an Problem 5. Consider following price competition between 2 firms. Both firms choose their prices (p, and p₂) simultaneously and the market demand function given by q = 10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit) function for firm i is: (10-P.)P. u.(P.P)= (10-pi)p. 2 Notice that this function is not continuous in pi if Pi < Pj if p. = Pj if p > Pi

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Chapter1: Making Economics Decisions
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Problem 5. Consider following price competition between 2 firms. Both firms choose
their prices (p, and p2) simultaneously and the market demand function given by q
10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit)
function for firm i is:
u.(Pi. Pj)
(10-P.)Pi
(10-pi)Pi
2
Notice that this function is not continuous in pi
1
if Pi < Pj
if p. = Pj
if Pi> Pj
Transcribed Image Text:an Problem 5. Consider following price competition between 2 firms. Both firms choose their prices (p, and p2) simultaneously and the market demand function given by q 10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit) function for firm i is: u.(Pi. Pj) (10-P.)Pi (10-pi)Pi 2 Notice that this function is not continuous in pi 1 if Pi < Pj if p. = Pj if Pi> Pj
an
Problem 5. Consider following price competition between 2 firms. Both firms choose
their prices (p, and p2) simultaneously and the market demand function given by q
10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit)
function for firm i is:
u.(Pi. Pj)
(10-P.)Pi
(10-pi)Pi
2
Notice that this function is not continuous in pi
1
if Pi < Pj
if p. = Pj
if Pi> Pj
Transcribed Image Text:an Problem 5. Consider following price competition between 2 firms. Both firms choose their prices (p, and p2) simultaneously and the market demand function given by q 10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit) function for firm i is: u.(Pi. Pj) (10-P.)Pi (10-pi)Pi 2 Notice that this function is not continuous in pi 1 if Pi < Pj if p. = Pj if Pi> Pj
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