Microeconomics
Microeconomics
2nd Edition
ISBN: 9781464187025
Author: Austan Goolsbee, Steven Levitt, Chad Syverson
Publisher: Worth Publishers
Question
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Chapter 9, Problem 17P

(a)

To determine

The competitive price and quantity.

(a)

Expert Solution
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Explanation of Solution

The competitive price in the given situation is equal to the marginal cost. Thus, the competitive price is $0.10 per package. The inverse demand function can be calculated using Equation (1) as follows:

P=10.01Q (1)

The quantity can be calculated by substituting the value of price in Equation (1) as follows:

0.1=10.01Q0.01Q=10.1Q=0.900.01=90

Thus, the competitive quantity is 90.

(b)

To determine

The consumer surplus and producer surplus.

(b)

Expert Solution
Check Mark

Explanation of Solution

Figure 1 shows the price and quantity of packages.

Microeconomics, Chapter 9, Problem 17P

The horizontal axis of Figure 1 measures the quantity of packages and the vertical axis measures the price.

The consumer surplus is the area of the triangle ABD. The consumer surplus is given by Equation (2) as follows:

Consumer surplus=12×(Maximum willing priceEquilibrium price)×Quantity (2)

Consumer surplusInitial=12×(10.1)×90=12×0.9×90=40.5

Thus, the consumer surplus is $40.50.

In the given situation, the producer surplus is zero.

Economics Concept Introduction

Consumer Surplus: Consumer surplus is defined as the difference between the maximum amount a person is willing to pay for consuming a commodity and the actual price the person pays for it.

Producer Surplus: Producer surplus is defined as the difference between the actual market price for which a commodity is sold and the minimum cost at which a producer is willing to sell a commodity. This minimum accepted price is usually the cost of production of the commodity.

(c)

To determine

The monopoly price and quantity.

(c)

Expert Solution
Check Mark

Explanation of Solution

The marginal revenue can be calculated as follows in Equation.

MR=(P×Q)Q=(10.01Q)QQ=(1Q0.01Q2)Q=10.02Q

The marginal revenue function is MR=10.02Q.

Given that the marginal cost is $0.10 and the marginal revenue is MR=10.02Q.

The profit of a firm is maximized when marginal revenue is equal to the marginal cost.

MR=MC10.02Q=0.1010.10=0.02QQ=0.90.02=45

The profit is maximized when the quantity of output produced is 45.

The price charged by the monopolist to maximize the profit can be calculated by substituting the value of profit maximizing output in Equation (1).

P=10.01(45)=10.45=0.55

Thus, the profit maximizing output is 45 and the profit maximizing price is $0.55.

Economics Concept Introduction

Profit: Profit is defined as the excess revenue earned over the total cost of production.

(d)

To determine

The consumer surplus and producer surplus.

(d)

Expert Solution
Check Mark

Explanation of Solution

The new consumer surplus can be calculated as follows:

Consumer surplus=12×(Maximum willing priceEquilibrium price)×Quantity

Consumer surplus=12×(10.55)×45=12×0.45×45=10.125

Thus, the consumer surplus is $10.125.

The producer surplus can be calculated as follows.

Producer surplus=(Equilibrium priceMinimum willing price)×QuantityProducer surplus=(0.550.1)×45=0.45×45=20.25

Thus, the producer surplus is $20.25.

Economics Concept Introduction

Consumer Surplus: Consumer surplus is defined as the difference between the maximum amount a person is willing to pay for consuming a commodity and the actual price the person pays for it.

Producer Surplus: Producer surplus is defined as the difference between the actual market price for which a commodity is sold and the minimum cost at which the producer is willing to sell the commodity. This minimum accepted price is usually the cost of production of the commodity.

(e)

To determine

The deadweight loss.

(e)

Expert Solution
Check Mark

Explanation of Solution

The change in consumer surplus can be calculated as follows.

Change in consumer surplus=Consumer surplusNewConsumer surplusInitial=10.12540.50=30.375

Consumer surplus is decreased by $30.375.

The change in producer surplus can be calculated as follows:

Change in producer surplus=Producer surplusNewProducer surplusInitial=20.250=20.25

Producer surplus is increased by $20.25.

The dead weight loss can be calculated as the difference between the loss in consumer surplus and the gain in producer surplus.

The dead weight loss=Change in producer surplusChange in consumer surplus=20.25(30.375)=10.125

Thus, the dead weight loss is $10.125.

Economics Concept Introduction

Consumer Surplus: Consumer surplus is defined as the difference between the maximum amount a person is willing to pay for consuming a commodity and the actual price the person pays for it.

Producer Surplus: Producer surplus is defined as the difference between the actual market price for which a commodity is sold and the minimum cost at which the producer is willing to sell the commodity. This minimum accepted price is usually the cost of production of the commodity.

Deadweight loss: Deadweight loss is defined as the loss of the total consumer surplus and producer surplus due to overproduction or underproduction.

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