Question

You are the manager of a monopoly, and your analysts have estimated your demand and cost functions as P=300−3Q and C(Q)= 1,500+2Q

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, respectively. a. What price-quantity combination maximizes your firm's profits? Price: $ Quantity: units b. Calculate the maximum profits. $ c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price-quantity combination? Unit elastic Elastic Inelastic

Answer 1

In a monopoly, the profit-maximizing quantity is determined by finding the point where marginal revenue equals marginal cost. The price charged is then determined by drawing a line up from the profit-maximizing quantity to the demand curve. Finally, total revenue, total cost, and profit are calculated to find the maximum profit.

Step-by-step explanation:

Step 1: The monopolist determines its profit-maximizing level of output by calculating total revenue using points on the demand curve and then determining the marginal revenue curve. The profit-maximizing quantity occurs where MR = MC. In this case, MR = MC occurs at an output of 5.

Step 2: The monopolist decides what price to charge by drawing a line straight up from the profit-maximizing quantity to the demand curve. This price is above the average cost curve, indicating that the firm is earning profits. In the example given, the price charged is $800.

Step 3: The monopolist calculates total revenue, total cost, and profit. Total revenue is the quantity sold multiplied by the price. Total cost is the quantity multiplied by the average cost. The larger box of total revenues minus the smaller box of total costs equals the profit. Using the given numbers, the maximum profit is $2350.