Suppose that Yoko's utility function for inter-temporal consumption is:

U(C₀,C₁) = [ln(C₀)] + [ln(C₁)]/(1+)

where C₀is his current period consumption, C₁is his future period consumption and (=10%) is his subject rate of time preference. If Dipo is endowed with m₀= $1000 this period and m₁= $50 in the next period. Suppose the risk-free interest rate is 3%.

A.What is his optimal consumption path (i.e., the optimal level of current and future consumption) if he can only allocate wealth through lending and borrowing?

B.Suppose now Dipo discovers Three investment opportunities. Project A is a risk-free project that needs initial investment of $1000 and it generates $1050 in the next period. Project B is another risk-free project that needs initial investment of $500 and it generates $530 in the next period. Project C is a risk-free project that needs initial investment of $225 and it generates $230 in the next period. What is his optimal consumption path now?