(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?

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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%

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Students have asked these similar questions

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.

In the graph on the right, the demand for syrup has changed because the price of frozen waffles has risen from $2.80 to $3.80 per package. The cross-price elasticity of demand between frozen waffles and syrup is (Use the midpoint formula and enter your response rounded to two decimal places. Be sure to include the minus sign if necessary.) Price (dollars per package of syrup) 4.00- 3.75- 3.50- 3.25- 3.00- 2.75- 2.50- 2.25- 2.00-1.89 1.75- 1.50- 1.25- 1.00- 0.75- 0.50- 0.25- 0.00+ 0 Syrup S D₁ D₂ 6,000 7,0009,000 3,000 6,000 9,000 12,000 15,00 Quantity (packages of syrup per week)

7. Which of the following statements is (are) correct? (x) If the coefficient of price elasticity of demand has a value of 1, then the absolute value of the percentage change in price equals the absolute value of the percentage change in quantity demanded. (y) The coefficient of price elasticity of demand for a vertical demand curve equals zero because the quantity demanded does not change as the price changes. (z) The midpoint method is used to compute elasticity because it gives the same answer regardless of the direction of change A. (x), (y) and (z) В. (x) and (y) only C (x) and (z) only D (y) and (z) only E. (z) only

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%

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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%

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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%

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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...

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