A monopolist faces the following conditions: Q = 500 - .5P and TC = 1000 + Q + Q².What is the monopolist's profit maximizing price? A)P = $650 B)P = $667 C)P = $675 D)P = $688

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Quizplus · Accepted Answer

To find the monopolist's profit maximizing price, we need to first find the monopolist's profit function. Profit = Revenue - Total Cost Revenue = P*Q Substituting Q = 500 - 0.5P, we get: Revenue = P*(500 - 0.5P) = 500P - 0.5P^2 Total Cost = 1000 + Q + Q² Substituting Q = 500 - 0.5P, we get: Total Cost = 1000 + (500 - 0.5P) + Q² Total Cost = 1500 - 0.5P + Q² Now we can write the profit function as: Profit = 500P - 0.5P^2 - (1500 - 0.5P + Q²) Simplifying and setting the derivative of the profit function with respect to price equal to zero, we get: dProfit/dP = 500 - P + Q² = 0 Solving for P, we get: P = $667 Therefore, the profit maximizing price for the monopolist is $667.

A Monopolist Faces the Following Conditions: Q = 500 -