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 theprice and quantity sold of product 1, and P2 and X2 the price and quantity sold ofproduct 2. We have that X1 = 1,000 (90 –P1 +P2) and X2 = 1,000 (90 –P2 +P1). Each company has incurred a fixed cost for designing their software and writingprogrammes, but the cost of selling to an extra user is zero. As the firms compete inprices, 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 pricethat 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 that maximisesits profits given the price of product 2 is P2. Similarly, company's 2 best responsefunction BR2(P1) is the price of product 2 that maximises its profits given the price ofproduct 1. Using these functions, write the best response function of each companyand then calculate the Nash equilibrium prices and the total revenue of each company.Show diagrammatically the BRs and the Nash equilibrium in prices.

X1=1000*(90-0.5P1+0.25P2)X1=1000*(90-0.5P2+0.25P1)MC=0Fixed cost>0

8. 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 = 1,000 (90-P1+¹P2) and X2 = 1,000 (90-1/P2 + P1). 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.

8. 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 = 1,000 (90-P1+¹P2) and X2 = 1,000 (90-1/P2 + P1). 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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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