Three firms, in a Cournot oligopoly, are facing the market demand given by P = 1
ID: 2429320 • Letter: T
Question
Three firms, in a Cournot oligopoly, are facing the market demand given by P = 140 – 0.4Q, where P is the market price and Q is the market quantity demanded. Each firm has (total) cost of production given by C(qi) = 120 + 10qi, where qi is the quantity produced by firm i (for i from 1 to 3). Find: 5. Equilibrium profit made by each firm in the Cournot oligopoly equilibrium. 6. Profit made by each firm in the collusive outcome where the three firms equally split the monopoly profit-maximizing output (i.e., each firm produces one-third of the monopoly profitmaximizing output).
Explanation / Answer
5)
P = 140 – 0.4Q,
C(qi) = 120 + 10qi
MC = 10
Competitive output; P = MC
140 - 0.4Q = 10
130 = 0.4Q
Q = 130 / 0.4
= 325
Cournot output
= (3/4) *325
= 243.75
P = 140 - 0.4(243.7)
= 140 - 97.5
= 42.5
Profit = TR - TC
= 42.5*243.7 - 120 - 10(243.7)
= 7800
Each firm profit = $ 2,600
6)
Monopoly output
P = 140 - 0.4Q
TR = 140Q - 0.4Q^2
MR = 140 - 0.8Q
MR=MC
140 - 0.8Q = 10
Q = 130 /0.8
= 162.5
P = 140 -0.4 (162.5)
=75
Profit = 162.5 *75 - 120 - 10(162.5)
=10,442
Each firm profit = $3,480
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