(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 1.1PA

(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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Problem 3 You are given the following demand for European luxury automobiles: Q=1,000 P-0.5.2/1.6 where P-Price of European luxury cars PA = Price of American luxury cars P, Price of Japanese luxury cars I= Annual income of car buyers Assume that each of the coefficients is statistically significant (i.e., that they passed the t-test). On the basis of the information given, answer the following questions 1. Comment on the degree of substitutability between European and American luxury cars and between European and Japanese luxury cars. Explain some possible reasons for the results in the equation. 2. Comment on the coefficient for the income variable. Is this result what you would expect? Explain. 3. Comment on the coefficient of the European car price variable. Is that what you would expect? Explain.

Problem 2: A manufacturer of computer workstations gathered average monthly sales figures from its 56 branch offices and dealerships across the country and estimated the following demand for its product: Q=+15,000-2.80P+150A+0.3P+0.35Pm+0.2Pc (5,234) (1.29) (175) (0.12) (0.17) (0.13) R²=0.68 SER 786 F=21.25 The variables and their assumed values are P = Price of basic model = 7,000 Q==Quantity A = Advertising expenditures (in thousands) = 52 P = Average price of a personal computer = 4,000 P. Average price of a minicomputer = 15,000 Pe Average price of a leading competitor's workstation = 8,000 1. Compute the elasticities for each variable. On this basis, discuss the relative impact that each variable has on the demand. What implications do these results have for the firm's marketing and pricing policies? 2. Conduct a t-test for the statistical significance of each variable. In each case, state whether a one-tail or two-tail test is required. What difference, if any, does it make to…

Answer 2

Textbook Question

Chapter 5, Problem 1.1PA

(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 1.1PA

(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 1.1PA

(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. 2.4PA 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. 4.8PA Ch. 5 - (Other Elasticity Measures) Complete each of the...

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