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# 1. A monopolist looks at their market and sees two distinct types of consumer; young and old. D D Q Q The demand curve for young people is given by:

I have 2 questions I need assistance with. Please refer to the attached document to find the 2 questions. Please answer both questions fully and show all work so I understand how each problem is worked out. If you have any questions please let me know. Thanks.

1. A monopolist looks at their market and sees two distinct types of consumer; young and old. The demand curve for young people is given by: P = 40 Q Y D 4 , and MR Y = 40 Q Y D 2 . The demand curve for old people is P = 40 Q O D , and MR O = 40 2 Q O D . The market demand is thus: P = 40 Q M D 5 , and MR M = 40 2 5 Q M D . The monopolist has constant MC = 2 . (12pts total) a) What would the perfectly competitive price and quantity be? (2pts) b) Without price discrimination, what is the profit maximizing price and quantity for the monopolist? (2pts) c) With price discrimination, what is the profit-maximizing price and quantity in the young market? (2pts) d) What is the profit-maximizing price and quantity in the old market? (2pts) e) What are the profits for i) a perfectly competitive market, ii) monopolist market w/o discrimination, and iii) monopolist market with price discrimination? (4pts) Extras credit: f) If the monopolist could perfectly price discriminate, what would her profits be? (+2pts) 2. A duopolistic market (Firm A and Firm B) has demand P = 1000 4Q D and MR = 1000 8Q D . Marginal cost for each firm is MC = 520 . Assume the goods are homogeneous. (7pts total) a) What would the monopoly price and quantity be? (2pts) b) If the firms compete according to the Bertrand price model, what are their profits? (1pt) c) Again under Bertrand price competition: What quantity does each produce? (1pt) d) If the firms compete according to the Cournot quantity model, and Firm A sets its quantity at 50 units, then the demand that Firm B sees is P = 800 4Q D and MR = 800 8Q D . What is Firm B's best response quantity? What is B's profit? (3pts)

Q1
a.
in perfect competition MC= P
2 = 40 –Q/5
Q= 190
P= 40-(190/5) = 2
b.
Monopolist equalizes MR with MC
40-2Q/5 =2
Q= 95
P= 40-(95/5) = 21
c.
In young market
MR= MC
40- Q/2 =2
Q= 76
P=...

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