Exercise 6

Due Thursday 10/16 [note unusual day]

Part A

Suppose four people, "A" through "D", are asked to rank several hypothetical cars with different combinations of features. Each person is to assign a rank of 1 to the car they like the most, a 2 to the car they like second most, and so on. If they like two cars equally, both receive the same number (eg, there may be two cars ranked 2). The table below shows the results:

Using this data, please answer the following questions:

1. Compute the marginal rate of substitution between horsepower and fuel efficiency for person A.
2. Is person D rational? Explain.
3. Sketch some possible indifference curves for each person for different combinations of horsepower and fuel efficiency (MPG). Please use one graph per person, and put Q MPG on the horizontal axis. Note that you won't be able to compute the MRS for some of the people, but it's still possible to sketch some appropriate curves.
   
   

Part B

A graduate student has $72 to spend on entertainment during a typical month. His favorite activities are reading novels and going to the movies. The price of a movie is $8 and the price of a novel is $16.

1. Draw the student's monthly budget constraint for entertainment, with movies on the vertical axis. Show which bundles are in his feasible set and which are not. Calculate the slope and intercepts of the budget constraint and briefly discuss what they mean.
2. Suppose that one month the student receives two free movie tickets. Draw a second diagram showing how the free tickets change his budget constraint that month. The free tickets apply only to this question; do not include them in the remaining calculations. Also, you may assume that the student cannot sell the tickets.
3. Suppose the government imposes a tax on movies and the price of a movie rises to $10. Show how the student's budget constraint changes and calculate its new slope. The tax only applies in this question.
4. Now suppose that the student's coursework is building up and he feels he can only spend 30 hours each month on recreation. Watching a movie takes him three hours and reading a novel takes 10 hours. Draw an appropriate graph showing his feasible set after the time constraint has been added.
   
   

Part C

A recent MPA graduate looking is looking for an apartment in the Washington area. She would like to have a spacious apartment but also plans to use enough heating and air-conditioning to be comfortable in winter and summer. She knows from experience that she will use exactly one kilowatt-hour (kwh) of electricity per square foot of floor space per month. Rents in the neighborhood where she would like to live are $0.90 per square foot per month, and electricity costs $0.10 per kwh.

1. Assuming she has $1000 a month to spend on rent and utilities, draw her budget constraint and a couple of her indifference curves. Show her equilibrium and calculate how many square feet of apartment space and kwh of electricity she consumes.
2. Now suppose she gets a promotion and can afford to spend $1500 on rent and utilities. Show her new equilibrium and calculate her consumption of each good.
3. Starting from the initial equilibrium in part (1), suppose the price of electricity rises to $0.20 per kwh. Calculate her new consumption bundle and show your results on a graph.