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Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x1,x2)-a-x1- x2, where x is...
= Consider an industry consisting of two firms which produce a homogeneous commodity. The industry demand...
= Consider an industry consisting of two firms which produce a homogeneous commodity. The industry demand function is Q = 100 – P, where Q is the quantity demanded and P is its price. The total cost functions are given as C1 = 50q1 for firm 1, and C2 = 60qz for firm 2, where Q 91 +92. a. (6 points) Suppose both firms are Cournot duopolists. Find and graph each firm's reaction function. What would be the equilibrium price,...
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...
Cournot vs. Stackelberg Oligopoly Suppose the inverse demand function and the cost functions for two duopolists...
Cournot vs. Stackelberg Oligopoly Suppose the inverse demand function and the cost functions for two duopolists are given by: P = 100 – (Q1 + Q2) C1(Q1) = 2Q1 C2(Q2) = 2Q2 a. Cournot: Assume two Cournot duopolists. i. What is firm 1’s Quantity and Profit? R1 = (100-Q1-Q2) * Q1 R1 = 100Q1 - Q12 - Q2Q1 MR1 = 100 - 2Q1 - Q2 C1(Q1) = 2Q1 MC1 = 2 MR1 = MC1 ii. What is firm 2’s Quantity...
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose...
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose that the market demand is p(Q) = 60−Q, where as in class Q is the aggregate quantity. The const function for firm 1 is c1(q1) = 10q1 and the cost function for firm 2 is c2(q2) = q2. Firm 1 is the leader and Firm 2 is the follower. (a) Solve for the follow’s reaction function, and the leader’s maximization problem. (b) Describe the...
Two firms are participating in a Stackelberg duopoly. The demand function in the market is given...
Two firms are participating in a Stackelberg duopoly. The demand function in the market is given by Q = 2000 − 2P. Firm 1’s total cost is given by C1(q1) = (q1) 2 and Firm 2’s total cost is given by C2(q2) = 100q2. Firm 1 is the leader and Firm 2 is the follower. (1) Write down the inverse demand function and the maximization problem for Firm 1 given that Firm 2 is expected to produce R2(q1). (2) Compute...
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...
2*. Consider a market with two firms where the inverse demand function is given by p...
2*. Consider a market with two firms where the inverse demand function is given by p = 28 - 2q and where q = q1 + q2. Each firm has the total cost function c(qi) = 4qi, where i = {1,2}. a) Compare price level, quantities and profits in this market calculating the Cournot equilibrium and the Stackelberg equilibrium. Draw a graph with best response functions and illustrate the Cournot and Stackelberg solutions in that graph. b) Compare your solutions...
2*. Consider a market with two firms where the inverse demand function is given by p...
2*. Consider a market with two firms where the inverse demand function is given by p = 28 - 2q and where q = q1 + q2. Each firm has the total cost function c(qi) = 4qi, where i = {1,2}. a) Compare price level, quantities and profits in this market calculating the Cournot equilibrium and the Stackelberg equilibrium. Draw a graph with best response functions and illustrate the Cournot and Stackelberg solutions in that graph. b) Compare your solutions...
2*. Consider a market with two firms where the inverse demand function is given by p...
2*. Consider a market with two firms where the inverse demand function is given by p = 28 - 2q and where q = q1 + q2. Each firm has the total cost function c(qi) = 4qi, where i = {1,2}. a) Compare price level, quantities and profits in this market calculating the Cournot equilibrium and the Stackelberg equilibrium. Draw a graph with best response functions and illustrate the Cournot and Stackelberg solutions in that graph. b) Compare your solutions...
A homogeneous product duopoly faces a market demand function given by p = 300 - 3Q,where...
A homogeneous product duopoly faces a market demand function given by p = 300 - 3Q,where Q = q1 + q2. Both firms have constant marginal cost MC = 100. (part 2) 1a. What is the Bertrand equilibrium price and quantity in this market? 1b. Suppose Firm 1 is the Stackelberg leader, what is the equilibrium price in this market if Firm 2 plays the follower in this duopoly market? What is the equilibrium quantity? How much does each firm...
= Consider an industry consisting of two firms which produce a homogeneous commodity. The industry demand function is Q = 100 – P, where Q is the quantity demanded and P is its price. The total cost functions are given as C1 = 50q1 for firm 1, and C2 = 60qz for firm 2, where Q 91 +92. a. (6 points) Suppose both firms are Cournot duopolists. Find and graph each firm's reaction function. What would be the equilibrium price,...
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...
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...
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