > 0, the representative consumer is supposed to derive utility from the maximization of real consumption and real balances according to:

[[integral].sup.[infinity]] [e.sup.-gt]U(c, m)dt, g > 0, (1)

where U is a concave...

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