3.2 Price cap monopoly question

Imagine a university called Bavis that is the monopoly in the market for economics degrees, with cost-function C(Q) = 25Q2 + 360. Imagine the inverse demand function for economics degrees is p(Q) = 4000 25Q. The government has decided it would ensure that there is no deadweight loss in this market for economics degrees by setting a price cap on Bavis.

A. What would be the equilibrium price and equilibrium quantity if the govern_

ment did not impose a price cap and Bavis was able to operate as an un-regulated monopoly?

B. At what optimal price should the government cap economics degree sales?

C. What are the new post-price cap equilibrium price and equilibrium quantity?

D. What is Bavis's new profifit at the equilibrium?

E. Prove that this new profifit level is a global maximum.

F. Show the new equilibrium price and equilibrium quantity graphically. Include

the original and regulated inverse demand curves, fifirm's marginal revenue curve, and fifirm's marginal cost curve.

G. What are consumer surplus, producer surplus, and deadweight loss at the

equilibrium? How do they compare to the case of the un-regulated monopoly??