6. Two identical firms that have the cost function C(q) = 4qj, where j = {1,2} are competing in a homogenous good market. The two firms make simultaneous decisions on price, and they face industry demand Q(P) = 20-p. What is the Bertrand-Nash equilibrium profit of each firm? Hints for (b) and (c): Solve for each firm j's output (q;) and use the fact that II, = pjqj - С₁(a). b. Now, suppose the two firms are deciding whether to set a collusive market price of $6 (this means that they would both charge $6). Solve for their profits under this pricing scheme. a. C. If one of the firms decides to deviate from the collusive scheme and undercut its rival's price by $1, how much profit would it earn? d. Reproduce and then fill in the table below using your findings from parts (a)-(c). e. Firm 1 Collude Compete Collude col, πt col dev, fol Firm 2 Compete oldev Bert., Bert. *col and Bert. are the collusive and Bertrand profit levels, respectively. dev is the profit level of a firm when it undercuts its rival who is pricing at the collusive level. Finally, Tol is the profit level of a firm when it sets the collusive price but gets undercut by its rival. If a firm is indifferent between Compete and Collude assume that it will choose Compete. Is there a Nash equilibrium in pure strategies? If so, what is it?
6. Two identical firms that have the cost function C(q) = 4qj, where j = {1,2} are competing in a homogenous good market. The two firms make simultaneous decisions on price, and they face industry demand Q(P) = 20-p. What is the Bertrand-Nash equilibrium profit of each firm? Hints for (b) and (c): Solve for each firm j's output (q;) and use the fact that II, = pjqj - С₁(a). b. Now, suppose the two firms are deciding whether to set a collusive market price of $6 (this means that they would both charge $6). Solve for their profits under this pricing scheme. a. C. If one of the firms decides to deviate from the collusive scheme and undercut its rival's price by $1, how much profit would it earn? d. Reproduce and then fill in the table below using your findings from parts (a)-(c). e. Firm 1 Collude Compete Collude col, πt col dev, fol Firm 2 Compete oldev Bert., Bert. *col and Bert. are the collusive and Bertrand profit levels, respectively. dev is the profit level of a firm when it undercuts its rival who is pricing at the collusive level. Finally, Tol is the profit level of a firm when it sets the collusive price but gets undercut by its rival. If a firm is indifferent between Compete and Collude assume that it will choose Compete. Is there a Nash equilibrium in pure strategies? If so, what is it?
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.3P
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Transcribed Image Text:6.
Two identical firms that have the cost function C(q) = 4qj, where j = {1,2} are
competing in a homogenous good market. The two firms make simultaneous decisions on price,
and they face industry demand Q(P) = 20-p.
What is the Bertrand-Nash equilibrium profit of each firm?
Hints for (b) and (c): Solve for each firm j's output (q;) and use the fact that II; = p;q; - C;(qj).
b. Now, suppose the two firms are deciding whether to set a collusive market price of
$6 (this means that they would both charge $6). Solve for their profits under this pricing
scheme.
a.
C.
d.
e.
If one of the firms decides to deviate from the collusive scheme and undercut its
rival's price by $1, how much profit would it earn?
Reproduce and then fill in the table below using your findings from parts (a)-(c).
Firm 1
Collude
Compete
Collude
ποι ποι
dev,
fol
Firm 2
Compete
oldev
Bert., Bert.
*col and Bert. are the collusive and Bertrand profit levels, respectively. dev is the
profit level of a firm when it undercuts its rival who is pricing at the collusive level.
Finally, Tol is the profit level of a firm when it sets the collusive price but gets undercut
by its rival.
If a firm is indifferent between Compete and Collude assume that it will choose
Compete. Is there a Nash equilibrium in pure strategies? If so, what is it?
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