Microeconomics
Microeconomics
2nd Edition
ISBN: 9781464187025
Author: Austan Goolsbee, Steven Levitt, Chad Syverson
Publisher: Worth Publishers
Question
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Chapter 11, Problem 16P

(a)

To determine

The reaction function of the company.

(a)

Expert Solution
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Explanation of Solution

The total revenue of the firm is the price multiplied with the quantity of the firm. The demand for the cable internet service is given as qc=1003Pc+2Pr where qand pc represent the quantity demanded as well as the price of the cable internet services. Pr represents the price of the internet services from the telephone. The demand for the telephone via internet is similar and it is qr=1003Pr+2Pc. Thus, the revenue of the internet service for the cable providers can be calculated as follows:

The marginal revenue curve of firm cable internet service can be derived as follows:

MRC=(qC×pC)pC=(1003pC2pT)pCpC=(100pC3pC22pTpC)pC=1006pC2pT

The marginal revenue is MRC=1006pC2pT.

Through equating the marginal revenue with the marginal cost, the reaction curve of the cable internet service providing firm can be calculated. Here, the marginal cost of providing internet service is assumed to be zero and the reaction curve can be calculated as follows:

MR=MC1006PC+2Pr=06PC=100+2PrPC=100+2Pr6PC=16.67+0.33Pr

Thus, the reaction function of the cable internet service providing firm is PC=16.67+0.33Pr.

Economics Concept Introduction

Bertrand competition: The Bertrand competition is the model of imperfect competition where the relation and interactions between the firms set their price and their consumers demands their quantities at the price set.

(b)

To determine

The reaction curve of the telephone internet service provider.

(b)

Expert Solution
Check Mark

Explanation of Solution

The demand for the telephone via internet is similar and it is qr=1003Pr+2Pc. Thus, the revenue of the internet service for the cable providers can be calculated as follows:

The marginal revenue curve of firm cable internet service can be derived as follows:

MRT=(qT×pT)pT=(1003pT2pC)pTpT=(100pC3pT22pCpT)pT=1006pT2pC

The marginal revenue is MRC=1006pT2pC.

The marginal revenue curve of the firm will be MR=1006Pr+2PC. Through equating the marginal revenue with the marginal cost, the reaction curve of the DSL internet service providing firm can be calculated. Here, the marginal cost of providing internet service is assumed to be zero and the reaction curve can be calculated as follows:

MR=MC1006Pr+2PC=06Pr=100+2PCPr=100+2PC6Pr=16.67+0.33PC

Thus, the reaction function of the telephone DSL internet service providing firm is Pr=16.67+0.33PC.

(c)

To determine

Price, quantity, and profits of each firm when the ATC is zero.

(c)

Expert Solution
Check Mark

Explanation of Solution

The equilibrium quantity and price can be calculated with the help of the two reaction functions. The reaction function of the firm r can be substituted in the reaction function of firm c to calculate the price as follows:

PC=16.67+0.33Pr=16.67+0.33×(16.67+0.33PC)=16.67+5.50+0.11PC0.89PC=22.17PC=22.170.89=24.9

Thus, the price charged should be 25 for the cable internet service firm,  since the DSL internet firm is also facing the similar problem. The DSL firm should also charge the same price. It can be verified as follows:

Pr=16.67+0.33PC=16.67+0.33×(16.67+0.33Pr)=16.67+5.50+0.11Pr0.89Pr=22.17Pr=22.170.89=24.9

By substituting the value of P in the demand function, the quantities can be calculated for each firm as follows:

qc=1003Pc+2Pr=100(3×25)+(2×25)=10075+50=15075=75

Thus, the quantity that the cable internet service provider provides is 75, since the DSL firm faces the similar problem. It also serves 75 customers at a price of $25. The ATC of the firm is zero. Therefore, the total revenue of each firm is their total profit and the total profit of each firm can be calculated as follows:

Profitc=QC×PC=75×25=1,875

Thus, each firm would make a profit of $1,875.

(d)

To determine

Price, quantity, and profits of each firm when the cable internet becomes faster.

(d)

Expert Solution
Check Mark

Explanation of Solution

The demand for the cable internet service is given as qc=1002Pc+3Pr where the qand pc represent the quantity demanded as well as the price of the cable internet services. Pr represents the price of the internet services from the telephone. The demand for the telephone via internet is qr=1004Pr+Pc. Thus, the revenue of the internet service for the cable providers can be calculated as follows:

TR=QC×PC=PC×(1002PC+3Pr)=100PC2PC2+3PCPr

The total revenue is 100PC2PC2+3PCPr.

Marginal revenue can be calculated as follows:

MR=Total revenuePC=100PC2PC2+3PCPrPC=1004PC+3Pr

The marginal revenue is MR=1004PC+3Pr.

By setting the MR equal to MC which is zero, the reaction curve of the cable internet firm can be calculated as follows:

MR=MC1004PC+3Pr=04PC=100+3PrPC=100+3Pr4PC=25+0.75Pr

The total revenue for the DSL firm can be calculated as follows:

TR=Qr×Pr=Pr×(1004Pr+PC)=100Pr4Pr2+PCPr

The total revenue is 100Pr4Pr2+PCPr.

Marginal revenue can be calculated as follows:

MR=Total revenuePC=100Pr4Pr2+PCPrPr=1008Pr+PC

By setting the MR equal to MC which is zero, the reaction curve of the DSL internet firm can be calculated as follows:

MR=MC1008Pr+PC=08Pr=100+PCPr=100+PC8Pr=12.5+0.125PC

The equilibrium quantity and price can be calculated with the help of the two reaction functions. The reaction function of the firm r can be substituted in the reaction function of firm c to calculate the price as follows:

PC=25+0.75PrPC=25+0.75×(12.50+0.125PC)PC=25+9.375+0.093PCPC0.093PC=34.375PC=34.3750.907=37.9

Thus, the price charged should be 37.9 for the cable internet service firm and DSL internet firm price can be calculated as follows:

Pr=12.50+0.125PC=12.50+0.125×(37.9)=12.50+4.74=17.24

By substituting the value of P in the demand function, the quantities can be calculated for each firm as follows:

qc=1002Pc+3Pr=100(2×37.78)+(3×17.17)=10075.56+51.51=151.5175.56=75.95

Thus, the quantity that the cable internet service provider provides is 76 and the DSL firm can be calculated as follows:

qr=1004Pr+Pc=100(4×17.17)+37.78=10068.68+37.78=137.7868.68=69.10

The output of DSL firm is 69 consumers. The ATC of the firm is zero and the total revenue of each firm is their total profit and the total profit of each firm can be calculated as follows:

Profitc=QC×PC=76×37.93=2,882.68

Similarly, the profit of DSL firm can be calculated as follows:

Profitr=Qr×Pr=69×17.24=1,189.56

Thus, cable services increases their price and profit through providing increased speed for their internet services. The DSL firm faces a decline in their price and profitability.

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