Hi tutor,

could you tell me how to solve this 3 period utility maximizing problem? thanks!

Consider a representative consumer who lives for three periods, he or she has an exogenous endow ment stream given by y1,y2,y3 and can borrow and lend at a given interest rate it, which is the interest rate between period t 1 and period t. Assume that he/ she starts out with no wealth (that is, f0 = 0). The discount factor is ,3 = 1. The consumer's problem is: maxcljcz 1:,(01) + Meg) + u(03) subject to C1+b1=y1 C2+bg=yz+(1+i1)bl Cs=ys+ll+12)'b2 1. For simplicity, assume that it = 0. Further assume the following form for the utility function: u(c) = ln(c). Solve for the optimal consumption plan for the three periods