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Lecture 15

Economics 2151B - Lecture 15.docx

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Department
Economics
Course Code
Economics 2150A/B
Professor
Kristin Denniston

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Economics 2151B Wednesday March 5 Lecture 15 Chapter 13 (con’t…) Note: HOMEWORK HAS BEEN EXTENDED UNTIL MONDAY MARCH 10 Oligopoly with Differentiated Products (page 7 and 8 of part 2 ch. 13 notes) Product Differentiation 1. Vertical – potential substitutes but perceived quality differences 2. Horizontal – imperfect substitutes  eg. the customer views a McDonalds hamburger differently than a Wendy’s hamburger (they are somewhat similar but imperfect substitutes)  If your product is more popular among the public, you can choose a higher price for it (you won’t lose market share because it is an imperfect substitute) • Example: Store brand battery has half the life of a Duracell brand battery. o IF the store brand price = ½ price of Duracell o THEN they are perfectly substitutable o SO they are vertically differentiated Bertrand Price setting, differentiated products • Example: Coke vs. Pepsi are horizontally differentiated (people see them as two different products) o **Each firm takes the other’s price as given and then sets their price based on what they think the competitor’s price will be o Coke:  MC =15  Q 1 64 – 4P + 1P 2  Q 1 (64 + 2P ) 2 4P (ta1ing the price of Pepsi as fixed) o Pepsi:  MC =24  Q 2 50 -5P + 2 1  Q 2 (50 + P ) 1 5P (t2king the price of Coke as fixed) o Find the residual demand curve.  Q 1 (64 + 2P ) 2 4P 1  We need to convert to the inverse demand firm P = f(Q) to find MR.  P = (16 + .5P ) - .25Q 1 2  Find MR = 116 + .5P ) –2.5Q  Set MR =1MC : 1 • (16 + .5P 2 - .5Q 1 5  Q =122 + P (su2stitute into residual demand) • P1= (16 + .5P2) • P1* = 10.5 + .25P 2 o This is the price firm 1 should set given a price for P ,2 the reaction function  If P2= 8, then P *1= 10.5 + 0.25(8) = 12.50 o Find firm 2’s reaction function  P 2 = f(P 1  Find residual demand with P = f(2 ) 2 • Q 2 (50 + P ) 1 5P 2 • 5P 2 (50 + P ) 1 Q 2 • P2= (10 + .2P )1– 2Q 2  Find MR2: • P2= (10 + .2P )1- .4Q 2  MR =2MC : 2 • (10 + .2P ) - .4Q = 4 1 2 • Q 2 15 + .5P 1  Substitute Q b2ck into residual D : 2 • P2= (10 + .2P )1- .4(15 + .5P ) 1 • P2* = 7 + 0.1P 1 o Solve the 2 Price Reaction Functions  To get the equilibrium optimal prices for P *, 1 * 2
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