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) + 1/3 ln(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. For questions (a), (b), (c), (d) only, suppose that c0 = 10, c1 = 5 and r = 40%:

(a) Define the competitive equilibrium of this economy.

(b) Show that, in this case, the value of one unit of period 0 consumption in terms of period 1 consumption is worth 1.5 units.

(c) Is the consumer choosing his optimal consumption bundle with the above values for c0, c1 and r? Justify your answer.

(d) What should the consumer do in this case? Illustrate with a graph (label it well).

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. 2