Exercise 8

Due Wednesday 11/10.

Part A

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:

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

Part B

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.

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

Part C

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%.

1. 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?
2. Illustrate your results with an appropriate graph.

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