Syracuse University

The Maxwell School

Syracuse University

Syracuse University

*Due Sunday 11/8 at 11:59 pm*

The head of a household is concerned about consumption in two periods: 0 and 1. In period 0, she will be working and raising a family, and her income will be $200,000; in period 1, she will be retired and her income will be $50,000. Her preferences over bundles of consumption in the two periods, `C_0` and `C_1`, are given by a Cobb-Douglas utility function: `U=C_0^0.75 C_1^0.25`. She can borrow or save at an interest rate of 20 percent. In case it helps, the general Cobb-Douglas utility function and its demand equations are given below:

Utility |
Demand X |
Demand Y |

`U=Q_x^a Q_y^(1-a)` | `Q_x=(a*M)/P_x` |
`Q_y=((1-a)*M)/P_y` |

- Please calculate her intertemporal equilibrium and report how much she consumes in each period. How much does she borrow or save in period 0?
- Illustrate your results with an appropriate graph.

A student considering medical school is concerned about consumption in two periods: 0 and 1 (surprise!). In period 0 he will be in school and then doing his residency and his income will be $50,000. In period 1, he will be practicing and his income will be $400,000. He would like to have exactly 4 times as much consumption in period 1 as in period 0, and can borrow or save at an interest rate of 10 percent.

- Please calculate his intertemporal equilibrium and report how much he consumes in each period. How much does he borrow or save in period 0?
- Illustrate your results with an appropriate graph.

An individual is concerned about consumption in two periods: 0 and 1. In period 0 her income is $70,000 and in period 1 it will be $110,000. However, she also has an opportunity to spend $20,000 on a training program in period 0 that will cause her to get a $33,000 raise in period 1. Her preferences over bundles of consumption are given by the Cobb-Douglas utility function `U=C_o^0.5 C_1^0.5`. She can borrow or save at an interest rate of 10%.

- Please determine whether or not she should take the training program. Then calculate how much she consumes in each periods. How much does she borrow or save in period 0?
- Illustrate your results with an appropriate graph.

- Resources on Intertemporal Choice
- Additional information on two-period intertemporal choice and human capital decisions.

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URL: https://wilcoxen.maxwell.insightworks.com/pages/4702.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 11/09/2020

URL: https://wilcoxen.maxwell.insightworks.com/pages/4702.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 11/09/2020