Question

You are a monopolist with the following cost and demand conditions: P = 100 - 2Q and C(Q) = 50 + Q2. a. Determine the profit-maximizing output and price. b. Graph this solution. c. Show your profits and the deadweight loss to society in your graph. d. Determine the actual amount of deadweight loss.

Answer 1

To determine the profit-maximizing output and price for a monopolist, we need to find the quantity where marginal revenue equals marginal cost. By solving this equation, we can determine the profit-maximizing output level and price. In this case, the profit-maximizing output is approximately 16.67 units and the price is approximately $66.66.

Step-by-step explanation:

To determine the profit-maximizing output and price, we need to find the quantity where marginal revenue (MR) equals marginal cost (MC). In this case, MR = 100 - 4Q and MC = 2Q. So, we need to solve the equation 100 - 4Q = 2Q.By rearranging the equation, we get 6Q = 100, which gives us Q = 16.67 (rounded to two decimal places). Therefore, the profit-maximizing output is approximately 16.67 units.To find the price, we plug this value of Q into the demand equation: P = 100 - 2Q. P = 100 - 2(16.67) = 100 - 33.34 = $66.66 (rounded to two decimal places). Therefore, the profit-maximizing price is approximately $66.66.