Suppose an industry has three identical firms competing on quantities with demand P = 100 ― (2)Q and constant marginal costs of MC = 1. What are the firms’ best response functions?
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Suppose an industry has three identical firms competing on quantities with demand P = 100 ― (2)Q and constant marginal costs of MC = 1. What are the firms’ best response functions?
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- Two firms produce complementary products. Suppose the demand for their products is given by q1(p) = a−2p1−p2, and q2(p) = a−p1−2p2. Both firms face a constant marginal costs k, and a fixed cost of 0 (so TCi(qi) = kqi). . For each firm, write profit as a function of prices. Derive the best response function of each firm. Thus, write p1 = R1(p2) as a function of p2, and similarly p2 = R2(p1) as a function of p1. For a = 8 and k = 1, sketch the best response functions on a graph. Are the prices strategic substitutes or complements? Let a = 8 and k = 1. Compute the equilibrium prices, quantities and profits. Suppose now the two firms decide to merge as one so that they want to maximize the joint profit πm = π1 +π2. Write down the profit function and derive the first order conditions for maximizing the joint profit. Compute the equilibrium prices, quantities, and profits. Compare the results with when the firms were independent and comment on if the firms are better off with the…Suppose an industry has three identical firms competing on quantities with demand P = 100 ― (2)Q and constant marginal costs of MC = 1. What are the firms’ best response functions? What could lead the firms to have asymmetric best response functions? What is the simplest assumption that could change?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
- Two firms who make identical products engage in Cournot competition. The inverse market demand curve is: P(Q) = 60 - 10Q, where Q=9₁ +92. The cost functions are C₁(9₁) 1091 and C₂ (92) : 592 for firms 1 and 2, respectively. Find the Nash equilibrium quantities for each firm. (a) 9₁ = = 1.5, 92 2 (b) q₁ = 92 = 2 (c) q₁ = 92 = 1.5 (d) 9₁ = 1.5, 92 = 3 (e) None of the above options is correct.Suppose that Raleigh and Dawes are the only sellers of bicycles in the UK. The inverse market demand function for bicycles is ?(?)=200−2?. Both firms have the same total cost function: ??(?)=12? and the same marginal cost: ??(?)=12.Suppose this market is a Stackelberg oligopoly and Raleigh is the first mover.a) Write down a formula for the reaction function of Dawes.b) Calculate the equilibrium quantity that each firm produces and the equilibrium price in the market.c) At the Stackelberg equilibrium, how much profit does each firm make?Suppose now that the two firms decide to act like a single monopolist.a) What will the total quantity of bicycles sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium.b) Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly.c) For the…Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete. Assume that Mytown engages in free trade in the dolls markets with Yourtown, who also faces a market with monopolistic competition. Because of this we can expect that, (a) The numbers of firms operating in this market will not change. (b) At equilibrium the profit of firms will increase. (c) The quantity of types of dolls available to consumers will increase. (d) All the above answers are correct.
- Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete. If the number of firms entering the dolls market increase, we know that, (a) The price of dolls will drop. (b) The average cost of UD will increase. (c) The quantity sold by UD will drop. (d) All the above answers are correct.A market comprises three firms i E {1, 2, 3} competing in quantities. Inverse market demand is given by p(Q) = 100 - 50, where Q = 9₁ +92 +93. Each firm i has marginal cost c₁, and therefore profit function Ti (91, 92, 93) = (p - ci)qi. a) Suppose c₁ = 1, c₂ = 4, and c3 = 7. Find the best response functions for each firm by filling numbers in the blanks below. 9 (92, 93) = (92 +93). 9₂ (91, 93) = (91 +93). 93 (91, 92) = (91 +92). b) In equilibrium, we know that the level of output for each firm is q₁ = 5.4, 92 = = 4.8, 93 = 4.2. Compute the profit of firm 1: ₁ = Compute the profit of firm 2: ₂ =Consider the following market demand function: Q= 20-2P, where P is the market price. Suppose there are two firms- A,B in the market and they have the same cost function: the per unit cost of producing output is 4. The firms compete by choosing quantities. Find the reaction functions for both the firms if they are maximizing profits. What is the profit maximizing output for each firm and corresponding market price? If there was only one firm in the market how would your answer change?
- Suppose that there are two lemonade stands competing with one another via Bertrand (price) competition. There are 100 potential customers who walk by the two stands each day. Each of these customers will buy lemonade from whichever stand is cheapest as long as the price is less than $1. If they charge the same price then the customer chooses randomly between the two. The marginal cost of lemonade is the $0.25 for both stands. Fixed Costs are equal to $5 for each stand. What is the Nash equilibrium price of lemonade? a. $0.25 b. $1.00 c. $0.30 d. $0.35Consider an industry with two identical firms (denoted firm 1 and 2) producing a homogenous good. Firms compete in quantities. Firm 1 has a constant marginal cost of 20. Firm 2 has a constant marginal cost of 80. Demand in the industry is given by D(p) = 380 - p. Let q1 and 92 denote the quantities of firm 1 and 2, respectively. Derive the Nash equilibrium in quantities. What is the total production in this industry?Consider Hotelling's model (a street of length one, consumers uniformly distributed along the street, each consumer has a transportation cost equal to 2t, where t is the distance traveled). Suppose there are two gas stations, one located at 1/4 and the other located at 1. (a) Calculate the demand functions for the two firms. (b) If the two gas stations compete in prices and settle at a Nash equilibrium, will they charge the same price for gasoline? (assume that production costs are zero, that is, firms maximize revenue).