question archive A two-firm cartel that produces at a constant marginal cost of $20 faces a market inverse demand curve of P = 100 - 0
A two-firm cartel that produces at a constant marginal cost of $20 faces a market inverse demand curve of P = 100 - 0
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A two-firm cartel that produces at a constant marginal cost of $20 faces a market inverse demand curve of P = 100 - 0.50Q. Initially, both firms agree to produce half of the monopoly quantity, each producing 40 units of output. If one of the firms cheats on the agreement (assuming the other firm is compliant and continues to produce at 40 units), how much output should the cheating firm produce to maximize profits?
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The cheating firm will choose quantity to maximize profit, taking as given that the other firm will produce 40, which implies a residual demand that is given by:
- P = 100 - 0.5(Q + 40)
- P = 80 - 0.5Q
Using the twice-as-steep rule, the marginal revenue curve is:
- MR = 80 - Q
To maximize profit, the firm will produce until marginal revenue is equal too marginal cost, i.e.,
- 80 - Q = 20
- Q = 60
That is, the cheating firm will produce 60 units.
