Two software companies sell competing products. These products are substitutes so that the number of units that either company sells is a decreasing function of its own price and an increasing function of the other product’s price. Let P1 and X1 be the price and quantity sold of product 1, and P2 and X2 the price and quantity sold of product 2. We have that and . Each company has incurred a fixed cost for designing their software and writing programmes, but the cost of selling to an extra user is zero. As the firms compete in prices, each company will choose a price that maximises its profits. a) Explain why the price that maximises each company’s profits is the same as the price that maximises its total revenue. b) Write an expression for the total revenue of each company as a function of it its price and the other company’s price. c) Company’s 1 best response function BR1(P2) is the price of product 1 that maximises its profits given the price of product 2 is P2. Similarly, company’s 2 best response function BR2(P1) is the price of product 2 that maximises its profits given the price of product 1. Using these functions, write the best response function of each company and then calculate the Nash equilibrium prices and the total revenue of each company. Show diagrammatically the BRs and the Nash equilibrium in prices.
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Two software companies sell competing products. These products are substitutes so that the number of units that either company sells is a decreasing function of its own price and an increasing function of the other product’s price. Let P1 and X1 be the price and quantity sold of product 1, and P2 and X2 the price and quantity sold of product 2. We have that and . Each company has incurred a fixed cost for designing their software and writing programmes, but the cost of selling to an extra user is zero. As the firms compete in prices, each company will choose a price that maximises its profits.
a) Explain why the price that maximises each company’s profits is the same as the price that maximises its total revenue.
b) Write an expression for the total revenue of each company as a function of it its price and the other company’s price.
c) Company’s 1 best response function BR1(P2) is the price of product 1 that maximises its profits given the price of product 2 is P2. Similarly, company’s 2 best response function BR2(P1) is the price of product 2 that maximises its profits given the price of product 1. Using these functions, write the best response function of each company and then calculate the Nash
d) Suppose that company 1 sets its price first. Company 2 knows the price P1 the company has chosen, and it knows that company 1 will not change its price. Also, company 1 is aware of how company 2 will react to its own choice of price. Explain and calculate the prices of the two companies and their total revenues. Comment on whether there is a first or second mover advantage in this model in terms of the size of the change in the total revenue of each company relative to its total revenue in the simultaneous price setting game.
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