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26. (8 points) Consider a monopolist who faces a constant average and marginal cost of $5 and a linear demand curve of P = 20-2Q, where P is the price the monopolist charges and Q is the quantity consumers purchase. To obtain the optimal quantity and price, the monopolist needs to obtain the marginal revenue, which has the same intercept as the demand curve but twice as steep. Obtain the monopolists marginal revenue, optimal output, and price.
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From the demand function, intercept of marginal revenue is also 20 but the slope is now twice at 4. Hence the marginal revenue is MR = 20 - 4Q. With MC = $5, optimal quantity is MR = MC or 20 - 4Q = 5. This gives Q = 15/4 = 3.75 units. Optimal price at this quantity is P = 20 - 2 x 3.75 = 12.50. Hence monopolist's MR is 20 - 4Q, optimal output is 3.75 units and price is $12.50 per unit

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