Claire consumes 1 and 2 in period 1 and period 2 respectively, and her intertemporal utility function is (1, 2 ) = 21/2 2/2 . Her income in period 1 is 1 = $1,500 and period 2 is 2 = $2,000. Assume that the interest rate is 10% for both borrowing and saving.

1. Find the intertemporal budget constraint for Claire.

2. Find the optimal consumption.

3. Assume now that the interest rate for saving is only 5%. Find the new intertemporal budget constraint.

4. Would Claire be better off at the new interest rate in (c)? Discuss