1. Cristina 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 earning from working is $60,000 and when old, she earns no labor income - she is retired. Furthermore, suppose that she can put her savings into an IRA with a rate of return of 30%. (a) Derive Cristina's budget constraint when young and when old as well as her intertemporal budget constraint. (b) Plot Cristina's 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? (c) 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 should she save for retirement to achieve this? (d) Suppose that her utility function is given by Inc+ 31Incf and 8 = 0.9. What is the level of consumption when young and old that maximize her utility? How much should she save for retirement to achieve this? Hint: Use the derivation in lecture to calculate the optimal level of consumption when young and old