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Ans_HW9

# Ans_HW9 - Answer to Practice Homework9 12.3 a With demand P...

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Answer to Practice Homework9 12.3 a) With demand 20 P Q = - , 20 2 MR Q = - . A profit-maximizing firm charging a uniform price will set MR MC = . 20 2 2 5 Q Q Q - = = At this quantity, price will be 15 P = . At this price and quantity profit will be 2 15(5) ( 5 ) 50 F F π π = - + = - Therefore, the firm will earn positive profit as long as 50 F < . b) A firm engaging in first-degree price discrimination with this demand will produce where demand intersects marginal cost: 20 – Q = 2 Q or Q = 6.67 units. Its total revenue will be the area underneath the demand curve out to Q = 6.67 units; .5(20 13.33)(6.67) 13.33(6.67) 111.16 TR = - + = . Profit will be 2 111.16 ( 6.67 ) 66.67 F F π π = - + = - Therefore, profit will be positive as long as 66.67 F < . Comparing the solution to parts (a) and (b), for values of F between 50 and 66.67 the firm would be unwilling to operate unless it is able to practice first-degree price discrimination. 12.4 a) The firm would maximize profit by producing until MR = MC , or 40 – 6 Q = 2 Q . Thus Q = 5 and the profit-maximizing price is P = 25. With MC = 2 Q and no fixed costs, its total costs are C = Q 2 , so π = 25(5) – 5 2 = 100. b) With perfect first degree price discrimination, the firm will charge a price on the demand curve for all units up to the quantity at which the demand curve intersects the marginal cost curve. The demand curve intersects the marginal cost curve when 40 – 3 Q = 2 Q , or when Q = 8. Total revenue will be the area under the demand curve, or 0.5(40 – 16)8 + 16(8) = 224. Total variable cost is the area of the triangle under its marginal cost curve up to the quantity produced, that is, 0.5(16)(8) = 64. Economic profit will be 224 – 64 = 160. So by price

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Ans_HW9 - Answer to Practice Homework9 12.3 a With demand P...

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