Final answer:
The social cost of the firm's monopoly power, represented as deadweight loss, can be calculated using demand and marginal cost functions. By comparing monopoly outcomes to competitive market outcomes, the social cost is found to be $475.00.
Step-by-step explanation:
The social cost of monopoly power can be estimated by the deadweight loss, which is the loss of economic efficiency when the equilibrium outcome is not achievable or not achieved. In order to calculate this, we need to determine the profit-maximizing quantity and price for the monopolist and then compare with the competitive market outcome where price equals marginal cost (P = MC).
Given the demand function Q = 115 - P and the constant marginal cost MC = $20, a competitive market would set P = MC, so the competitive price would be $20. However, a monopolist maximizes profit where marginal revenue (MR) equals marginal cost (MC). To find the MR function, we need to know the inverse demand function, which is P = 115 - Q, because MR is the derivative of total revenue (P*Q) with respect to Q. Total revenue is P*Q = (115 - Q)Q. Taking the derivative gives MR = 115 - 2Q. Setting MR = MC to find the quantity gives 115 - 2Q = 20, thus Q (monopoly quantity) = 47.5 and P (monopoly price) = $67.50.
The social cost is then the triangle formed by the difference between the monopoly price and the competitive price, along with the difference between the competitive quantity and the monopoly quantity. The base of the triangle is the difference in quantity (67.5 - 47.5 = 20) and the height is the difference in price ($67.50 - $20 = $47.50). The social cost or deadweight loss is then 0.5 * base * height = 0.5 * 20 * $47.50 = $475.00.