a) Suppose a consumer lives for three periods and maximizes a lifetime utility function: U(c1,c2,c3)=c1+c2+c3. i) If the consumer enters period 2 with an income of W2, find the value function, V, for the final two periods. The price of consumption each period is one. [15] i) Use this value function to convert the problem into a two-period problem and solve. The consumer enters period 1 with income W1. [20] ii) Determine the value function at the start of period 1. [10] a) Suppose a consumer lives for three periods and maximizes a lifetime utility function: U(c1,c2,c3)=c1+c2+c3. i) If the consumer enters period 2 with an income of W2, find the value function, V, for the final two periods. The price of consumption each period is one. [15] i) Use this value function to convert the problem into a two-period problem and solve. The consumer enters period 1 with income W1. [20] ii) Determine the value function at the start of period 1. [10]