3 Competition and Natural Monopoly (7 points) Consider two identical firms compe
ID: 1147256 • Letter: 3
Question
3 Competition and Natural Monopoly (7 points) Consider two identical firms competing in a market described by: . (Inverse) Demand: P-50-Q, where Q = 91 + g2 . Cost Firm 1: G = 2091 + ·Cost Firm 2: G = 2092 +91 a. (1 point) What is firm 1's marginal cost? Firm 2's marginal cost? What can you observe about these two firms? b. (2 points) What are the equilibrium price (P), production quantities (i2), and profits (,), if these firms are rivals-what is the outcome in the perfectly competitive model? c. (2 points) What are the equilibrium price (P'), production quantities (gi,2), and profits (m,), if these firms collude-what is the outcome in the monopoly model? d. (2 points) Now suppose that each firm must incur a fixed cost FC = 75 to operate, regardless of their production level. Would the firms cover their costs in the two cases above? DiscussExplanation / Answer
First question is answered below
A)
MC = dC/dQ
MC1 = 20+2q1
MC2 = 20+2q2
Both firms have similar structure of marginal cost
B)
A perfectly competitive firm produces at the point P = MC
That is, 50-Q = 20+Q
Or, Q* = 15
P* = $35
Q1 = Q2 = Q*/2 = 7.5 units
Profit of each firm: PQn - TCn = (35*7.5) - (20*7.5 + 7.5*7.5) = $56.25
C)
A monopolist produces at the point MR = KC
That is, 50-2Q = 20+Q
Q* = 10
P* = $40
Q1 = Q2 = Q*/2 = 5 units
Profits of each firm =(40*5) - (20*5 + 5*5) = $75
D)
Perfectly competitive firms will not be able to cover their costs while monopolist will.
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