Consider the melon market example used in the class, assume the marginal cost of Firm 2 is $0.31, the marginal cost of F
Posted: Fri Apr 29, 2022 11:37 am
Consider the melon market example used
in the class, assume the marginal cost of Firm 2 is $0.31, the
marginal cost of Firm 1 is still $.28.
a. Under Cournot quantity
competition, if Firm 2 believes that Firm 1 will produce
q1, derive the profit function and the
best-response function for Firm 2.
b. Consider Stackelberg
leader-follower competition. If Firm 1 is the leader and produces
q1, derive the profit function of Firm 2 and
the best-response function q2.
c. Are the results in a.
and b. the same? Why?
d. Under Bertrand price
competition, if Firm 1 sets the price P1 =
0.30, then how should Firm 2 response, why?
e. Under Cournot quantity
competition, compute each firm's optimal output.
Case 1: Quantity Competition Assume firms make independent decisions about how much to produce. Firm i believes that Firm 2 will sell q, melons, the residual demand of Firm i is 9.= Q(P) - 92 =1000-1000P-92, or P(9.)= 1-(9, +9)/1000 The profit that Firm 1 wants to maximize is P(q) q,-cq,=[1-(9, +9)/1000] 9.-287, • The optimal solution given q, is 9.= 360-92/2 Case 1: Quantity Competition Calculations • Profit= 4,-(1/1000)(q^2+929,)-.28 q, . Optimal condition: Marginal profit=d(profit)/d(9.)=0 • Profit=.72 9.-(1/1000) (q,^2+ 929.) Apply the first order condition. d(profit)/d(q.)=.72-(1/1000) (24,+q2)=0, then .72= (1/1000) (2 .+q2) 720=2 91 +92 291 =720-92 • The optimal output as a function of the other firm's output is 9. =360-92/2 Case 3: Quantity Competition • Same way, we find the profit that Firm 2 wants to maximize is P(q2) 92-Cq2=[1-(q, +92)/1000] 22-2892 Thus, the optimal solution given q, is 92= 360-91/2 Although we still don't know what the equilibrium outputs are, we know qı= 360-92/2 is the best response of Firm 1, and 92= 360-9./2 is the best response of Firm 2 • We know what a firm would do given the other firm's choice (That is what we need to solve for the Nash Equilibrium)
Consider the melon market example used in the class, assume the marginal cost of Firm 2 is $0.31, the marginal cost of Firm 1 is still $.28. a. Under Cournot quantity competition, if Firm 2 believes that Firm 1 will produce qı, derive the profit function and the best-response function for Firm 2. b. Consider Stackelberg leader-follower competition. If Firm 1 is the leader and produces qı, derive the profit function of Firm 2 and the best- response function 2. c. Are the results in a. and b. the same? Why? d. Under Bertrand price competition, if Firm 1 sets the price P1 = 0.30, then how should Firm 2 response, why? e. Under Cournot quantity competition, compute each firm's optimal output. f. Under Stackelberg leader-follower competition, compute the leader's optimal output. =
in the class, assume the marginal cost of Firm 2 is $0.31, the
marginal cost of Firm 1 is still $.28.
a. Under Cournot quantity
competition, if Firm 2 believes that Firm 1 will produce
q1, derive the profit function and the
best-response function for Firm 2.
b. Consider Stackelberg
leader-follower competition. If Firm 1 is the leader and produces
q1, derive the profit function of Firm 2 and
the best-response function q2.
c. Are the results in a.
and b. the same? Why?
d. Under Bertrand price
competition, if Firm 1 sets the price P1 =
0.30, then how should Firm 2 response, why?
e. Under Cournot quantity
competition, compute each firm's optimal output.
- Consider The Melon Market Example Used In The Class Assume The Marginal Cost Of Firm 2 Is 0 31 The Marginal Cost Of F 1 (364.3 KiB) Viewed 26 times
Consider the melon market example used in the class, assume the marginal cost of Firm 2 is $0.31, the marginal cost of Firm 1 is still $.28. a. Under Cournot quantity competition, if Firm 2 believes that Firm 1 will produce qı, derive the profit function and the best-response function for Firm 2. b. Consider Stackelberg leader-follower competition. If Firm 1 is the leader and produces qı, derive the profit function of Firm 2 and the best- response function 2. c. Are the results in a. and b. the same? Why? d. Under Bertrand price competition, if Firm 1 sets the price P1 = 0.30, then how should Firm 2 response, why? e. Under Cournot quantity competition, compute each firm's optimal output. f. Under Stackelberg leader-follower competition, compute the leader's optimal output. =