Suppose a monopoly firm has an annual demand function of Q^d = 20,000 - 250P,annual variable costs of VC = 16Q + 0.002Q² and marginal cost of MC = 16 + 0.004Q,where Q is the annual quantity of output.In addition,the firm has an avoidable fixed cost of $25,000 per year.If this firm maximizes its profit,what is the value of the deadweight loss caused by this monopoly?

Question

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Using the formula for marginal revenue, MR = Q^d/∆Q, we get MR = 80 - P. Setting MR = MC, we get 80 - P = 16 + 0.004Q. Solving for P, we get P = 78.4 - 0.004Q. Plugging this into the demand function, we get Q = 12,900, and P = $27.64. The firm's total cost, including the avoidable fixed cost, is TC = FC + VC = $25,000 + (16Q + 0.002Q²) = $25,000 + $211,818.69 = $236,818.69. The firm's profit is TR - TC = PQ - VC = ($27.64)(12,900) - ($211,818.69) = $55,056.31. The socially efficient quantity is where P = MC, which is 16 + 0.004Q = 78.4 - 0.004Q, or Q = 10,900. Plugging this into the demand function, we get P = $35.9. The socially efficient price is $35.9, while the monopoly price is $27.64, resulting in a deadweight loss of (35.9-27.64) * 12,900 / 2 = $30,257.50, or approximately $30,250.

Suppose a Monopoly Firm Has an Annual Demand Function of Qd

Suppose a Monopoly Firm Has an Annual Demand Function of Q^d