uppose 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 two firms to be willing to agree to act as a monopoly, how should they split the quantity to produce between them? We assume that if they do not agree to act like a monopoly, then the market structure is the Stackelberg oligopoly studied above. We further assume that no money transfer is possible between the two firms. In other words, each firm earns profit only by selling the bicycles that it has produced itself.
Suppose that Raleigh and Dawes are the only sellers of bicycles in the UK. The inverse
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
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 two firms to be willing to agree to act as a monopoly, how should they split the quantity to produce between them? We assume that if they do not agree to act like a monopoly, then the market structure is the Stackelberg oligopoly studied above. We further assume that no money transfer is possible between the two firms. In other words, each firm earns profit only by selling the bicycles that it has produced itself.
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