Hoisted from the Archives from a Year Ago: Externalities

Externalities can be subtle…

Let us move across the bay and 60 miles south from Avicenna to the town of Tall Stick, home of Crony Capitalism University…

The 10,000 students at CCU do two things with their disposable incomes of $5,000/year each: • Buy gourmet pizzas at$20/pizza
• Rent BMWs at \$5000/year

The utility of each student is:

U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs)

This utility function thus has both envy and spite…

Questions:

1. If nobody rents a BMW, what is the utility of a typical student?

2. If nobody else rents a BMW, what is the utility of a student who rents one?

3. If everybody else rents a BMW, how does a typical student spend his or her money?

4. If everybody else rents a BMW, what is the utility of a typical student given his or her choices?

5. Since it made sense for each student to rent a BMW, how come moving from a situation in which nobody rented one to one in which everybody rented one reduced average utility from 250 (which is the answer you should have gotten for D.1) to 1/20 (which is the answer you should have gotten for (D.4)?

6. What is the optimal externality-compensating Pigovian tax on BMW rentals at CCU?