Money Demand and Seigniorage-Maximizing ... - William Easterly

WILLIAM R. EASTERLY, PAOLO MAURO, AND KLAUS SCHMIDT-HEBBEL : 585
those obtained when using conventional but incorrect measures of inflation. Section
3 concludes.
1. THE MODEL
This section develops a simple model of money demand, inflation, and seigniorage.
It shows that both the semielasticity of money demand with respect to the opportunity
cost of holding money and the inflation rate that maximizes seigniorage in
the steady state depend on the degree of substitutability between money and bonds.
In addition, the inflation semielasticity of money demand is shown to vary with
inflation.
An infinitely lived optimizing representative agent takes consumption, investment,
and portfolio decisions in a closed economy. This agent holds money and
bonds for transaction purposes and maximizes a standard intertemporal utility
function:
rX cl-J - 1
max J e-Pt dt (1)
where p is the discount rate, c is consumption, and 1/cr is the intertemporal elasticity
of substitution.
Production (y) in the one-good economy is assumed to depend only on a broad
concept of capital (k), as in Barro (1990) and Rebelo (1991):3
y = A k . (2)
There are three assets available to the consumer capital k, nonindexed money
(real value m), and indexed money (real value b, referred to as "bonds" for short).
Bonds pay no interest, but are fully indexed to the price level.4 We assume that
inflation cannot fall below-A. There is no uncertainty. Since capital has real return
A (net of depreciation), it always dominates bonds and money. However, a cash-in-
advance constraint requires that some combination of money and bonds must be
held in order to purchase consumption goods:
f(m, b)-c-O (3)
3. Population is assumed fixed and normalized at one, so all variables can be interpreted
in per capita
terms.
4. The classic example of this kind of asset in developing countries is foreign currency, which main-
tains its value as the nominal exchange rate moves with the domestic price level. Other kinds of highly
liquid financial assets often pay a nominal return adequate to compensate for inflation but little or no real
return. Formally inflation-indexed assets paying a zero real return exist in some developing countries.
This was the case of selected bank deposits held by households in China between mid-1988 and late
1991. UPAC deposits held in Colombia's savings and loan associations are highly liquid deposits indexed
by consumer prices. Real assets are also often used as inflation hedges.