Question

4. Bertrand Competition (29 points) Consider a Betrand Model. The market demand is P-180-Q. Consumers only buy from the firm charging a lower price. If the two firms charge the same price, they share the market equally. The marginal cost for firm 1 is 30, and the marginal cost for firm 2 is also 30. There are no fixed costs. A. (5 points) Would any firm charge a price below 30 at the market equilibrium? Briefly explain your reason B. (6 points) If firm 2 charges p2110, then what price p, will be firm l's best response? Briefly explain your reason. C. (6 points) Could (p.70, p2-80) be the Nash Equilibrium? Briefly explain your reason. D. (6 points) Suppose now firm l's marginal cost is sill 30 but firm 2's marginal cost is reduced to 20. All the other conditions remain the same. What is the Nash equilibrium of the new game? (You can answer it by providing an intuitive argument.) E. Bertrand competition with Lowest Price Guarantee Price Match (6 points) Take the two firms in our previous Bertrand model as Staples and Bestbuy. They are selling the same HP printer model, with the demand given by P-180-Q and both share the same marginal cost 30 with no fixed costs. In addition now we assume that both Staples and Bestbuy promise their customers "Lowest Price Guarantee or Price Match." That is, a customer can get the refund for the overcharged price. For example, if Staples charges 50 and Bestbuy charges $60, then a Bestbuy customer is entitled to a 60-50=S10 refund from Bestbuy. With "Lowest Price Guarantee/Price Match" in this market, if now Bestbuy charges P2"100, then what price p will be Staples' best response? Briefly explain your reason.

Answer 1

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DATE: MC 30 Ml, 20 P 180-8 D 180-91-12 TR P.91 2 MRP 2lad 160- 241-9a 241 MR2 MC, 30 130-291-92 4S0-92 2 FA1 firm 1's bet is For ferim 2 MK MG 20 130-241-9 190-29-41 MAy-ML L 20 9.-(60-2, 2 160 )l40-4) 75-1/1) Put 2

35 80 40 7 75- + A91 37T40746 466 190 2 2.U 13 240-70 80-70 3. 60 -1 (0 2 170 5.6 2T d5 3 2 180 P = 180 140 +17O 3 5 27d7 S 40-710 230 21J - 76.6 Tt-76-6-30 ) (46-6) 1 217/.56 T,- 76-6-20( 56 6)- 3207.53 The forim 2 he exphleibd MC ly grabbuny the market share firin s drgher
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