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Managerial economics theory and practice phần 7

Điều kiện tối đa hóa lợi nhuận trong phương trình (11,17), nó rất dễ dàng để thấy rằng công ty sẽ tính phí trong cùng một mức giá tại hai thị trường chỉ khi e1 = e2. Khi e1 e2 π, giá tại hai thị trường sẽ không phải là cùng. | PRICE DISCRIMINATION 437 FIGURE 1 1.5 Third-degree price discrimination. 1 I . MR2 P2 1 I 11.20 where 1 and e2 are the price elasticities of demand hl the two markets. By the profit-maximizing condition in Equations 11.17 it is easy to see that the firm will charge the same price in the two markets only if 1 e2. When 1 2 theprices inthe two markets willnot.bc th esame.Infact whenEi e2 the csicrcharaEdãn the titetmtekcl. vcóniae -nco itc-rtliÁin thaprict charged tnthere condmreket.pigurell.5iltnsacat nsthisiolpaton frrline or demand curves tcl.hr two macPetsnnnropntacemarginatcast. Problem ntrSi ate n Cieaptntỵrdio IK F .r.ii . in two nep aNe and at tillable marnEeS rrcompnno a 00 0 et ttatCn nc n t02 The demt ntie q t n lorils ochiel in tht Swomarketnnre Ổ1 10- 0.2 d etii ttm.nv where Q Qi J. a. Assuming that the second-order conations are satisfied calculate the profit-maximizing price and output level in each market. b. Verify that tOe dernanO tor Red Company s product is less elastic in the markit witetSehignEnprice. c. Give thein m rtotalpee fìtattheprtfit-maximizmgpricer roa output levels. Solution a. This is aaexample of price discrimination. Solving the demand equations in both markets for price yields p1 50-5a 438 PRICING PRACTICES P2 3O-2Ổ2 The corresponding total revenue equations are 7 5021- 5212 t P. tiiC. lC Red Company s total profit equationis n TR1 TR2 -TC 5021 - 5Qn 30Q0 - 2-2 - 6 - 10 21 Ổ2 Maximizingthisexpression withrespectto 2i and Q2 yields is - 50-1021-10 40-1021 0 rj tS 21 4 s 4 ổ2 5 Pi 52-5 4 50-20 30 P2 30-2 5 30-10 20 b. The relationships between the sc Hire price and the 0rice elasticity of demand in the two markets are MR1 P1Sl i V El 7 . ods where i o l p2i Ỵ PO I dP2 JI 21 J p _PQ2Y de From the demand equations dQJdP -C .2 hnd dQ2 dP2 -0.5. Substituting these results into preceding abooe relationships we obtain tr G .2sfr J nSZ-d- 0.5 t4 r PRICE DISCRIMINATION 439 o n 4 20 -10 o ON -04fJ -2 This verifies that the higher price is .