Econ 1: Spring 2016: U.C. Berkeley: Final Exam

Live from the RSF Fieldhouse: Looks like this question on the final was a little too much of a curveball:

Across the bay and 60 miles south from Avicenna to the town of Tall Stick, home of Crony Capitalism University with 10,001 students. The 10,001 students at CCU do two things with their money over the school year:

  • They eat gourmet pizzas
  • They rent BMW convertibles
  • There are no fixed costs to enter the BMW conertible-rental business, and the marginal cost to car rental companies of renting a BMW is $10,000/year.
  • Willingnesses-to-pay of the 10,001 students are evenly distributed between $20,000 and $0.
  • Each CCU student has a status-anxiety externality cost of $1 imposed on them by another student’s renting a BMW.
  • CCU students’ willingness-to-pay for gourmet students is constant at $40/pizza

The CCU administration imposes a Pigovian tax on BMW rentals by its students, in order to make their well-being as great as possible. It spends the revenue collected from the tax distributing free gourmet pizzas (at a cost of $40/pizza) to the CCU students in their dorms.

  1. What Pigovian tax should the CCU administration place on BMW rentals if it wants to achieve the highest well-being for CCU students?
  2. With that tax, what is the quantity of BMWs rented by CCU students?
  3. With that tax, what is the well-being of CCU students—the sum of consumer surplus from BMW rentals minus externality costs plus consumer surplus from free pizzas eaten?
  4. Suppose student demonstrations at CCU lead the administration to abandon the BMW rental tax, and the market for BMW rentals goes to its free-market equilibrium. What is the well-being of CCU students—the sum of consumer surplus from BMW rentals minus externality costs plus consumer surplus from free pizzas eaten?

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