Consider a two-period 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 to 2/3(Y₀.-T₀ )+2/3(Y₁-T₁p/(1+r). Suppose that Yo = 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.

A major recession begins in period 0. As a result, economic activity falls by 18 in period 0. Economists expect this recession to continue into period 1: National income is expected to fall by 20 in period 1. Consumers believe these economists.

c) Use a graph to explain why the equilibrium interest rate r falls from 0.25 to 0.2 in period 0 as a consequence of this recession.