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ANSWERS+TO+EVEN-Chapter2

Managerial Economics

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ANSWERS TO EVEN-NUMBERED PROBLEMS (Chapter 2) 2. The revenue function is R = 170Q - 20Q 2 . Maximizing revenue means setting marginal revenue equal to zero. Marginal revenue is: MR = dR/dQ = 170 - 40Q. Setting 170 - 40Q = 0 implies Q = 4.25 lots. By contrast, profit is maximized by expanding output only to Q = 3.3 lots. Although the firm can increase its revenue by expanding output from 3.3 to 4.5 lots, it sacrifices profit by doing so (since the extra revenue gained falls short of the extra cost incurred.) 4. a. π = PQ - C = (120 - .5Q)Q - (420 + 60Q + Q 2 ) = -420 + 60Q - 1.5Q 2 . M π = d π /dQ = 60 - 3Q = 0 Solving yields Q * = 20 units. Revenue = PQ = (120 - .5Q)Q = 120Q - .5Q 2; MR = 120 - Q Cost = -420 + 60Q + Q 2 ; therefore, MC = 60 + 2Q Equating marginal revenue and marginal cost yields: 120 - Q = 60 + 2Q, or Q * = 20 units. b. Here, R = 120Q; it follows that MR = 120 Equating marginal revenue and marginal cost yields 120 = 60 + 2Q or Q * = 30 units. 6. a. If videos are given away (P = $0), demand is predicted to be: Q = 1600 - (200)(0) = 1,600. At this output, firm A’s cost is: 1,200 + (2)(1,600) =$4,400, and firm B’s cost is: (4)(1,600) = $6,400. Firm A is the cheaper option and should be chosen. (In fact, firm A is cheaper as long as Q > 600.)
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