If we know the quantity demanded is defined by Q = 16 - 2P, marginal revenue is MR = 8 - Q, and marginal cost is MC = 1/2 Q - 2. a. What is the equilibrium output if the firm is a monopoly? Show your work. b. What is the equilibrium price? Show your work. c. Illustrate on a graph the deadweight loss of a monopoly market structure compared to a competitive market structure.
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Given that MR = 8 - Q and MC = 1/2Q - 2, we can set them equal to each other: 8 - Q = 1/2Q - 2 Adding Q to both sides: 8 = 1/2Q + Q - 2 Combining like terms: 8 = 3/2Q - 2 Adding 2 to both sides: 10 = 3/2Q Multiplying both sides by 2/3: Q = 20/3 Show more…
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