I have been working on this question for a very long time and just need a little guidance to see that I am approaching these correctly.
w- Econ 6921 Assignment 5 - Saved to my Mac Home Insert Draw Design Layout References Mailings Review View ? Tell me Share Comments Times New... v 12 A" A Aa Ap AaBbCcDdE AaBbCcDdE AaBbCcDc AaBbCcDdE AaBb( AaBbCCDdEF Paste BIUvab X X|A DAY Norma No Spacing Heading 1 Heading 2 Title Subtitle Styles Dictate Sensitivity Pane 1. (12) Suppose that two clothing manufacturers, Lands' End and L.L. Bean, are deciding what price to charge for very similar field coats. The cost of producing these coats is $100. The coats are very close substitutes, so customers flock to the seller that offers the lowest price. If both firms offer identical prices, each receives half the customers. For simplicity, assume that the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices (Lands' Ends Profit, LL Bean's Profit) is shown in the payoff matrix below. LL Bean $103 $102 $101 $103 ($150, $150) ($0, $220) ($0, $120) Lands' End $102 ($220, $0) ($1 10, $110) ($0, $120) $101 ($120, $0) ($120, $0) ($60, $60) a. What is the Nash equilibrium and expected profits to LL Bean and Lands' End of this game? Nash equilibrium exists when no play can improve his or her playoff by unilaterally changing his or her action given the actions chosen by other players. In this the Nash equilibrium would be for each company to choose $101 and profit of $60 each. This is because neither is going to change to the next price up because they will both be at a profit of ZERO. There is not incentive to change their minds and charge $102 and lose profits. Expected Profits = $60 for Land's End and $60 for LL Bean Page 1 of 4 1576 words English (United States) Focus + 222%b. Suppose Lands' End and LL. Bean decide to collude and jointly determine prices? Is this collusion likely to work. Briey explain why or why not. (Note: don't worry about the legality of collusion in your answer). The two could collude and charge $103 each to maximize prot for both but this agreement will not last due to the fact that both have the incentive to cheat. LL Bean can increase their prots to $220 and leave Lands End with zero if they charge $102. Same situation with Lands End if they chose to charge $102 to maximize prot of $220 and leaving LL Bean with zero prot. c. Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a price of $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while Lands End has a 1/3 chance of choosing each strategy. What's the expected payo to LL Bean? 0.25 0.33 X 120 + 0.25 X 0.33 X 220 + 0.50 X 0.33 X 150 = $52.80 d. ISuppose that in hopes of raising prices, LL. Bean announces the price for its coat early in the summer (before Lands' End announces their prices). Represent this using a sequential game tree diagram. Will this strategic move be successful for LL Bean? Explain. If LL. Bean announces their price early in season they would chose / \\ the highest price of $103. Now End has 2 choices, either charge the same which would be collusion equilibrium or $6102, 103) lag133:3?\" igibmm charge $102 and grab the entire market share and maximize profit for themselves. Now that will leave LL. Bean with 2 /\\ strategies, change their price to $102 or grab the entire market share themselves by going to $101 to maximize profit. Now this $102, 102 $ , _ . . M ) g 102 101) Will leave LE to also charge $101 and now they wr/l reach their Nash equilibrium. This will be successful for LL Bean because they will either reach Collusion or Nash equilibrium. $55101, 101) Nash equilibrium
