1. Suppose that a firm holds a monopoly on a good X. The firm can produce X at a
ID: 1115487 • Letter: 1
Question
1. Suppose that a firm holds a monopoly on a good X. The firm can produce X at a constant marginal cost of 20. Men and women have different demand curves for this product. pw = 100-qw Pm = 150-4m What conditions would need to be true in order for the firm to successfully price discriminate between men and women? If the firm is able to charge different prices to men and women, what price will it charge to each? Calculate profits, consumer surplus, and total welfare in part (a). Now suppose that the firm is legally required to charge the same price to men and women. What price will it charge? (Assume there are equal numbers of men and women in the population.) Calculate profits, consumer surplus, and total welfare in part (c). a. b. c. d. e.Explanation / Answer
1) The required conditions are: knowledge of different demand with different price elasticites, prevention of resale, market power, ability to segregate the market
2) It will charge according to the marginal revenue and marginal cost function
MRw = 100 - 2qw and MRm = 150 - 2qm
20 = 100 - 2qw and 20 = 150 - 2qm
qw* = 40 and qm* = 65
Pw* = $60 and Pm* = 150 - 65 = $85
These will be the prices charged
c) Consumer surplus (men) = 0.5*(150 - 85)*65 = 2112.50. Consumer surplus (women) = 0.5*(100 - 60)*40 = 800
Profit = 60*40 + 85*65 - 20*(40 + 65) = 5825. Total welfare = CSW + CSM + Profit = 2112.50 + 800 + 5825 = $8737.50
d) When a single price is charged, market demand is required.
Q = 250 - P or P = 250 - Q
MR = 250 - 2Q
MC = 20
This implies we use MC = MR
250 - 2Q = 20
230 = 2Q
Q = 115
P* = 250 - 115 = $135
This is the single price charged by the monopolist
e) CS = 0.5*(250 - 135)*115 = 6612.50
Profit = 115*135 - 20*115 = 13225
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