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%

(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 CO, C1