Assignment:
Consider the liability example in the powerpoint for the lecture of September 11. Suppose
p(x, y) = 1 - x - y/2
c(x)= x2 and g(y)= y2.
Dx =Dy=0.5.
1. Find the optimal level of care x and y and the optimal accident probability.
2. How would double strict liability work in this example?
3. Suppose the legal system is strict liability, with X being strictly liable. How much care does each exert? What is the probability of an accident?
4. The friends of X say that Y should be strictly liable not X. Without doing arithmetic explain why this change would not be a potential Pareto improvement.
5. Now suppose that legal system is negligence, with the acceptable level of care being set at the optimal level for X. How much care does each exert? What is the probability of an accident?
6. Consider 100 identical men in a theater who want to use the men's room exactly 3 minutes before the movie starts. The number of men who can use the men's room in a minute is 10. Each man bears a cost of $1 per minute if he leaves the men's room early (he has to sit through inane commercials and coming attractions), and $4 for every minute he is late. Waiting (waiting on line) cost is $2.50 per minute.
7. Suppose that this is a normal men's room with no congestion pricing in effect. Suppose you exit the men's room 6 minutes before the movie begins (3 minutes before the optimal time) (after washing your hands, of course). How long did you have to wait?
8. If the optimal congestion pricing scheme were in effect, and you exit 6 minutes before the movie starts, how much would you pay?
9. Sketch the optimal congestion pricing scheme for the men's room.
10. There are 75 women with the same costs per minute as the men for being early, being late, and waiting. The women's room, however, accommodates only 5 women per minute. Consider a woman who exits 6 minutes before the movie begins (3 minutes before the optimal time). How long did she wait?