PROBLEM 2 (20 POINTS). A monopolistic firm sells two kinds of goods: high qualit
ID: 1108914 • Letter: P
Question
PROBLEM 2 (20 POINTS). A monopolistic firm sells two kinds of goods: high quality and low quality. The firm's marginal costs are 2 for either quality good. The firm maximizes profits. It sells to two types of customers: type-one and type-two. There are 50 type-one and 100 type-two consumers. The type-one consumers value the high-quality good at 12 and the low- quality good at 6. The type-two consumers value the high-quality good at 7 and the low- quality good at 5. a. Assume that the firm can only sell one type of good (high or low quality), what would be the profit maximizing quality (h, 1) and at what price p? b. Assume that the firm can price discrimination. Write down the relevant constraints that must be satisfied in order for this monopolist to successfully price discriminate. c. What are the profit maximizing prices, consumer surplus, and profits for the firm? (Explain your reasoning) d. Given your results in parts a. & c., does the firm prefer the price discrimination scheme to a single price good? Do the consumers prefer the price discrimination scheme to a single price good? Problem 3. (30 Points) The following game is called "Battle of the Sexes." If a couple go to the opera or to a football game together, they experience joy. However if they do not go to together, they do not (just imagine that they get mad at each other the next timeExplanation / Answer
a) Given the situation, the firm has tow type of consumers one who value high-quality goods at 12 and low-quality goods at 6. His total revenue form these people will be High quality (12 x 50 ) 600 and from low quality good will be (6 x 50) 300.
Similarly, another group will give him a profit of (100 x 7) 700 for high quality good and (100 x 5 ) 500 for low-quality goods.
His total profit high-quality goods (600 + 700) will be 1300 and for low-quality goods will be (300 + 500) 800 only.
Taking the above calculation into account he will only sell high quality good at tow different price that is 12 and 7 and makes a profit of 1300.
b) Constraints for price discrimination are given below:
c) Profit-maximizing prices are 12 and 7 for the firm and total profit they are making is 1300. On the other hand, the consumer surplus is zero but maximum producer surplus. Consumer surplus can be defined as the difference in the amount the consumer is willing to pay and the actual amount he is paying. Because of price discrimination, the monopoly is charging them the maximum amount the group of consumers is ready to pay, this will make their consumer surplus zero.
d) The firm definitely prefers the price discrimination as that would increase its producer surplus to the maximum. But the consumer group didn't prefer price discrimination because it will only reduce their surplus to zero and transfer it as producer surplus.
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