Profit Maximization in the Long Run

Rick Rentaheap owns a small car rental agency. His long run total cost function given by TC(Q) = 36 + 6*Q + Q^2. The car rental business is perfectly competitive and the public's willingness to pay for car rentals (the demand curve) is given by P = 78 - Q.

1. What is the minimum price at which Rick is willing to be in the car rental business in the long run? What quantity would he produce at that price? Show all your work.
2. Suppose all car rental companies have cost functions just like Rick's. What will be the equilibrium price and quantity in the car rental market? How many firms will there be? Draw graphs showing Rick's and the market's equilibria.
3. Suppose the government imposes a tax of $6 on each car rented by anyone in the industry. Show what happens to Rick's firm and the market equilibrium in the long run. What will be the new price and quantity in the market? How much will Rick produce?
4. Is the tax in part (3) efficient? Why or why not?

Solution