Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
9th Edition
ISBN: 9781259290619
Author: Michael Baye, Jeff Prince
Publisher: McGraw-Hill Education
Question
Chapter 8, Problem 15PAA
To determine

To know: The profit-maximizing amounts of electricity, optimal price and company’s profit.

Expert Solution & Answer
Check Mark

Explanation of Solution

Electricity is produced by two facility which is public utility.

Given is the inverse demand function:

  P=1200-4Q

To find the marginal revenue of a public utility, derivation is done for total revenue.

  P=12004QTR=PQ=1200Q4Q2MR=TRQ=12008Q

Cost function of facility 1 for producing electricity:

  C1(Q1)=8000+6Q12

Marginal cost of facility is given as follows:

  MC1(Q1)=12Q1

Cost function of facility 2 for producing electricity:

  C2(Q2)=6000+3Q22

Marginal cost of facility is given as follows:

  MC2(Q2)=6Q2

Condition for profit maximizing situation is as follows:

  MR=MC1=MC2

For facility 1, profit maximizing condition is:

  MR=MC1

  12008(Q1+Q2)=12Q1

  20Q1+8Q2=1200

  5Q1+2Q2=300

For facility 2, profit maximizing condition is:

  MR=MC2

  12008(Q1+Q2)=6Q2

  8Q1+14Q2=1200

  4Q1+7Q2=600

Solving equations simultaneously,

  5Q1+2Q2=30010Q1+4Q2=60010Q1+4Q2=4Q1+7Q26Q1=3Q22Q1=Q2Q1=33.33Q2=66.66

Thus, the profit maximizing amounts of electricity produced at facility 1 are 33.33 kilowatts hours and that produced in facility 2 is 66.66 kilowatts hours ,thereby totaling the output combined for facility 1 and facility 2 to 100kiilowatt hours.

The optimal price is given as:

  P=12004Q=12004(Q1+Q2)=12004(33.33+66.66)=800

Hence, the optimal price charged by the public utility provider of electricity is $800 per kilowatt hours.

The utility company’s profit is given by:

  π=TRTC=PQ(8000+6Q12)(6000+3Q22)=800×100800060006(33.33)23(66.66)2=800001400020000=46000

Hence, the utility company’s profit is $46000.

Economics Concept Introduction

Introduction:

Profit of a firm is maximized when marginal revenue is equal to marginal cost.

Marginal benefit is the additional benefit to the total for receiving a particular good or service.

Marginal cost is the addition to total cost when one more unit of good is produced.

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