A monopolist faces a demand curve given by P = 30-Q and has constant marginal (and average cost) of $24. What is the economic profit made by this profit-maximising monopolist when practicing perfect price discrimination? [Round your answer to 2 decimal places where necessary]
Question
A monopolist faces a demand curve given by P = 30-Q and has constant marginal (and average cost) of $24. What is the economic profit made by this profit-maximising monopolist when practicing perfect price discrimination? [Round your answer to 2 decimal places where necessary]
Solution 1
To find the economic profit made by a profit-maximising monopolist when practicing perfect price discrimination, we need to follow these steps:
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First, we need to find the quantity where the marginal cost (MC) equals the marginal revenue (MR). In this case, the marginal cost is constant at $24.
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The demand curve is given by P = 30 - Q. To find the marginal revenue, we need to find the derivative of the revenue function (R = PQ). However, since this is a case of perfect price discrimination, the monopolist is able to sell each unit at the highest possible price, so the marginal revenue is equal to the price for each unit, which is given by the demand curve.
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Setting P = MC, we get 30 - Q = 24. Solving for Q, we get Q = 6.
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The total revenue (TR) made by the monopolist is then P * Q = (30 - 6) * 6 = $144.
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The total cost (TC) is MC * Q = 24 * 6 = $144.
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The economic profit is then TR - TC = 144 = $0.
So, the economic profit made by this profit-maximising monopolist when practicing perfect price discrimination is $0.00.
Solution 2
To find the economic profit made by a profit-maximising monopolist practicing perfect price discrimination, we need to follow these steps:
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First, we need to find the quantity where the marginal cost (MC) equals the marginal revenue (MR). In this case, the marginal cost is constant at $24.
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The demand curve is given by P = 30 - Q. To find the marginal revenue, we need to derive the inverse demand function, which is Q = 30 - P.
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The marginal revenue is the derivative of the total revenue with respect to quantity. The total revenue (TR) is P*Q = (30 - Q)*Q = 30Q - Q^2. The derivative of TR with respect to Q is MR = 30 - 2Q.
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Setting MC equal to MR gives 24 = 30 - 2Q. Solving for Q gives Q = 3.
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Now, we need to find the total revenue and total cost to calculate the economic profit. The total revenue (TR) is P*Q = (30 - 3)3 = 243 = $72.
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The economic profit is TR - TC = 72 = $9.
So, the economic profit made by this profit-maximising monopolist when practicing perfect price discrimination is $9.
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