What is the deadweight loss associated with monopoly in question 1?
Question
What is the deadweight loss associated with monopoly in question 1?
Solution
To calculate the deadweight loss associated with the monopoly, we first need to find the quantity and price that would occur under perfect competition. In a perfectly competitive market, price equals marginal cost (P = MC).
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Set the marginal cost (MC) equal to the price (P) to find the competitive quantity: 5 + Q = 95 - Q. Solving this equation gives Q = 18.
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Substitute Q = 18 into the demand function to find the competitive price: P = 95 - Q = 95 - 18 = $77.
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The deadweight loss is the area of the triangle formed by the demand curve (P = 95 - Q), the marginal cost curve (MC = 5 + Q), and the line from the quantity produced under monopoly to the quantity produced under competition.
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The base of the triangle is the difference in quantities (Q_competition - Q_monopoly) = 18 - 30 = -12.
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The height of the triangle is the difference in prices (P_competition - P_monopoly) = 77 - 65 = 12.
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The area of the triangle, which represents the deadweight loss, is (1/2) * base * height = (1/2) * 12 * 12 = 72.
So, the deadweight loss associated with the monopoly is $72.
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