Due Wednesday 11/7
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:
Utililty: `U=Q_x^a Q_y^(1-a)` Demands: `Q_x=(a*M)/P_x` and `Q_y=((1-a)*M)/P_y`
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.
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 `U=C_o^0.5 C_1^0.5`. She can borrow or save at an interest rate of 10%.