An industry contains two firms producing homogenous goods, one whose cost function is C(Q1) = 30Q1 and another whose cost function is C(Q2) = 30Q2. The demand function for the market is given by: P = 65 - QT where QT = Q1 + Q2. a. Assuming firms are choosing quantities according to the Cournot model, what is each firm’s reaction function? b. Graph each firm’s reaction curve (on same graph). c. How much does each firm produce in the Nash equilibrium of Cournot's model?
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An industry contains two firms producing homogenous goods, one whose cost
function is C(Q1) = 30Q1 and another whose cost function is C(Q2) = 30Q2. The demand
function for the market is given by:
P = 65 - QT where QT = Q1 + Q2.
a. Assuming firms are choosing quantities according to the Cournot model, what is
each firm’s reaction function?
b. Graph each firm’s reaction curve (on same graph).
c. How much does each firm produce in the Nash equilibrium of Cournot's model?
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- Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given by: C(q) = 10+20q + q^2, where q is number of widgets produced. The market demand for widgets is represented by the inverse demand equation: P = 200 - 2Q where Q = q1 + q2 is total output. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm__ price__ profit__ b) It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm__ price__ profit__ c) What minimum discount factor is required…There are two soda firms Pepsi and Coke in Bertrand completion . They face demand with the following features: If their price is the lowest Q = 40-.5P, if their price is the same they face demand of half of the market, and if their price is the higher they face demand of zero. Both firms have a marginal cost of 10. Describe each firms reaction functions and the equilibrium price and quantity for each firm. Show your work and clearly mark your answers. Request: Please provide a graph if applicable and don't provide the handwritten answer. Thank you! Your help is much appreciated!Suppose that Raleigh and Dawes are the only sellers of bicycles in the UK. The inverse market demand function for bicycles is P(Y)=200-2Y. Both firms have the same total cost function: TC(Y)=12Y and the same marginal cost: MC(Y)=12. Suppose this market is a Stackelberg oligopoly, and Raleigh is the first mover. Write down a formula for the reaction function of Dawes. Calculate the equilibrium quantity that each firm produces and the equilibrium price in the market. Give typing answer with explanation and conclusion
- 1) The two firms in an industry, A and B, use a constant returns to scale technology, so face marginal cost c. Market demand conditions are described by the relationship p + p₁x po = 0, where po and p₁ are (constant) parameters, x is the industry output, and p is the market price. Write a report in which you a) Set out the assumptions which underlie the Cournot, and Bertrand, models of competition. b) Demonstrate that in Cournot competition, firms produce less than in Bertrand competition, so that the market price is higher in Cournot competition, and firms make greater profits. c) Explain how we can adapt the Cournot model of competition to set up the Stackelberg model (you should assume that firm A acts as the quantity leader). Define the concept of subgame perfection, and apply that to derive the subgame perfect equilibrium in the Stackelberg model, demonstrating how firm A benefits from being the quantity leader.Suppose the Boston to Philadelphia airline route is serviced by three airlines – US Airways (Firm A) and JetBlue (Firm B) and Continental (Firm C). The demand for airline travel between these two cities is Q = 150 – p. The cost function is C(Q) = 30Q. The cost function is the same for all three airlines. Assume that the three airlines are making investments in airline capacity. In other words, they are simultaneously choosing quantity. (Cournot Competition) Derive US Airways’ residual demand function given JetBlue’s output, qB, and Continental’s output, qC. What is the Marginal Revenue for US Airways? Derive US Airways reaction function Derive the market equilibrium quantity, Q*, price, p*, and Profit.Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is x = 88 – p, thousand units and the demand for brand 2 is y = 98 – p, %D thousand units, where p, and p, are prices in dollars. If the joint cost function is C = xy, in thousands of dollars, how many of each brand should be produced to maximize profit? brand 1 thousand units brand 2 thousand units What is the maximum profit? thousand dollars Need Help? Read It Watch It