Consider a two-period economy populated with consumers thai have the same income and the same preferences. There is also a government whose objective is to spend 60 in period O and 150 in period 1. This government can Issue bonds in period O. 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 Cd is equal to { (Yo To) + {(YI + r). Suppose that Yo = 300 and that income is expected to remain at this level in period 1.

b)Show that, together, the three conditions given in a) imply that the equilibrium value of r is given by

2(YI - Gl)