Academic journal article Federal Reserve Bank of St. Louis Review

The Inflation Tax and the Marginal Welfare Cost in a World of Currency and Deposits

Academic journal article Federal Reserve Bank of St. Louis Review

The Inflation Tax and the Marginal Welfare Cost in a World of Currency and Deposits

Article excerpt

HOW HIGH IS THE OPTIMAL rate of inflation? The answer depends on the range of benefits and costs associated with inflation that are considered by the monetary authority in choosing the inflation rate. For example, if one considers the effects of inflation on the distributions of income and wealth, its interactions with the tax code or the transition cost of changing the expected rate of inflation, or if one adopts the alternative perspectives of different economic agents, the benefits and costs can be relatively large and difficult to assess. This article abstracts from transitory and largely avoidable aspects of inflation, and focuses instead on the fundamental public finance aspects of the monetary authority's problem. In this case, the net benefits and costs are those associated with an inflation rate that is perfectly anticipated; the benefit of inflation that accrues to the monetary authority (typically the government) is the revenue from inflationary money creation. This benefit is analogous to the revenue arising from a specific tax on any other good or service.

Inflation imposes a tax on money holdings because it is the rate at which individuals lose the purchasing power of a dollar. To lower the total cost of holding money, individuals change their holdings and their use of money when inflation rises. Their efforts to do so, however, reduce their total services from real money balances, thereby lowering individuals' real income. This loss is the welfare cost of inflation. The optimal rate of inflation is found by comparing the marginal welfare cost of revenue from inflation with the marginal cost of alternative sources of revenue. An efficient system of tax collection minimizes the welfare cost of a given flow of tax revenue; this requires that the inflation rate must be chosen so that the marginal cost per dollar of revenue from inflation is the same as the marginal cost of alternative sources of revenue.

In the analysis below, these concepts are developed for models involving a money stock made up of currency only, competitively priced bank deposits only, and a mix of both. The differences in each case clarify the analysis as well as provide some insight into the implications of the analysis for the optimal inflation rate.

THE MARGINAL WELFARE COST OF REVENUE FROM MONEY CREATION: THE CURRENCY CASE

Almost two decades ago, it was shown that a simple formula provides a method of calculating the additional welfare cost of collecting a dollar of revenue from money creation. This measure is the ratio of the marginal welfare cost of inflation to the marginal revenue from a change in anticipated inflation.(1) To derive this formula, assume the only money is currency and that the demand for real money balances depends only on the nominal rate of interest, holding other influences constant:

(1) m = [Phi](i)

The welfare loss, W, is

(2) W = [integral of][Phi](x)dx - i[Phi](i), between limits i and 0

and the marginal welfare loss from a rise in inflation, [Pi], is reflected in the incremental loss from a rise in the nominal interest rate:

(3) dw/di = - i[Phi][prime](i).

Using the Phelps-Auernheimer (Phelps, 1973; Auernheimer, 1974) definition of the revenue, R, we have

(4) R = [Phi](i)i,

and the marginal revenue is

(5) dR/di = [Phi](i) + i[Phi][prime](i).

Since the elasticity of demand for real balances is

(6) [N.sub.i] = - i[Phi][prime](i)/[Phi](i),

the marginal welfare cost per unit of revenue, the ratio of equations 3 and 5, is

(7) dW/dR = [N.sub.i]/1 - [N.sub.i].

Equation 7 is a variant of the well-known Ramsey tax rule (tax more heavily goods in inelastic demand) and assumes, as does the Ramsey rule, cross effects absent within the taxed sector. The formula is useful in answering the question: What rate of inflation (money rate of interest) would equalize the marginal welfare cost per dollar revenue accruing to inflation tax with an index of such costs due to other distortionary taxes? …

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