## Economic Commentary on the Costs of Inflation

### 2. Measuring the Costs of Inflation

In any product market, the socially efficient quantity of output is determined by the quantity at which the marginal costs of production equal the marginal social benefit of an additional unit of output. In general, we can think of the latter as the price of the product in question. In the case of money, the relevant "price" is a nominal interest rate since it tells us the return that must be foregone to hold dollars instead of some other asset that yields the market interest rate.

What is the marginal cost of producing money? In the United States, the Federal Reserve is the sole supplier of central bank money (currency and bank reserves - the accounts that commercial banks hold with the Fed). The marginal cost of producing central bank money is, effectively, zero. Applying the principle that the most desirable level of production requires setting the price equal to marginal cost, the socially efficient quantity of money would be that amount at which the nominal interest rate (the "price" of money) equals zero. An implication of this analysis is that an optimal monetary policy would result in nominal interest rates equal to zero - a proposition widely known as the Friedman rule.

If optimal monetary policy implies a zero nominal interest rate, what should the inflation rate be? A relationship known as the Fisher equation tells us that the nominal interest rate is (approximately) equal to the inflation rate plus the real rate of interest. Consequently, the optimal inflation rate is the negative of the real interest rate. For example, if the real interest rate is 3 percent, then theoptimal rate of inflation is –3 percent. By similar reasoning, the value of the nominal interest rate tells us how much the inflation rate exceeds its socially optimal level.

Clearly, the zero nominal interest rate implied by the Friedman rule typically is not observed in practice. How large are the implied costs of deviations from the socially optimal rate of inflation? In extreme cases, these costs can be substantial. Using evidence for seven European hyperinflations between 1920 and 1946, Martin Bailey found that the largest welfare cost was on the order of half of income, while a "typical" cost was around a third of income.

What "real-world" phenomena do these welfare cost calculations capture? Bailey describes them as the costs associated with changes in habits and payment procedures. For example, during hyperinflations, it is common to see people eschew the use of currency in favor of less efficient barter transactions. (Barter is less efficient than using money because barter requires a double coincidence of wants, while money only requires a single coincidence since everyone will accept money). As inflation becomes more severe, workers demand to be paid more frequently. Having received their wage payments, households rush to purchase consumers goods or assets like foreign currencies. All of these activities are costly and disruptive to an economy.

What about more modest inflation experiences? Stanley Fischer, using money demand estimates for the United States, calculated that lowering the inflation rate from 10 percent to 0 percent would generate a welfare gain of between 0.3 and 0.8 percent of output. While this figure may seem fairly modest, when applied to U.S. GDP for 1999, it implies a deadweight loss of between $28 billion and $74 billion. The magnitude of this welfare cost is comparable to that associated with other distortionary taxes. Furthermore, this welfare gain can be achieved each and every year - it is not a once-off gain.