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 carms 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?

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 carms 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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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
carns 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 e + B log efand 8 = 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.
5. 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?

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