Task 5: Consumption as young and consumption as old Now suppose Mary is thinking about her retirement and wants to understand how much to save. Today she can either con- sume or save for retirement. During her young, working life she will make 100.000 euros. Thus, her current budget constraint is Cy + S = 100.000. In her retirement she has no income, only the amount she saved as young. She can save at a rate of (1+r). So, her budget constraint as old is Co = (1+r)S. (a) Write Mary's lifetime budget constraint as plot it in a graph. Tip: Solve for savings while old and substitute in the young budget constraint. (b) Mary's utility from consumption as young and consumption as old is U(Cy,Co) 1-0 1- 0 Solve Mary's maximization problem. What is the MRS and the MRT? (c) Suppose Mary wins the lottery while young. What is the effect on her optimal decision for consumption as young and as old? (d) The local bank decided to increase the interest rate on savings. Discuss the effect of this increase on Mary's optimal consumption decision. Include a graphical discussion of the results.

Task 5: Consumption as young and consumption as old Now suppose Mary is thinking about her retirement and wants to understand how much to save. Today she can either con- sume or save for retirement. During her young, working life she will make 100.000 euros. Thus, her current budget constraint is Cy + S = 100.000. In her retirement she has no income, only the amount she saved as young. She can save at a rate of (1+r). So, her budget constraint as old is Co = (1+r)S. (a) Write Mary's lifetime budget constraint as plot it in a graph. Tip: Solve for savings while old and substitute in the young budget constraint. (b) Mary's utility from consumption as young and consumption as old is U(Cy,Co) 1-0 1- 0 Solve Mary's maximization problem. What is the MRS and the MRT? (c) Suppose Mary wins the lottery while young. What is the effect on her optimal decision for consumption as young and as old? (d) The local bank decided to increase the interest rate on savings. Discuss the effect of this increase on Mary's optimal consumption decision. Include a graphical discussion of the results.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.3P

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