(Calculating Price Elasticity of Demand ) Suppose that 50 units of a good are demanded at a price of Si per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 percent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?

Question

Want to see more full solutions like this?

Answer 1

Textbook Question

Chapter 5, Problem 1P

(Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of Si per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 percent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?

Expert Solution & Answer

To determine

The price elasticity of demand by using a midpoint formula.

ConceptIntroduction:

Price Elasticity of Demand: It is the degree of responsiveness to change in quantity demanded due to change in price level.

Midpoint formula for measuring the elasticity of demand is given as follows:

$e = \frac{Δ Q}{Δ P} \times [\frac{\frac{P_{1} + P_{2}}{2}}{\frac{Q_{1} + Q_{2}}{2}}]$

Where,

$Δ Q = Q_{2} - Q_{1}$

$Δ P = P_{2} - P_{1}$

Explanation of Solution

We have presented the information in following table:

Price (in $)	Quantity (in units)
$1	50
$0.20	70

By applying the mid-point formula, we get

$e = \frac{20}{0.80} \times [\frac{\frac{1 + 0.20}{2}}{\frac{50 + 70}{2}}]$

On solving the above, we get,

e=0.25

Hence, elasticity of demand using midpoint formula is 0.25

Now, if the elasticity of demand remains constant along the demand curve, then a 10% rise in the price will reduce the quantity demanded. We can calculate the amount of reduction in quantity demanded in following way.

$e= [\frac{% change in quantity demanded}{% change in price}]$

$0 .25= [\frac{% change in quantity demanded}{10%}]$

So, the quantity demanded will decrease by 2.5%

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!

Students have asked these similar questions

(Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of $1 per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 per cent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?

Suppose that your demand schedule for books is as follows: (PHOTO) (SHOW FORMULAS, STEP BY STEP PROCEDURE) Use the midpoint method to calculate your price elasticity of demand as the price of books increases from $10 to $12 if your income is $10,000. Is it elastic or inelastic? Explain. Use the midpoint method to calculate your price elasticity of demand as the price of books increases from $10 to $12 if your income is $12,000. Is it elastic or inelastic? Explain. Calculate your income elasticity of demand as your income increases from $10,000 to 12,000 if the price is $14. Calculate your income elasticity of demand as your income increases from $10,000 to 12,000 if the price is $8.

3

Answer 2

Textbook Question

Chapter 5, Problem 1P

(Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of Si per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 percent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?

Expert Solution & Answer

To determine

The price elasticity of demand by using a midpoint formula.

ConceptIntroduction:

Price Elasticity of Demand: It is the degree of responsiveness to change in quantity demanded due to change in price level.

Midpoint formula for measuring the elasticity of demand is given as follows:

$e = \frac{Δ Q}{Δ P} \times [\frac{\frac{P_{1} + P_{2}}{2}}{\frac{Q_{1} + Q_{2}}{2}}]$

Where,

$Δ Q = Q_{2} - Q_{1}$

$Δ P = P_{2} - P_{1}$

Explanation of Solution

We have presented the information in following table:

Price (in $)	Quantity (in units)
$1	50
$0.20	70

By applying the mid-point formula, we get

$e = \frac{20}{0.80} \times [\frac{\frac{1 + 0.20}{2}}{\frac{50 + 70}{2}}]$

On solving the above, we get,

e=0.25

Hence, elasticity of demand using midpoint formula is 0.25

Now, if the elasticity of demand remains constant along the demand curve, then a 10% rise in the price will reduce the quantity demanded. We can calculate the amount of reduction in quantity demanded in following way.

$e= [\frac{% change in quantity demanded}{% change in price}]$

$0 .25= [\frac{% change in quantity demanded}{10%}]$

So, the quantity demanded will decrease by 2.5%

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!

Answer 3

Textbook Question

Chapter 5, Problem 1P

(Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of Si per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 percent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?

Expert Solution & Answer

To determine

The price elasticity of demand by using a midpoint formula.

ConceptIntroduction:

Price Elasticity of Demand: It is the degree of responsiveness to change in quantity demanded due to change in price level.

Midpoint formula for measuring the elasticity of demand is given as follows:

$e = \frac{Δ Q}{Δ P} \times [\frac{\frac{P_{1} + P_{2}}{2}}{\frac{Q_{1} + Q_{2}}{2}}]$

Where,

$Δ Q = Q_{2} - Q_{1}$

$Δ P = P_{2} - P_{1}$

Explanation of Solution

We have presented the information in following table:

Price (in $)	Quantity (in units)
$1	50
$0.20	70

By applying the mid-point formula, we get

$e = \frac{20}{0.80} \times [\frac{\frac{1 + 0.20}{2}}{\frac{50 + 70}{2}}]$

On solving the above, we get,

e=0.25

Hence, elasticity of demand using midpoint formula is 0.25

Now, if the elasticity of demand remains constant along the demand curve, then a 10% rise in the price will reduce the quantity demanded. We can calculate the amount of reduction in quantity demanded in following way.

$e= [\frac{% change in quantity demanded}{% change in price}]$

$0 .25= [\frac{% change in quantity demanded}{10%}]$

So, the quantity demanded will decrease by 2.5%

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!

Answer 4

Textbook Question

Chapter 5, Problem 1P

(Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of Si per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 percent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?

Expert Solution & Answer

To determine

The price elasticity of demand by using a midpoint formula.

ConceptIntroduction:

Price Elasticity of Demand: It is the degree of responsiveness to change in quantity demanded due to change in price level.

Midpoint formula for measuring the elasticity of demand is given as follows:

$e = \frac{Δ Q}{Δ P} \times [\frac{\frac{P_{1} + P_{2}}{2}}{\frac{Q_{1} + Q_{2}}{2}}]$

Where,

$Δ Q = Q_{2} - Q_{1}$

$Δ P = P_{2} - P_{1}$

Explanation of Solution

We have presented the information in following table:

Price (in $)	Quantity (in units)
$1	50
$0.20	70

By applying the mid-point formula, we get

$e = \frac{20}{0.80} \times [\frac{\frac{1 + 0.20}{2}}{\frac{50 + 70}{2}}]$

On solving the above, we get,

e=0.25

Hence, elasticity of demand using midpoint formula is 0.25

Now, if the elasticity of demand remains constant along the demand curve, then a 10% rise in the price will reduce the quantity demanded. We can calculate the amount of reduction in quantity demanded in following way.

$e= [\frac{% change in quantity demanded}{% change in price}]$

$0 .25= [\frac{% change in quantity demanded}{10%}]$

So, the quantity demanded will decrease by 2.5%

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!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The price elasticity of demand by using a midpoint formula.

ConceptIntroduction:

Price Elasticity of Demand: It is the degree of responsiveness to change in quantity demanded due to change in price level.

Midpoint formula for measuring the elasticity of demand is given as follows:

$e = \frac{Δ Q}{Δ P} \times [\frac{\frac{P_{1} + P_{2}}{2}}{\frac{Q_{1} + Q_{2}}{2}}]$

Where,

$Δ Q = Q_{2} - Q_{1}$

$Δ P = P_{2} - P_{1}$

Explanation of Solution

We have presented the information in following table:

Price (in $)	Quantity (in units)
$1	50
$0.20	70

By applying the mid-point formula, we get

$e = \frac{20}{0.80} \times [\frac{\frac{1 + 0.20}{2}}{\frac{50 + 70}{2}}]$

On solving the above, we get,

e=0.25

Hence, elasticity of demand using midpoint formula is 0.25

Now, if the elasticity of demand remains constant along the demand curve, then a 10% rise in the price will reduce the quantity demanded. We can calculate the amount of reduction in quantity demanded in following way.

$e= [\frac{% change in quantity demanded}{% change in price}]$

$0 .25= [\frac{% change in quantity demanded}{10%}]$

So, the quantity demanded will decrease by 2.5%

Answer 8

Expert Solution & Answer

To determine

The price elasticity of demand by using a midpoint formula.

ConceptIntroduction:

Price Elasticity of Demand: It is the degree of responsiveness to change in quantity demanded due to change in price level.

Midpoint formula for measuring the elasticity of demand is given as follows:

$e = \frac{Δ Q}{Δ P} \times [\frac{\frac{P_{1} + P_{2}}{2}}{\frac{Q_{1} + Q_{2}}{2}}]$

Where,

$Δ Q = Q_{2} - Q_{1}$

$Δ P = P_{2} - P_{1}$

Explanation of Solution

We have presented the information in following table:

Price (in $)	Quantity (in units)
$1	50
$0.20	70

By applying the mid-point formula, we get

$e = \frac{20}{0.80} \times [\frac{\frac{1 + 0.20}{2}}{\frac{50 + 70}{2}}]$

On solving the above, we get,

e=0.25

Hence, elasticity of demand using midpoint formula is 0.25

Now, if the elasticity of demand remains constant along the demand curve, then a 10% rise in the price will reduce the quantity demanded. We can calculate the amount of reduction in quantity demanded in following way.

$e= [\frac{% change in quantity demanded}{% change in price}]$

$0 .25= [\frac{% change in quantity demanded}{10%}]$

So, the quantity demanded will decrease by 2.5%

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The price elasticity of demand by using a midpoint formula.

ConceptIntroduction:

Price Elasticity of Demand: It is the degree of responsiveness to change in quantity demanded due to change in price level.

Midpoint formula for measuring the elasticity of demand is given as follows:

$e = \frac{Δ Q}{Δ P} \times [\frac{\frac{P_{1} + P_{2}}{2}}{\frac{Q_{1} + Q_{2}}{2}}]$

Where,

$Δ Q = Q_{2} - Q_{1}$

$Δ P = P_{2} - P_{1}$

Answer 12

Explanation of Solution

We have presented the information in following table:

Price (in $)	Quantity (in units)
$1	50
$0.20	70

By applying the mid-point formula, we get

$e = \frac{20}{0.80} \times [\frac{\frac{1 + 0.20}{2}}{\frac{50 + 70}{2}}]$

On solving the above, we get,

e=0.25

Hence, elasticity of demand using midpoint formula is 0.25

Now, if the elasticity of demand remains constant along the demand curve, then a 10% rise in the price will reduce the quantity demanded. We can calculate the amount of reduction in quantity demanded in following way.

$e= [\frac{% change in quantity demanded}{% change in price}]$

$0 .25= [\frac{% change in quantity demanded}{10%}]$

So, the quantity demanded will decrease by 2.5%

Answer 13

Ch. 5 - (Calculating Price Elasticity of Demand) Suppose...Ch. 5 - (Price Elasticity and Total Revenue) Fill in the...Ch. 5 - (Categories of Price Elasticity of Demand) For...Ch. 5 - Prob. 4P Ch. 5 - (Determinants of Price Elasticity) Would the price...Ch. 5 - (Price Elasticity of Supply) Calculate the price...Ch. 5 - (Cross-Price Elasticity) Rank the following in...Ch. 5 - Prob. 8P Ch. 5 - (Other Elasticity Measures) Complete each of the...

Videos

Explanation of Solution

Want to see more full solutions like this?

Chapter 5 Solutions