Suppose the lifetime utility of a consumer is represented by the utility function

U(c, c') = c - 0.01c^2 + 0.9(c' - 0.01c'^2)

Maximize (1) with respect to c and c' subject to the lifetime budget constraint

c' = (1+r)we - (1+r)c

and prove that the consumer's utility maximizing bundle must satisfy

0.9(1+r) = (1 - 0.02c)/(1 - 0.02c')