Homework 4 Managerial Economics Due Tuesday, September 25, 2018 Instructions: Sh
ID: 1139713 • Letter: H
Question
Homework 4 Managerial Economics Due Tuesday, September 25, 2018 Instructions: Show all of y A monopolist with total cost function c(Q) - 10 + consumer groups with the first group having a demand function of qi(P) = 80-5P1 and the second having a demand function of q2(P) 40-2P2. 1. Q2 faces a market with two distinct a) Is this monopolist operating in the short run or the long run? Explain how you know b) Calculate the monopolist's profit-maximizing price and quantity sold if the monopolist must engage in uniform pricing. Find the monopolist's profits in this scenario. (Hint: use horizontal aggregation to form the total market demand curve). c) The monopolist can now engage in third degree price discrimination, setting a different price for each market segment. Calculate the monopolist's optimal prices charged to each market segment, the quantities consumed by each market segment, and the monopolist's profits Would the monopolist rather engage in this price discrimination or would they rather set a uniform priceExplanation / Answer
a)
Fixed is given as 10, hence we can conclude that firm operates in short run. Firm incurs fixed cost only in short run. thus firm is operating in short run only.
b)
Total demand = 80 -5P +40 -2P
Q = 120 -7P
P = 17.14 - 0.14Q
TR = 17.14Q - 0.14Q^2
MR = 17.14 - 0.28Q
Equilibrium ; MR = MC
17.14 - 0.28Q = Q
Q =13.39
P =13.39 - 0.14(13.39)
P = 15.26
Profit = 15.26 *13.39 - 10 - 1/2(13.39)^2
= 204.7 - 10 - 179.29
= $ 15.41
c)
First market; P = 80 /5 - 1/5Q
= 16 - 0.2Q
TR = 16Q - 0.2Q^2
MR = 16 - 0.4Q
MR = MC
16 - 0.4Q = Q
16 = 1.4Q
Q = 11.42
P = 16 - 0.2(11.42)
= 16 - 2.28
= 13.716
Market 2)
Q = 40 - 2P
P = 20 - 0.5Q
TR = 20Q - 0.5Q^2
= 20 - Q
MR =MC
20 -Q = Q
Q = 10
P = 20 - 0.5(10)
= 15
Profit = TR- TC
=15*10+13.7*11.42 -10 -229.4
= $ 67.04
Price discrimination leads to larger profit for firm.
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