Here are notes on the solution. This is not a complete answer to the exercise but it will let you check your work.
- MRS = (200-170)/(20-22) = -15 hp/mpg
- 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).
- 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.
- The graph is shown below. The slope of the budget constraint is -Pn/Pm = -16/8 = -2. All bundles in set A are feasible.
- 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.
- 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.
- 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