Microeconomics
Microeconomics
2nd Edition
ISBN: 9781464187025
Author: Austan Goolsbee, Steven Levitt, Chad Syverson
Publisher: Worth Publishers
Question
Book Icon
Chapter 2, Problem 3P

(a)

To determine

Graph the inverse demand curve.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Demand function for organic carrots:QDO=755PO+PC+2I (1)

In Equation (1), “PO” is the price of organic carrots, “PC” is the price of conventional carrots, and “I” is the average consumer income.

Price of conventional carrots (PC): 5

Average consumer income (I): 10

Calculation:

Demand equation can be simplified (with the price of the particular good alone) by substituting the respective values in Equation (1). This is done because when calculating the change in demand due to changes in the price of that good, all other factors are considered constant.

QDO=755PO+1(5)+2(10)

QDO=1005PO (2)

The demand equation when other things remain the same is QDO=1005PO.

Rearrange Equation (2) in terms of price of the goods to derive the inverse demand equation.

QDO=1005PO5PO=100QDOPO=1005QDO5

PO=200.2QDO (3)

Substitute quantity as zero in Equation (3) to calculate the price of organic carrots (maximum willing price).

PO=200.2QDOPO=20(0.2×0)PO=20

Price of organic carrots is $20.

Substitute price as zero in Equation (3) to calculate the maximum quantity demanded.

0=200.2QDO0.2QDO=20QDO=200.2=100

Quantity of organic carrots is 100 units.

By using this information, the demand curve of organic carrots is illustrated below in Figure 1.

Microeconomics, Chapter 2, Problem 3P , additional homework tip  1

In Figure 1, the vertical axis measures the price of organic carrots and the horizontal axis measures the quantity of organic carrots. The downward sloping curve “D” is the demand curve of organic carrots.

Economics Concept Introduction

Demand curve: A demand curve is a graph which shows the quantities of a commodity that the consumers will buy at different price levels.

(b)

To determine

The quantity demanded.

(b)

Expert Solution
Check Mark

Explanation of Solution

At price $5, the quantity demanded for organic carrots (QDO) is calculated by substituting the respective values in Equation (2).

QDO=1005POQDO=1005(5)QDO=75

Quantity demanded for organic carrots at price $5 is 75.

At price $10, the quantity demanded for organic carrots (QDO) is calculated by substituting the respective values in the inverse demand equation (Equation (2)).

QDO=1005POQDO=1005(10)QDO=50

Quantity demanded for organic carrots at price $10 is 50.

(c)

To determine

Changes in demand for organic carrots.

(c)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Price of conventional carrots (PC): 15

Average consumer income (I): 10

Calculation:

Demand equation can be simplified (with the price of the particular good alone) by substituting the respective values in Equation (1). This is done because when calculating the change in demand due to changes in the price of the good, all other factors are considered constant.

QDO=755PO+PC+2IQDO=755PO+1(15)+2(10)

QDO=1105PO (4)

The new demand equation when other things remain the same is QDO=1105PO.

Rearrange Equation (4) in terms of price of the goods to derive the inverse demand equation.

QDO=1105PO5PO=110QDOPO=1105QDO5

PO=220.2QDO (5)

Substitute quantity as zero in Equation (5) to calculate the price of organic carrots (maximum willing price).

PO=220.2QDOPO=22(0.2×0)PO=22

Price of organic carrots is $22.

Substitute price as zero in Equation (5) to calculate the maximum quantity demanded.

0=220.2QDO0.2QDO=22QDO=220.2=110

Quantity of organic carrots is 110 units.

Substitute the value of price ($10) to calculate the quantity demanded of organic carrots at this particular price. This is done to know the change in quantity due to change in the price of PC.

PO=220.2QDO10=220.2QDO0.2QDO=2210QDO=120.2QDO=60

Quantity demand of organic carrots at price $10 is 60. When the price of PC increases from $5 to $15, the quantity increases from $50 to $60.

By using this information, the change in demand curve of organic carrots is shown below in Figure 2.

Microeconomics, Chapter 2, Problem 3P , additional homework tip  2

In Figure 2, the vertical axis measures the price of organic carrots and the horizontal axis measures the quantity of organic carrots demanded. D1 is the initial demand curve of the organic carrots. The increase in the quantity demand for organic carrots shifts the demand curve from D1 to D2. It leads to increase the price from $20 to $22. At the initial demand curve, people demand 50 at the price $10; then it increases to 60 after the change in demand.

Economics Concept Introduction

Demand curve: A demand curve is a graph which shows the quantities of a commodity that the consumers will buy at different price levels.

(d)

To determine

Demand for organic carrots.

(d)

Expert Solution
Check Mark

Explanation of Solution

The demand for organic carrot increases. This increase in demand shifts the demand curve rightward. This rightward shift shows the two goods are substitute goods because increase in the price of conventional carrots increases the demand for organic carrots.

Economics Concept Introduction

Substitute goods: Substitute goods are those goods that can be used for the same purpose.

(e)

To determine

Demand for organic carrots.

(e)

Expert Solution
Check Mark

Explanation of Solution

The demand for organic carrot increases when the average income of consumer increases. Thus, it is clear that the organic carrots are normal goods.

Economics Concept Introduction

Normal good: It is the good whose quantity demanded increases when the income of the consumer increases and vice versa.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:9780190931919
Author:NEWNAN
Publisher:Oxford University Press
Text book image
Principles of Economics (12th Edition)
Economics
ISBN:9780134078779
Author:Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:PEARSON
Text book image
Engineering Economy (17th Edition)
Economics
ISBN:9780134870069
Author:William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:PEARSON
Text book image
Principles of Economics (MindTap Course List)
Economics
ISBN:9781305585126
Author:N. Gregory Mankiw
Publisher:Cengage Learning
Text book image
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Text book image
Managerial Economics & Business Strategy (Mcgraw-...
Economics
ISBN:9781259290619
Author:Michael Baye, Jeff Prince
Publisher:McGraw-Hill Education