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PAM200_Section10_Notes

PAM200_Section10_Notes - PAM200 Section 10 Problem 12.3 P Q...

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PAM200 – Section 10 Problem 12.3. a) With demand 20 P Q = - , 20 2 MR Q = - . (remember Q P Q P MR + = ). 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.

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Problem 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
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