Problem 4: Consumption and Saving Christina is a young worker who wants to plan for her retirement early in life. Suppose that she receives an inheritance of $50,000. When she is young, her earnings from working is $60,000 and when old, she earms no labor income –- she is retired. Furthermore, suppose that she can put her savings into an IRA with a rate of return of 30%. 1. Derive Christina's budget constraint when young and when old as well as her intertemporal budget constraint. 2. Plot Christina's intertemporal budget line – use the x-axis for consumption when young. What is the slope of her budget line? What is the highest level of consumption that she can achieve when young? What is the highest level of consumption that she can achieve when she is old? 3. Suppose (only for this part) that she likes to equate consumption when young and old. What would be her consumption level when young and old? How much would she save for retirement to achieve this? 4. Suppose that her utility function is given by log c+ B logeʻand ß = 0.9. What is the level of consumption when young and old that maximize her utility? How much would she save for retirement to achieve this? Hint: use the derivation done during the lecture to calculate the optimal level of consumption when young and old. S. The U.S. government is concerned about the well-being of retired individuals. A program is put in place that imposes a lump-sum tax of $10,000 on Christina when she is working and provides a social security benefit of $10,000 when she is old. How does this change Christina's budget line (assume that the interest rate does not change)? What happens to her optimal level of consumption when young and old compared to when there are no taxes and no benefits (part 5)? What about saving?