Herder will try to maximize the profit in best response. Hence first derivative of q1 should be equal to zero at best response.
Hence 0=d/dq1 (80q1-q1/2-q2/2)
Or, 0= 80-q1-q2/2
Or, q1= 80- q2/2
hence option d is correct
Consider a version of the Tragedy of the Commons in which herder 1 and 2 simultaneously...
In a Cournot game with homogeneous commodities, players are firms who simultaneously announce quantities they want to produce. Suppose there are two firms, 1 and 2, whose chosen quantities are q1 and q2 respectively. The market price is given by P = 31 − 3Q where Q = q1 + q2. The constant marginal cost of each firm is 4. a) (12 points) What is the best response function for each firm? b) (6 points) What is the best response...
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...
2. Cournot competition: P1 and P2 (independently and simultaneously) choose quantities, qi and q2. The cost of producing q units is c(ai)i and the demand curve is given by P(O) 10 Q: (i.e., if P1 produces qi and P2 produces q2; each sells all his units at price 10 1 92 (a) Find all NE. b) Now suppose that the game is played twice. Each firm chooses both a production quantity, and, firm 2 can choose to donate some of...
5. Consider a version of the Cournot duopoly game, which will be thoroughly analyzed in Chapter 10. Two firms (1 and 2) compete in a homogeneous goods market, where the firms produce exactly the same good. The firms simultaneously and independently select quantities to produce. 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-2 - q1 -q2. For simplicity, as...
imagine a market comprising two competing firms 1&2 which produce an identical product . the inverse demand function of the latter is p = 102 – Q, where Q = Q1 + Q2 , Qi = output of firm I (i=1,2) lastly , the cost of production equals TC(Qi)= 2 Qi . if the two firms choose Qi simultaneously , and only once , with a view to maximize their respective profit , find the nash equilibrium (Firm 1, firm...
PROBLEM #1 Consider a market with two firms that sell products that are identical. Su market demand is as follows: P-56-Q , where Q measures the total output produced by both firms (that is, Q=q +q.) and qi and q, are the quantities produced by firm 1 and firm 2, respectively. The per-unit cost of production is $6 for each firm, and so the firm's cost functions are 6q, and 6q, respectively. Each firm seeks to maximize profits. The firms...
There are two firms in a market, producing the same good. The firms simultaneously choose their output levels, q1 for firm 1 and q2 for firm 2. The price adjusts according to the inverse demand function p = 65−(q1 + q2). Each firm has a per-unit (average) cost of 5. Each firm’s payoff is its profit. a. (5 pts) Find firm 1’s profit as a function of q1 and q2 (profit equals revenue minus total cost). b. (10 pts) Find...
Consider the following game. Firm 1, the leader, selects an output q1, after which firm 2, the follower, observes the choice of q1, and then selects its own output, q2. The resulting price is one satisfying the industry demand curve P=200-q1-q2. Both firms have zero fixed costs and a constant marginal cost of c=60. Derive the equation for the follower firm’s best response function. Draw this equation on a graph with q2, on the vertical axis and q1 on the...
2. (30 pts) There are two firms in a market, producing the same good. The firms simultaneously choose their output levels, qı for firm 1 and q2 for firm 2. The price adjusts according to the inverse demand function p= 65 – (91 +92). Each firm has a per-unit (average) cost of 5. Each firm's payoff is its profit. a. (5 pts) Find firm l's profit as a function of qı and q2 (profit equals revenue minus total cost). b....
3. There are two firms that compete according to Cournot competition. Firm 1 has a cost function G(91) = 5.59+12. Firm 2 has a cost function C(q2) = 2.5q3 + 18. These firms cannot discriminate, so there is just one price that is determined by the aggregate demand. The inverse demand equation is P(Q) = 600 – 0 Where total supply Q-q1+92. (e) Use your best response equations to mathematically solve for the equilibrium quantities qi 9, Q". equilibrium price...