Intertemporal Choice Consider a consumer whose preferences over consumption today and consumption tomorrow are represented by the utility function U(c1, c2) = ln c1 + β ln c2, where c1 and c2 and consumption today and tomorrow, respectively, and β is the discounting factor. The consumer earns income y1 in the first period, and y2 in the second period. The interest rate in this economy is r, and both borrowers and savers face the same interest rate.
(a) Write down the intertemporal budget constraint of this consumer.
(b) Write down the optimization problem of the consumer.
(c) Solve for the optimal consumption in period 1 and period 2, i.e. c ∗ 1 and c ∗ 2 as a function of y1, y2, r, and β.