Problem 1: Monopoly
A monopolist faces a market demand curve given by
Demand: Q = 70 – P
such that the marginal revenue curve is MR = 70 - 2Q
The monopolist faces the following cost structure:
C = .25Q2 - 5Q + 300
such that the marginal cost curve is MC = .5Q – 5
What output level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist's profits? What is the deadweight loss (in dollars)? Why does deadweight loss arise?
Problem 2: Monopoly
The QXR Company has bought exclusive rights to sell hot dogs in a local sports arena. The fee it paid for this concession was $200. The variable cost of obtaining and marketing each hot dog is $0.10. The demand schedule for hot dogs in this arena is as follows:
Price per hot Thousands of hot
dog (cents) dogs sold per game
20 10
25 9
30 8
35 7
40 6
45 5
50 4
It is assumed that prices must be multiples of a nickel.
a) What price should the QXR Corporation charge for a hot dog?
b) What is the maximum amount that the QXR Corporation should pay for this concession for a single game? (Alternatively, you can think of the owner of the sports arena auctioning off the hot dog concession. What is the most that the owner of the sports arena can expect for this concession?)
Problem 3: Pricing with Market Power
The industry demand curve for a particular market is:
Q = 1800 - 200P
The industry exhibits constant long run average cost at all levels of output, regardless of the market structure. Long run average cost is a constant $1.50 per unit of output. Calculate market output, price (if applicable), consumer surplus, and producer surplus (same as profit here, as there are no fixed costs) for each of the scenarios below. Compare the economic efficiency (i.e., total welfare) of each possibility.
a) Perfect Competition
b) Pure Monopoly (Note that MR = 9 - .01Q)
c) First Degree Price Discrimination