3. 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. $103 ($0, $200) ($150, $150) ($200, $0) ($100, $100) ($120, $0) ($120, $0) a. What is the Nash equilibrium and expected profits to LL Bean and Lands' End of this game? Lands' End LL Bean $102 $103 $102 $101 $101 ($0, $120) ($0, $120) ($50, $50) b. Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a price of $101, a 259 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 payoff to LL Bean? hance c. Suppose that in hopes of raising prices, L.L. Bean announces a price of $103 for its coat before Lands' End announces their prices. Do you think this strategic move will be successful for LL Bean? Explain.
3. 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. $103 ($0, $200) ($150, $150) ($200, $0) ($100, $100) ($120, $0) ($120, $0) a. What is the Nash equilibrium and expected profits to LL Bean and Lands' End of this game? Lands' End LL Bean $102 $103 $102 $101 $101 ($0, $120) ($0, $120) ($50, $50) b. Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a price of $101, a 259 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 payoff to LL Bean? hance c. Suppose that in hopes of raising prices, L.L. Bean announces a price of $103 for its coat before Lands' End announces their prices. Do you think this strategic move will be successful for LL Bean? Explain.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Transcribed Image Text:3. 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.
a.
LL Bean
$102
$103
($150,
$103
($0, $200)
-A
$150)
Lands' End $102 ($200, $0)
($100, $100)
$101 ($120, $0)
($120, $0)
What is the Nash equilibrium and expected profits to LL Bean and Lands' End of this game?
$101
($0, $120)
($0, $120)
($50, $50)
b. 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 payoff to LL Bean?
c. Suppose that in hopes of raising prices, L.L. Bean announces a price of $103 for its coat before Lands'
End announces their prices. Do you think this strategic move will be successful for LL Bean? Explain.
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