PAI 723 Economics for Public Decisions > Exercise 5

Solution

Here are notes on the solution. This is not a complete answer to the exercise but it will let you check your work.

Part A

  1. MRS = (200-170)/(20-22) = -15 hp/mpg
  2. Yes, although his preferences are unusual (he dislikes horsepower and fuel efficiency), they are complete (ranks all cars) and transitive (C>A>D>B>E>F).
  3. The graphs are shown below. For some of the people, too little information is given to determine the slopes of their indifference curves precisely.

    Person 1 regards hp and mpg as perfect substitutes at a 15:1 ratio; Person 2 cares only (or mostly) about mpg; and person 3 cares only (or mostly) about hp. Person 4's preferences are odd: he basically likes poor quality cars: low hp and low mpg. Because 4's preferences are complete and transitive, however, they are not irrational.

Part B

 

  1. The graph is shown below. The slope of the budget constraint is -Pn/Pm = -16/8 = -2. All bundles in set A are feasible.

  2. Assuming the tickets cannot be sold, the new budget constraint looks as shown below. The free tickets have added the bundles in area B to the original feasible set.

  3. The new budget constraint is shown below and the new feasible set is shaded. Note that the x-intercept is not affected. For reference, the original BC is also shown.

  4. Adding the time constraint to the original diagram produces the graph below. The slope of the time constraint is -10/3 = -3.33, which is steeper than the money BC. The student's feasible set is the shaded area, which extends from the origin up to 9 movies, down along the money BC to the point where the two BCs cross, down along the time constraint to 3 novels, and then back to the origin.

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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 11/04/2012