3. Polly Pocket will live only for two periods. In the first period, she will earn $50,000. In the second period, she will retire and live on her savings. Her utility is (1, 2) = (1 + 100)(2 + 10), where 1 is what she consumes in period 1 and 2 is what she consumes in period 2, and the marginal rate of substitution is (2 + 10)/(1 + 100).

She can borrow and lend at the interest rate of 10%.

a. Write down Polly's intertemporal budget constraint and graph it below, with consumption in period 1 on the horizontal axis and consumption in period 2 on the vertical axis. Make sure to label the intercepts and endowment point.

b. What is her optimal amount of consumption in period 1 and in period 2?

c. Suppose the interest rate decreases. Graphically show the effect of this change to the budget constraint. Is Polly better or worse off than before, or uncertain? Briefly justify your answer