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Suppose there are two main manufacturers of snowboard, Burton and K2. Because many snowboarders view the...

  1. Suppose there are two main manufacturers of snowboard, Burton and K2. Because many snowboarders view the two companies’ products as similar but not identical, if either firm cuts its prices, it will gain market share from the other. But because the firm’s products aren’t perfect substitutes, the price-cutting company won’t take all of the business away from the other company just because it sets its price a bit lower. Suppose Burton’s demand function is given by

qB = 1,000 -1.5pB + 1.5pK

and K2’s demand function is given by

qK = 800 -2pK + 0.5pB

where pK is K2’s price and pB is Burton’s price. For simplicity we will assume that MC = $10.

a. derive each firms price reaction curve.

b. what is each firms optimal price?

c. what is each firms optimal quantity?

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Answer #1

Intal revenue for Burton = Po.a. Total rei a) = 1000 PB - 1.5 Pe? +1.5 pe pia é = 1000 - 388 +1.5 Pik At equilli briune, MRB

c) Optimal quantity for Burton, _ - 1000-1.5 (222.67)+ 1.5(325.33 = 1004 - Optimal quantity for Ka, av = 800 - 2 (225.33)+0.5

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