Modern Principles of Economics
Modern Principles of Economics
4th Edition
ISBN: 9781319098728
Author: Tyler Cowen, Alex Tabarrok
Publisher: Worth Publishers
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Chapter 13, Problem 22C
To determine

Calculation of deadweight loss.

Expert Solution & Answer
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Explanation of Solution

Case A:

In case “A”, profit-maximizing quantity (PMQ) can be calculated as follows:

Marginal revenue=Marginal cost(Price×Quantity)Quantity=10((50Q)×Q)Q=10((50QQ2))Q=10

502Q=102Q=5010Q=402=20

The profit-maximizing output is 20 units.

Substitute the profit-maximizing output in demand equation to calculate the profit-maximizing price (PMP).

Price=50Q=5020=30

The profit-maximizing price is $30.

Socially-optimal quantity (SOQ) can be calculated as follows:

Demand=Marginal cost50Q=10Q=5010=40

The socially-optimal quantity is 40.

Substitute the sociality-optimal output in demand equation to calculate the socially-optimal price (SOP).

Price=50Q=5040=10

The socially-optimal price is $10.

The deadweight loss is calculated as follows:

Deadweightloss=12(PMPSOP)×(SOQPMQ)=12(3010)×(4020)=0.5×(20×20)=200

The deadweight loss is $200.

Case B:

In case “B”, the profit-maximizing quantity (PMQ) can be calculated as follows:

Marginal revenue=Marginal cost(Price×Quantity)Quantity=10((1002Q)×Q)Q=10((100Q2Q2))Q=10

1002×2Q=104Q=10010Q=904=22.5

The profit-maximizing output is 22.5 units.

Substitute the profit-maximizing output in demand equation to calculate the profit-maximizing price (PMP).

Price=1002Q=1002(22.5)=10045=55

The profit-maximizing price is $55.

The socially-optimal quantity (SOQ) can be calculated as follows:

Demand=Marginal cost1002Q=102Q=10010Q=902=45

The socially-optimal quantity is 45.

Substitute the sociality-optimal output in demand equation to calculate the socially optimal price (SOP).

Price=1002Q=1002(45)=10090=10

The socially-optimal price is $10.

The deadweight loss is calculated as follows:

Deadweightloss=12(PMPSOP)×(SOQPMQ)=12(5510)×(4522.5)=0.5×(45×22.5)=506.25

The deadweight loss is 506.25.

Case C:

In case “C”, the profit-maximizing quantity (PMQ) can be calculated as follows:

Marginal revenue=Marginal cost(Price×Quantity)Quantity=20((1002Q)×Q)Q=20((100Q2Q2))Q=20

1002×2Q=204Q=10020Q=804=20

The profit-maximizing output is 20 units.

Substitute the profit-maximizing output in demand equation to calculate the profit-maximizing price (PMP).

Price=1002Q=1002(20)=10040=60

The profit-maximizing price is $60.

The socially-optimal quantity (SOQ) can be calculated as follows:

Demand=Marginal cost1002Q=102Q=10020Q=802=40

The socially-optimal quantity is 40.

Substitute the socially-optimal output in demand equation to calculate the socially optimal price (SOP).

Price=1002Q=1002(40)=10080=20

The socially-optimal price is $20.

The deadweight loss is calculated as follows:

Deadweightloss=12(PMPSOP)×(SOQPMQ)=12(6020)×(4020)=0.5×(40×20)=400

The deadweight loss is $400.

Economics Concept Introduction

Concept introduction:

Deadweight loss:  The fall in total surplus that results from a market distortion is termed as deadweight loss.

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