4. markets clear: labor,
z0∆ (z, dz0) λ (da × dz)= n (a, z) λ (da × dz) ,
W
deposits,
hh = p∣ aλ (da × dz) + p ʃ max [0, a — k (a, z)] λ (da × dz) ,
(4)
(5)
and loans,
--1) h — b = p ʃ max [0, k (a, z) — a] λ (da × dz) ,
5. the aggregate feasibility constraint holds at equality
[c (a, z0)+a0 (a, z0)] ∆ (z, dz0) λ (da × dz)
= (1 — δ)aλ (da × dz)+
z0f [k (a, z) ,n(a, z)] Q (z, dz0) λ (da × dz)
6. and the gross growth rate of nominal prices is
μ = 1 + RB b.
Of course, by Walras’ Law, one of these conditions is redundant. In this definition,
it is implicit that the markets for central bank’s certificates of deposits and reserves
clear. Once we know these variables, the price level is determined from
P = Xp.
Notice also the model is neutral with respect to changes in government lia-
bilities as long as the central bank changes certificates of deposit and reserves
proportionally. That is, for any proportional change in (H, B), individual deci-
sions are not affected, so the equilibrium is the same in terms of real or normalized
variables and the only difference is a change in the nominal price level P .One
way to see the determination of the price level is as a ratio of the units of account
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