Homework_ch11

Homework_ch11 - Practice Homework_ch11 Problems 11.1, 11.2,...

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Practice Homework_ch11 Problems 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.9, 11.11, 11.24, 11.25, 11.26 Answer 11.1 a) If demand is given by 100 5 Q P = - , inverse demand is found by solving for P . This implies inverse demand is 1 5 20 P Q = - . b) Average revenue is given by TR PQ AR P Q Q = = = Therefore, average revenue will be 1 5 20 P Q = - . c) For a linear demand curve P a bQ = - , marginal revenue is given by 2 MR a bQ = - . In this instance demand is 1 5 20 P Q = - implying marginal revenue is 2 5 20 MR Q = - . 11.2 a) Since the demand curve is written in inverse form and is linear, the MR curve has the same vertical intercept and twice the slop as the demand curve. Thus, MR = 40 – 4 Q. b) Total revenue will be maximized when MR = 0, or when Q = 10. At that quantity, the price will be P = 40 – 2 Q = 20. Total revenue is PQ = 20(10) = 200. 11.3 + = + = + = P Q P Q P P Q P Q P Q P MR , 1 1 1 ε . Since P > 0, MR = 0 if and only if 1 + ( 29 P Q , / 1 = 0, which is equivalent to 1 / 1 , - = P Q or 1 , - = P Q . 11.4 If demand is 9 P Q = - , then 9 2 MR Q = - . If the firm sets 7 Q = , then 5 MR = - . At this point, if the firm lowered its output it would increase total revenue, and with the lower level of output total cost would fall. Thus, decreasing output would increase profit. Therefore, a profit-maximizing monopolist facing this demand curve would never choose 7 Q = .
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11.5 Recall that the MR curve can easily be derived from the demand curve when the latter is written in the inverse form. The inverse demand curve is P = 50 – ( Q /20) so the marginal revenue curve is P = 50 – ( Q /10) (using the fact that the slope of the MR curve is twice that of the inverse demand curve, with the same intercept). Using the rule MR=MC , we get 50 – ( Q /10) = 8, so Q = 420. Plugging this back into the demand curve (or the inverse demand curve) we can calculate the profit maximizing price, P = 29. 11.6
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Homework_ch11 - Practice Homework_ch11 Problems 11.1, 11.2,...

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