Microeconomics
Microeconomics
2nd Edition
ISBN: 9781464187025
Author: Austan Goolsbee, Steven Levitt, Chad Syverson
Publisher: Worth Publishers
Question
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Chapter 2, Problem 10P

(a)

To determine

Graph the inverse supply curve demand curve.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Demand function for towel:QD=1005P  (1)

Supply function for towel:QS=10P  (2)

Calculation:

Rearrange Equation (1) in terms of price of that goods to derive the inverse demand equation.

QD=1005P 5P=100QDP=1005QD5

P=200.2QD (3)

The inverse demand equation isP=200.2QD.

Rearrange Equation (2) in terms of price of that good to derive the inverse supply equation.

QS=10PP=QS10  (4)

The inverse supply function isP=QS10.

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

P=200.2QDP=200.2(0)P=20

The maximum willing price is $20.

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

P=200.2QD0=200.2QD0.2QD=200QD=200.2QD=100

The maximum willing quantity is 100 units.

Substitute quantity as 0 in Equation (4) to calculate the price.

P=QS10P=010P=0

The minimum willing price is 0.

Substitute quantity as 200 units in Equation (4) to calculate the price.

P=QS100=20010QS=20

The minimum willing quantity is 20.

From these information, the inverse demand and supply curve are shown in Figure 1 below.

Microeconomics, Chapter 2, Problem 10P , additional homework tip  1

In Figure 1, the vertical axis measures the price of the towel and horizontal axis measures the quantity of the towel. The upward sloping curve “S” is the supply curve of the towel and downward sloping curve “D” is the demand curve for the towel.

Economics Concept Introduction

Demand curve: Demand curve shows the quantity demand at different price levels.

(b)

To determine

Equilibrium price and quantity.

(b)

Expert Solution
Check Mark

Explanation of Solution

Intersecting point of the demand and supply curve is the equilibrium point. The corresponding price and quantity are the equilibrium price and quantity. Equilibrium price can be calculated as follows: 

QD=QS1005P=10P 5P+10P=100P=10015P=6.67 

Equilibrium price is $6.67.

Equilibrium price can be calculated by substituting the equilibrium price into supply equation (Equation (2)).

QS=10P QS=10(6.67)QS=66.7

Equilibrium quantity is 66.7 units.

Economics Concept Introduction

Equilibrium price:  The equilibrium price is the market price determined by the interaction between the quantity demanded and the quantity supplied.

Equilibrium quantity: The equilibrium quantity is the point where the quantity demanded is equal to the quantity supplied.

(c)

To determine

New inverse supply curve. 

(c)

Expert Solution
Check Mark

Explanation of Solution

Given information:

At each price, 20 fewer towels are offered for sale. 

Calculation:

At each price, 20 fewer towels are offered for sale. Thus, the new inverse supply curve is shown below:

QS=10PDecreasing quantity

QS=10P20  (5)

Substitute quantity as zero in Equation (5) to calculate the price (minimum willing price).

QS=10P200=10P2010P=20+0P=2010P=2

The minimum willing price is $2.

Substitute quantity as 110 in Equation (5) to calculate the price.

QS=10P20200=10P2010P=20+200P=22010P=22

The minimum willing price is $2.

By using this information, change in supply curve of towel is shown in Figure 2 below.

Microeconomics, Chapter 2, Problem 10P , additional homework tip  2

In Figure 2, the vertical axis measures the price of the towel and horizontal axis measures the quantity of the towel. The upward sloping curve “S1” is the supply curve of the towel and downward sloping curve “D” is the demand curve for the towel. The reduction in 20 fewer towels shifts the supply curve to the left. Thus, curve “S2” is the new inversee supply curve, where the minimum willing price is 2.

Economics Concept Introduction

Supply curve: Supply curve shows the quantity supplied at different price levels.

(d)

To determine

Equilibrium price and quantity.

(d)

Expert Solution
Check Mark

Explanation of Solution

The calculation of equilibrium price is shown below:

QD=QS1005P=10P20 5P+10P=100+20P=12015P=8 

Equilibrium price is $8.

Equilibrium quantity can be calculated by substituting the equilibrium price in to new supply equation (Equation (5)).

QS=10P20 QS=10(8)20QS=8020QS=60

Equilibrium quantity is 60 units.

Economics Concept Introduction

Equilibrium price:  The equilibrium price is the market price determined by the interaction between the quantity demanded and the quantity supplied.

Equilibrium quantity: The equilibrium quantity is the point where the quantity demanded is equal to the quantity supplied.

(e)

To determine

Equilibrium price and quantity.

(e)

Expert Solution
Check Mark

Explanation of Solution

At each price, 25 fewer towels are offered for sale. Thus, the new inverse demand curve is shown below:

QD=1005PDecreasing quantityQD=1005P25

QD=755P (6)

Equilibrium price can be calculated as follows:

QD=QS755P=10P5P+10P=7515P=75P=7515P=5

Equilibrium price is $5.

Equilibrium quantity can be calculated by substituting the equilibrium price in to new demand equation (Equation (6)).

QS=755PQS=755(5)QS=50

Equilibrium quantity is 50 units. The equilibrium quantity and price are reducing. The new equilibrium price and quantity are less than the initial equilibrium quantity and price.  

Economics Concept Introduction

Equilibrium price:  The equilibrium price is the market price determined by the interaction between the quantity demanded and the quantity supplied.

Equilibrium quantity: The equilibrium quantity is the point where the quantity demanded is equal to the quantity supplied.

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