onsider a Bertrand oligopoly where two firms (Firms 1 and 2) sell goods that are imperfect substitutes and compete by choosing prices simultaneously. Their market demands are q!= 1,200 − 3/2p!+ 3/2p", q"= 800 − 2p"+ 1/2p! For simplicity, assume the marginal cost is zero for both firms (MC!= MC"= 0). Find the best response curve of each firm. Which of the following alternatives is correct? (a) Firm 1’s best response curve is p!= 400 + 0.5p" (b) Firm 2’s best response curve is p"= 400 + 0.5p! (c) Firm 1’s best response curve is q!= 45 − 0.5q" (d) Firm 2’s best response curve is q"= 200 + 0.8p! Then, find the optimal price and quantity of each firm. Hint: Start by finding the Nash equilibrium, that is, the combination of mutual best responses. Which of the following alternatives is correct? (a) For firm 1, p!= $1,600/3 and q!= 800/3 (b) For firm 1, p!= $800 and q!= 1,600/3 (c) For firm 2, p"= $800 3⁄ and q"= 1,600/3 (d) For firm 2, p"= $1,600 and q"= 800
Consider a Bertrand oligopoly where two firms (Firms 1 and 2) sell goods that are imperfect
substitutes and compete by choosing prices simultaneously. Their market demands are
q!= 1,200 − 3/2p!+ 3/2p",
q"= 800 − 2p"+ 1/2p!
For simplicity, assume the marginal cost is zero for both firms (MC!= MC"= 0). Find the best
response curve of each firm. Which of the following alternatives is correct?
(a) Firm 1’s best response curve is p!= 400 + 0.5p"
(b) Firm 2’s best response curve is p"= 400 + 0.5p!
(c) Firm 1’s best response curve is q!= 45 − 0.5q"
(d) Firm 2’s best response curve is q"= 200 + 0.8p!
Then, find the optimal
Hint: Start by finding the Nash equilibrium, that is, the combination of mutual best responses.
Which of the following alternatives is correct?
(a) For firm 1, p!= $1,600/3 and q!= 800/3
(b) For firm 1, p!= $800 and q!= 1,600/3
(c) For firm 2, p"= $800 3⁄ and q"= 1,600/3
(d) For firm 2, p"= $1,600 and q"= 800
key: !=1 "=2
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