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The author is grateful to Joshua Aizenman, Mohsin Khan, and Jonathan Ostry for helpful comments and suggestions. He retains responsibility, however, for any remaining errors.
The results holds either under a constant-returns-to-scale technology or, in the presence of decreasing returns to scale, if all pure profits are taxed away.
The nominal interest rate will be also referred to as the inflation tax rate or, simply, inflation tax. The consumer’s expenditure on holding money accrues to the government because by printing money the government avoids interest costs on the public debt. Phelps (1973) discusses alternative definitions of the concept “inflation tax”.
Végh (1987b) shows that the presence of currency substitution can also render the use of inflationary finance optimal. The reason is that the foreign nominal interest rate distorts the consumption/leisure choice faced by the consumer because it acts as an indirect tax on consumption. A positive inflation rate can be shown to reduce that distortion.
Aizenman (1983) derives a similar result. However, Aizenman’s model differs sharply from the paradigm used in this paper in that it is not a public finance setup because the government makes use of no distortionary taxes other than the inflation tax.
Instead of incorporating collection costs, Aizenman (1986) assumes that consumption taxes are not feasible and studies the optimal combination of capital controls, tariffs, and inflation in financing government spending.
The analysis can be readily reinterpretated as applying to a closed economy where a domestic bond is issued.
Use has been made of the condition β=1/1+r. This condition is needed to ensure the existence of a steady state. It also implies that there are no intrinsic dynamics in the model, in the sense of Obstfeld and Stockman (1985).
where X≡m/cyθ. By substituting these expressions into the optimality condition for real money balances from the government’s optimization problem, Equation (9) obtains.
In what follows, time subscripts will be dropped. Since government spending is constant over time and undergoes only unexpected and permanent changes, the adjustment of the economy will be instantaneous because, as indicated earlier, there are no intrinsic dynamics in the model.
For simplicity, it has been assumed that b-1 =0.
Since I≡i/1+i is an increasing function of i, it makes no difference whether one refers to I or i.
The following assumptions, which remain in effect for the rest of this section, are sufficient to ensure that expression (24) is negative. Suppose that φ(z)=φ0+kz, where k>0 is a parameter, and that φ0+k<3/4. Then, 1-φ(z)-φ′(z)z=1-φ0-2kz. Taking into account that 2z<1 (because z has to be less than available resources which are one half), the condition φ0+k<3/4 is sufficient to ensure that 1-φ(z)-φ′(z)z>0 and thus that the second term in square brackets is positive. With respect to the first term in square brackets in (22), it follows from the optimality condition (21) that X>(1/2)(1/1+φ0+k). Taking d to be 1/4, it follows that the expression X2-(1+d)4X+(1+d) is negative for the range of possible values of X, which makes this term negative.
The result that the nominal interest rate remains the same is a general one, as indicated earlier. The particular specification of the model adopted here, however, also implies that, when marginal collection costs are constant, revenues from the inflation tax remain unchanged (i.e., real money balances are independent of g). This feature may not be robust to alternative specifications.
If the (steady state) budget deficit is defined as government spending minus net revenues from the consumption tax, if follows from the analysis that higher government spending leads to larger budget deficits and higher nominal interest rates.
Owing to the consideration of this particular initial equilibrium, there is no need to restrict the value of k, as before.
We choose the simplest specification (i.e., linear) for the marginal collection costs to pursue matters as far as possible. It also shows that even the simplest specification can generate more than one equilibria (in this case two equilibria); hence more complicated schedules could generate more than two equilibria. It is not clear, however, what the economic meaning of a marginal collection cost schedule of order higher than one would be. Note that a linear marginal collection costs function implies that total collection costs are a convex function of gross revenues, which has a familiar economic interpretation. If the marginal collection costs were, say, quadratic, it would mean that total collection costs have non-zero third derivatives which have no obvious economic interpretation.
Note that, in equilibrium, neither X nor z can exceed one-half (which explains the scales chosen for figures III and V). When d=1/4, X*=1/2, so that this is the maximum value of X that can be chosen without the non-negative constraint of the nominal interest rate being violated. On the other hand, z, gross revenues from the consumption tax, cannot exceed total output, which is one-half.
Lower values of k have the effect of moving upwards the upper branch of FE thus rendering it irrelevant in the sense that the intersection denoted by E1 occurs at non-admissible values (i.e., the intersection takes place outside the box depicted in Figure III).
Or, more precisely, assuming that marginal utility tends to infinity when consumption approaches zero, any level arbritarily close to 100% of GDP.
Note that there are also multiple equilibria for k-1.5.