Ck 7 C) 121

Consider the following Cash-in-Advance (CIA) constraint model with inelastic labor. The representative household chooses {c,,k1lAft}rie to max-imize

subject to

and

00 E u (co

Mt ML-I + kt+ + = F(kt-t) + (I – 45)kt-t + Pt

et < Pt

r, is lump-sum taxes (or transfers if r < 0). The government finances purchases {Th.} with lump•sum taxes and money creation to satisfy

Ms – MI-1 91= +

As in the lecture note, we assume that the money supply is given by

Aft = pat-1 where p, is the money growth. Assume that in the steady suits money growth and government spending are constant: it, = p, g, = g. Assume preferences and production functions satisfy the usual properties.

(i) Define equilibrium of this economy (i.e., complete the following statement: “The equilibrium of this economy is defined as endogenous variables … satis-fying … equations”). Be explicit on the endogenous variables and make sure that the number of endogenous variables are equal to the number of equations characterizing equilibrium (mentions. Also, when writing the equilibrium con-ditions, use Ira, E * and r, art- in place of M, and Pt so that Af„ Pt do not appear in the equilibrium conditions. Finally, note that 9, is an exogenous variable in this model.

(ii) Characterize how the steady state equilibrium depends on money growth p. lb be more specific, derive the steady state of each variable as a function of parameters (e.g., rt, 9, /I, 6, …). If needed, you can denote inverse function of an arbitrary function f as f-1. Then, show how the steady state capital stock, consumption, inflation, and real money supply depend on the steady state money growth p.

Sample Solution

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