Suppose that Yokos utility function for inter-temporal consumption is:

U(C₀,C₁) = [ln(C₀)] + [ln(C₁)]/(1+)

where C₀ is his current period consumption, C₁ is 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%. 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 (C₀,C₁)?

1. C₀=567.0365; C₁=530.9524
2. C₀=549.2372 , C₁=514.2857:
3. C₀=1050; C₁=0
4. C₀=1000; C₁=50