Consider a two period economy populated by identical consumers that have the same income. All consumers' preferences over C0 and C1 are described by the same utility function

u(C0, C1)=ln(C0)+1/3ln(C1)

There is also a government whose objective is to spend G0 in period 0 and G1 in period 1. This government collects lump-sum taxes each period and can issue bonds in period 0 (B0). Each bond pays interest rate (r) and must be fully repaid in period 1. Consumers save and borrow with the same interest rate r of the government. Consumers' optimal decision, given r, imply that

C0*(r)=3/4(Y0-T0)+3/4((Y1-T1)/(1+r))

Finally assume that Y0=100 and Y1=40

suppose that C0=10 C1=5 and r=40%

For the next questions only, suppose that G0 = 40, G1 = 16, and that the government borrows (has a debt) of 5 in period 0:

(e) Calculate taxes in period 0 (T0) and taxes in period 1 (T1) when r = 20%.

(f) Calculate period 0 private saving and national saving when r = 20%.

(g) What can you conclude about the market from your calculations in part (f)?

(h) Why is this economy not in equilibrium when r=25%? Should r increase or decrease in this case? Explain.