This paper offers a monetary model with two applications: to measure the welfare cost of inflation, and to analyze the behavior of prices after an interest rate shock. The link between inflation and welfare is the deviation of resources from consumption to the management of money. Prices are flexible, but they do not adjust instantaneously to a change in the nominal interest rate.
As in Baumol (1952) and Tobin (1956), money is useful for transactions but agents incur a transfer cost whenever they exchange bonds for money. Moreover, money holdings do not receive interest. The economy has infinitely-lived consumers with different endowments and constant relative risk aversion utility. The utility function is in terms of goods only: neither money nor the transfer cost enter in the utility function.
The analysis offers two contributions. The first is to measure the welfare cost of inflation for different preference parameters with infinitely-lived consumers, consumption smoothing, and transfer cost in goods. The second is to describe the behavior of prices after a permanent increase in the nominal interest rate.
The welfare cost of inflation is defined as the income compensation required to leave consumers indifferent between an economy under positive interest rate and one with zero interest rate. According to the model, consumers are indifferent between an economy with 10% p.a. inflation and an economy with zero inflation if the income of each consumer is 1% higher in the first economy. This estimate agrees with the findings in Lucas (2000). The elasticity of intertemporal substitution has a small effect on the welfare cost of inflation. The model is calibrated using U.S. data from 1900 to 1997.
When the nominal interest rate is positive, agents use their resources to maintain the optimal level of money holdings. An increase in the interest rate decreases average consumption and increases the variation of consumption. The first effect happens because agents exchange bonds for money more frequently. The second effect is a consequence of the concentration of consumption in the beginning of each holding period.
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Monetary Dynamics in a General Equilibrium Version of the Baumol-Tobin Model
