Question

Consider a two-period model economy populated with consumers that have the same income and the same preferences. There is also a government whose objective is to spend 60 in period 0 and 150 in period 1. This government can issue bonds in period 0. Each bond pays interest rate r. Consumers can also issue bonds at the same interest rate .Consumers’ optimal decisions, given r, imply that aggregate consumption C*0 is equal to2/3(Y0− T0) +2/3(Y1− T1)/(1 + r). Suppose Y0= 300 and that income is expected to remain at this level in period 1
a)define the competitive equilibrium of this economy
b) Show that, together, the three conditions given in a) imply that the equilibrium value of r is given by
r = (2(Y1-G1)/Y0-G0)-1.

Answer 1

$A) Y0=C0+G0$

$300=\frac{2}{3}*(Y0-T0)+\frac{2}{3}*\frac{Y1-T1}{1+r}+60$

if the economy is closed, G=T

$300=\frac{2}{3}*(300-60)+\frac{2}{3}*\frac{300-150}{1+r}+60$

$r=0.25$

$B) r=2*\frac{Y1-G1}{Y0-G0}-1$

$r=2*\frac{300-150}{300-60}-1$

$r=0.25$