Peter J Wilcoxen > PAI 723 Economics for Public Decisions

Exercise 5

Due Wednesday 3/8

Part A

Suppose four people, person 1 (P1) through person 4 (P4), 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:

Car Horsepower MPG P1 Rank P2 Rank P3 Rank P4 Rank
A
170 22 1 2 4 2
B
200 20 1 3 3 4
C
140 24 1 1 5 1
D
200 16 2 4 3 3
E
230 14 2 5 2 5
F
260 12 2 6 1 6

Using this data, please answer the following questions:

  1. Compute the marginal rate of substitution between horsepower and fuel efficiency for person 1.
  2. Is person 4 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.

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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 03/01/2017