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Unformatted text preview: which is better for firm 2. But then firm 1 can respond making profits
profit1 p1b, p2a , profit2 p1b, p2a
108 728., 113 796. which is (slightly) better for firm 1 than after firm 2 cut price. In the next two steps profit went to
profit1 p1b, p2c , profit2 p1b, p2c
106 760., 113 918. better then for firm 2, and then
profit1 p1d, p2c , profit2 p1d, p2c
106 769., 113 470. better then for firm 1. Of course, each firm is lowering price to meet the competition, but each is making less than it
was initially. Is there an end to this price cutting? Prices appear to be leveling off, starting at 110. then 99.5 then
97.77 for product 2 and starting at 100. then 92.14 then 91.66 for product 1. The prices for product 1 can be lower
because it is cheaper to make. On the other hand, the demand for product 1 is slightly less elastic than the demand for
product 2 and a less elastic demand results in a final price which is a higher multiple of the marginal cost. What we
really want are Nash equilibrium prices. We can rewrite the Nash equilibrium conditions again, but we computed the
first order conditions symbolically above and since then assigned all of the relevant parameters. We have also already 8 m256hw03soln.nb better then for firm 1. Of course, each firm is lowering price to meet the competition, but each is making less than it
was initially. Is there an end to this price cutting? Prices appear to be leveling off, starting at 110. then 99.5 then
97.77 for product 2 and starting at 100. then 92.14 then 91.66 for product 1. The prices for product 1 can be lower
because it is cheaper to make. On the other hand, the demand for product 1 is slightly less elastic than the demand for
product 2 and a less elastic demand results in a final price which is a higher multiple of the marginal cost. What we
really want are Nash equilibrium prices. We can rewrite the Nash equilibrium conditions again, but we computed the
first order conditions symbolically above and since then assigned all of the relevant parameters. We have also already
solved this system symbolically.
D profit1 p1, p2 , p1
5200. 80. p1 0, D profit2 p1,...
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This note was uploaded on 07/12/2013 for the course MATH 256 taught by Professor Schantz during the Spring '11 term at Vanderbilt.
 Spring '11
 Schantz
 Math

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