8. Two software companies sell competing products. These products are substitutes sothat the number of units that either company sells is a decreasing function of its ownprice and an increasing function of the other product's price. Let P1 and X1 be the priceand quantity sold of product 1, and P2 and X2 the price and quantity sold of product 2. Wehave that X1 = 1,000|90--P1+2and X2 = 1,000(90-P2+P1). Each company hasincurred a fixed cost for designing their software and writing programmes, but the cost ofselling to an extra user is zero. As the firms compete in prices, each company will choosea price that maximises its profits.(a) Explain why the price that maximises each company's profits is the same as theprice that maximises its total revenue.(b) Write an expression for the total revenue of each company as a function of it its priceand the other company's price.(c) Company's 1 best response function BR1(P2) is the price of product 1 thatmaximises its profits given the price of product 2 is P2. Similarly, company's 2 bestresponse function BR2(P1) is the price of product 2 that maximises its profits giventhe price of product 1. Using these functions, write the best response function ofeach company and then calculate the Nash equilibrium prices and the total revenueof each company. Show diagrammatically the BRs and the Nash equilibrium in prices.(d) Suppose that company 1 sets its price first. Company 2 knows the price P1 thecompany 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. Explainand calculate the prices of the two companies and their total revenues. Comment onwhether there is a first or second mover advantage in this model in terms of the sizeof the change in the total revenue of each company relative to its total revenue in thesimultaneous price setting game.

Demand function for company 1 : X1 = 1000 (90 - p1/2 + p2/4 ) Demand function for company 2 : X2 =…

3. 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 X1 = 1,00090-P1+P2) and X2 = 1,000 90-P2+P1). Each company has 4 4 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.

3. 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 X1 = 1,00090-P1+P2) and X2 = 1,000 90-P2+P1). Each company has 4 4 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.

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter4: The Market Forces Of Supply And Demand

Section: Chapter Questions

Problem 10PA

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