Solution:
Market demand: P = 80 - 2Q = 80 - 2(q1 + q2)
a) Profit function for firm i, Wi = P*qi - TCi
Wi = (80 - 2qi - 2qj)*qi - 20qi ; where j is the other firm
Wi = (60 - 2qj)*qi - 2qi2
Then, finding the best response function of firm i (using the first order condition of partial derivative being equal to 0, that is, = 0)
= 60 - 2qj - 2*2qi
= 0 then gives us, 4qi + 2qj = 60
qi*(qj*) = (60 - 2qj*)/4. This is the best response function of firm i to optimal quantity production by firm j.
So, firm 1's best response function becomes: q1* = (60 - 2q2*)/4
And firm 2's best response function becomes: q2* = (60 - 2q1*)/4
Solving the two equations simultaneously, we get the equilibrium quantity levels as:
q1* = q2* = 10
So, equilibrium total quantity in the market, Q* = 10 + 10 = 20 units, and equilibrium price, P = 80 - 2(20) = $40
Since the cost and quantity are same for both firms for a price level, their profits will also be same. So, profits are
W1 = W2 = 40*10 - 20*10 = $200
(b) If the firms decide to form a cartel, they will act as a monopoly. Then the profit of cartel firm is
W = total revenue - total cost
W = P*(q1 + q2) - (TC1 + TC2)
Or (with similar cost it becomes), W = P*Q - 20*Q
W = (80 - 2Q)*Q - 20*Q
W = 60Q - 2Q2
Again using the first order condition: = 0
So, = 60 - 2*2Q
60 - 4Q = 0 gives us, Q = 60/4 = 15 units (total quantity).
q1 = q2 = Q/2 = 15/2 = 7.5 units (by each firm)
So, we have found that in cartel both firms produce 7.5 units each and in cournot, both produce 10 units each. We can easily form the required payoff matrix.
Problem 1 Consider the following Cournot's duopoly, where two identical firms compete by setting quantities. Suppose...
1. Consider the following asymmetric version of the Cournot duopoly model. Two firms compete by simultaneously choosing the quantities (q, and q2) they produce. Their products are homogeneous, and market demand is given by p- 260-2Q, where Q-q +q2. Firm 1 has a cost advantage; Firm 1 produces at zero cost, while Firm 2 produces at a constant average cost of 40. (The difference in costs is what makes this an asymmetric game.) a. Derive both firms' profit functions, as...
5. Consider a version of the Cournot duopoly game, where firms 1 and 2 simul taneously and independently select quantities to produce in a market. The quantity selected by firm i is denoted q, and must be greater than or equal to zero, for i -1,2. The market price is given by p - 100 - 2q Suppose that each firm produces at a cost of 20 per unit. Further, assume that each firm's payoff is defined as its profit....
Two identical firms compete as a Cournot duopoly. The inverse market demand they face is P = 120-2Q. The total cost function for each firm is TC1(Q) = 4Q1. The total cost function for firm 2 is TC2(Q) = 2Q2. What is the output of each firm? Find: Q1 = ? Q2 = ?
MomCorp (M) and Planet Express, Inc. (E) are two firms that compete in a Cournot duopoly by simultaneously setting quantities (of package deliveries). Denote MomCorp's quantity by Q and Planet Express's quantity by Qe. The package deliveries they offer are identical, so the price is determined in a combined market according to the inverse demand equation, P = 120-Q, where Q = Qu + Qe. Suppose that MomCorp has constant marginal cost, MCM = 20, while Planet Express has constant...
MomCorp (M) and Planet Express, Inc. (E) are two firms that compete in a Cournot duopoly by simultaneously setting quantities (of package deliveries). Denote MomCorp's quantity by Q n and Planet Express's quantity by Qe. The package deliveries they offer are identical, so the price is determined in a combined market according to the inverse demand equation, P = 120 -0, where Q = QM+QE. Suppose that MomCorp has constant marginal cost, MCM = 20, while Planet Express has constant...
2.13. Recall the static Bertrand duopoly model (with homoge- neous products) from Problem 1.7: the firms name prices simul- taneously; demand for firm i's product is a - Pi if Pi < Pi, is 0 if Pi > Pi, and is (a – Pi)/2 if Pi = Pj; marginal costs are c < a. Consider the infinitely repeated game based on this stage game. Show that the firms can use trigger strategies (that switch forever to the stage-game Nash equilibrium...
Consider two identical firms with no fixed costs and constant marginal cost c which compete in quantities in each of an infinite number of periods. The quantities chosen are observed by both firms before the next play begins. The inverse demand is given by p = 1 − q1 − q2, where q1 is the quantity produced by firm 1 and q2 is the quantity produced by firm 2. The firms use ‘trigger strategies’ and they revert to static Cournot...
Suppose identical price setting duopoly firms have constant marginal costs of $50 per unit and no fixed costs. Consumers view the firms' products as perfect substitutes. The market demand is Q = 90 - p. In Bertrand equilibrium, firm 1's price is $_and firm 2's price is $ . (Enter numeric responses using integers.)
Problem 1. Cournot Competition with Two Firms Suppose there are two identical firms engaged in quantity competition (Cournot competition). The demand is P=1-Q where Q =91 +92. Assume that firm's i total cost of production is TC(qi) Compute the Cournot equilibrium (i.e., quantities, price, and profits).
Two identical firms compete as a count duopoly. The inverse market demand they face is Risto P=120-QQ. The total cost function for firm 1 is Te, CQ) = AQ. The total cost function for firma is TC, (Q) = 2Qz. What is the output of each firm? A.Q, = 19, Q=20 B. Q = 20, Q = 19 C.Q=19 , Q = 19 D. Q,= 19, Q, 18 E. Q, = 19, 2,319