indeed is implied by the usual money-demand
relation. Then,
e(t) = m(t) - ai(t) , a > 0 (2)
where i(t) is the one-period interest rate. Fi-
nally suppose that i(t) is equal to a fixed real
rate, taken here as zero, plus an inflation pre-
mium:
i(t) = tpe(t + l) - p(t) (3)
Now if bond-market participants are aware
of the relations (1) and (2), their price expec-
tations, and therefore interest rates, will be
based upon their forecasts of future money.
Substituting (1) into (2), that is,
p(t) = m(t) - a(,pe(t + l) - p(t)) (4)
Taking the p(t) on the right over to the left
and repeatedly substituting then gives,*
1 ŋ / a ∖i
pω-τ^∑(ι+a) +
,me(t + j); where ,me(t) = m(t) (4)
Defining permanent money as the discounted
value of present and future money in the above
gives an infinite-horizon analog to the relation
in the text. In arriving at this, rational expec-
tations in its strictest sense need not be in-
voked: (4,) will be valid regardless of how
“rationally” future money is forecast. The re-
lation (4,) effectively reflects a “Fisher” inter-
est-rate impact upon prices; the implications
of this for inflation were described in detail in
Cagan’s classic article on hyperinflation.**
B. “Permanent” Money Demand
Suppose that (1) is valid but that now,
e(t) = ɪ [m(t) + tme(t + l) +
. . .tme(t + n- 1)] (2)
That is, current expenditure depends not only
upon current money but upon an average of
current and expected future money. Evidently
p(t) then will respond proportionately to per-
manent money, as defined by the right-hand-
side of the above expression.
C. Contracts and Pricing
A still simple but somewhat richer model of
permanent money and prices is based upon
contracts. Suppose in a given industry that
prices are set for several periods, say i, at a
time. Imagine also that the supply of output is
given exogenously, so that the task of the price
setter is essentially to forecast demand over
the life of the contract.*** Assume finally that
the value of industry sales in a given period is
a fixed fraction of aggregate expenditure,
which in turn varies proportionately with cur-
rent money (i.e., e(t) = m(t) ).
Now in each period, there will be a single
price which will allow the firms in the industry
to sell just the amount available, no more nor
less; define this as the “desired” price, since
if firms were not constrained by contract this
would be the price they would actually set. It
seems reasonable to suppose, then, that con-
tract prices will be set at some average of ex-
pected “desired” prices over the life of the
contract. Let p(t) now refer to the log of the
industry price. Then since “desired” prices
vary proportionately with money,
Pi(0 = ɪ[m(t) + ,mε(t + l) +
■ ■ ∙,me(t + i-l)] ≡ m*(t) (5)
where the price is newly set at the beginning
of period t (and fixed through the next i-1
periods), and where we assume m(t) is known
at that point (this is not essential). The money
forecasts might also be discounted.****
In relating aggregate prices to money, we
must take account of the fact that contracts are
likely to be staggered (i.e. expire at different
times) and to be of different lengths. Suppose
first that all contracts are of the same length
but are staggered evenly in the following man-
ner: in each period, industries whose contracts
are being renegotiated account for the same
fraction (l∕i) of aggregate expenditure. Defin-
ing the aggregate price index (in logs) as a
simple average of industry prices then gives,
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