Consider a three firm oligopoly in which the market demand for the homogeneous good is given...
Consider a three firm oligopoly in which the market demand for the homogeneous good is given by q = 24 - p, and costs are zero. Suppose firm 1 and 2 simultaneously pick their output, and then firm 3, observing these choices, picks its output (i.e. two “leaders”, one “follower”). Find the subgame perfect equilibrium for this model. Also show that the outcome in which each firm produces 6 units of output can be supported as Nash equilibrium, but not as a subgame perfect equilibrium outcome.
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Consider a three firm oligopoly in which the market demand for
the homogeneous good is given...
Consider the following oligopoly model. The market demand is p(Q) = 100−Q. There are three identical...
Consider the following oligopoly model. The market demand is p(Q) = 100−Q. There are three identical firms 1, 2 and 3 producing the homogeneous product. Each firm has a constant marginal cost of 0. The three firms choose their outputs simultaneously , without observing the quantity decisions by others. Find the Cournot-Nash equilibrium in this model. Obtain the profits in equilibrium for each firm.
A duopoly market in which demand is given by 180-2q. The total cost for firm 1...
A duopoly market in which demand is given by 180-2q. The total cost for firm 1 is TC = 60q1, the total cost for firm 2 is TC1 = 66q2. The good is homogeneous. A) Solve for when Firm 1 chooses the quantity before firm 2. What is the subgame Nash equilibrium? b) Solve when the firms compete simultaneously. What is the Nash equilibrium?
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring...
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring non-negativity) and and unit cost c= 3. Again, firms simultaneously pick quantities qı > 0 and q2 > 0 and the price is set to clear the market given the quantities chosen. 1. Write down the optimization problems that define the best responses, solve explicitly for the best response functions, and find all Nash equilibria. 2. Formulate the problem for a cartel that maximizes...
Problem 4. Three firms operate in an oligopoly market with inverse demand function given by D(Q)a...
Problem 4. Three firms operate in an oligopoly market with inverse demand function given by D(Q)a Q, where Q- 1 42 +q3 and q, represents the quantity produced by firm i. Each firm has constant marginal cost of production c and no fixed cost, assume that 0<c<a. The firms compete in the market by choosing quantities in the following way. Firm 1, the industry leader, chooses gi20. Firms 2 and 3 both observe qi. Firm 2 then chooses q2 2...
2. Two firms produce homogeneous products. Market demand is given by Q = 40-P, and each firm face...
2. Two firms produce homogeneous products. Market demand is given by Q = 40-P, and each firm faces a marginal cost of production of 4 per unit The timing of the game is as follows. In Period 1, firm 1 chooses the quantity q it will sell. In Period 2, firm 2 (who observed firm 1s choice in period 1) chooses whether or not to enter the market. If firm 2 chooses to enter it must pay an entry fee...
3. (35 points Suppose that there are K( 3) firms operate in a market with demand...
3. (35 points Suppose that there are K( 3) firms operate in a market with demand function given by P(Q) = 100-Q, where Q=91 +92 + ... +2K, and qi is the quantity produced by firm i. Each firm has a constant marginal cost of production, c = 10, and no fixed cost. The firms choose their quantities dynamically as follows: Firm 1, which is the industry leader, chooses qı € (0, 100). All other firms i = 2,..., K...
Suppose that the inverse market demand for a commodity is given by P = 240 Q...
Suppose that the inverse market demand for a commodity is given by P = 240 Q The cost curves of the three firms which could serve this market are TC,(a) 30q +300 and TC2() (d) Suppose that firms engage in Stackelberg rather than Cournot competition. Firm 1 moves first by choosin its output level. After Firm 1 has chosen its output level, Firm 2 observes ql and chooses its output leve Find the subgame-perfect Nash equilibrium of the Stackelberg game....
Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x1,x2)-a-x1- x2, where x is...
Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x1,x2)-a-x1- x2, where x is the quantity chosen by firm 1, x2 the quantity chosen by firm 2, and a > 0. The cost functions are C1 (x1)-x follower. and C2(x2)- . Firm I is a Stackelberg leader and firm 2 a Stackelberg Q.2.a Find the subgame-perfect quantities. Q.2.b Calculate each firm's equilibrium profit.
I. Consider a three firm (n = 3) Cournot oligopoly. The market inverse demand function is...
I. Consider a three firm (n = 3) Cournot oligopoly. The market inverse demand function is P()-24 Q. Firm 1 has constant average and marginal costs of $12 per unit, while firms 2 and 3 have constant average and marginal costs of $15 per unit. p (Q) (a) Verify that the following are Nash equilibrium quantities for this market: q,-. and g2 = g3 We were unable to transcribe this image
3. Cournot competition: The inverse demand for a homogeneous good is given by p(Q) = 100...
3. Cournot competition: The inverse demand for a homogeneous good is given by p(Q) = 100 - Q if Q< 100 and p(Q) = 0 if Q > 100, where p is the price in the market and Q > 0 is the total quantity supplied in the market. There are two firms, labeled 1 and 2, each of which produce the good at a constant marginal cost of 10 per unit. There are no fixed costs. Denoting the output...
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring non-negativity) and and unit cost c= 3. Again, firms simultaneously pick quantities qı > 0 and q2 > 0 and the price is set to clear the market given the quantities chosen. 1. Write down the optimization problems that define the best responses, solve explicitly for the best response functions, and find all Nash equilibria. 2. Formulate the problem for a cartel that maximizes...
Problem 4. Three firms operate in an oligopoly market with inverse demand function given by D(Q)a Q, where Q- 1 42 +q3 and q, represents the quantity produced by firm i. Each firm has constant marginal cost of production c and no fixed cost, assume that 0<c<a. The firms compete in the market by choosing quantities in the following way. Firm 1, the industry leader, chooses gi20. Firms 2 and 3 both observe qi. Firm 2 then chooses q2 2...
2. Two firms produce homogeneous products. Market demand is given by Q = 40-P, and each firm faces a marginal cost of production of 4 per unit The timing of the game is as follows. In Period 1, firm 1 chooses the quantity q it will sell. In Period 2, firm 2 (who observed firm 1s choice in period 1) chooses whether or not to enter the market. If firm 2 chooses to enter it must pay an entry fee...
3. (35 points Suppose that there are K( 3) firms operate in a market with demand function given by P(Q) = 100-Q, where Q=91 +92 + ... +2K, and qi is the quantity produced by firm i. Each firm has a constant marginal cost of production, c = 10, and no fixed cost. The firms choose their quantities dynamically as follows: Firm 1, which is the industry leader, chooses qı € (0, 100). All other firms i = 2,..., K...
Suppose that the inverse market demand for a commodity is given by P = 240 Q The cost curves of the three firms which could serve this market are TC,(a) 30q +300 and TC2() (d) Suppose that firms engage in Stackelberg rather than Cournot competition. Firm 1 moves first by choosin its output level. After Firm 1 has chosen its output level, Firm 2 observes ql and chooses its output leve Find the subgame-perfect Nash equilibrium of the Stackelberg game....
Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x1,x2)-a-x1- x2, where x is the quantity chosen by firm 1, x2 the quantity chosen by firm 2, and a > 0. The cost functions are C1 (x1)-x follower. and C2(x2)- . Firm I is a Stackelberg leader and firm 2 a Stackelberg Q.2.a Find the subgame-perfect quantities. Q.2.b Calculate each firm's equilibrium profit.
I. Consider a three firm (n = 3) Cournot oligopoly. The market inverse demand function is P()-24 Q. Firm 1 has constant average and marginal costs of $12 per unit, while firms 2 and 3 have constant average and marginal costs of $15 per unit. p (Q) (a) Verify that the following are Nash equilibrium quantities for this market: q,-. and g2 = g3 We were unable to transcribe this image
3. Cournot competition: The inverse demand for a homogeneous good is given by p(Q) = 100 - Q if Q< 100 and p(Q) = 0 if Q > 100, where p is the price in the market and Q > 0 is the total quantity supplied in the market. There are two firms, labeled 1 and 2, each of which produce the good at a constant marginal cost of 10 per unit. There are no fixed costs. Denoting the output...
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