Chapter 4Elasticity

Odd-number Questions

Problem #1, Chapter 4

• On the accompanying demand curve, calculate the price elasticity of demand at points A, B, C, D and E.

0

Quantity

Price

100A

B

C

D

E

100

75

50

25

25 50 75

Solution to Problem #1 (1)

• Price elasticity of demand refers to the percentage change of quantity demanded relative to the percentage change of price

• In other words, price elasticity of demand indicates how much will the quantity demanded change with respect to a 1% change in price

• Thus, it measures the responsiveness of quantity demanded to change in price

Solution to Problem #1 (2)

• Price elasticity of demand is always a negative index, as the demand curve is downward sloping

• For convenience, we always take absolute value of a price elasticity of demand

• When the absolute value of a price elasticity of demand is greater than one, that means percentage change in quantity demanded is greater than percentage change in price– If this is the case, we regard the highly responsive demand as ELASTIC

Solution to Problem #1 (3)

• When the absolute value of a price elasticity of demand is less than one, that means percentage change in quantity demanded is less than percentage change in price– If this is the case, we regard the weakly responsive demand as

INELASTIC

• When the absolute value of a price elasticity of demand is exactly equal to one, that means percentage change in quantity demanded is the same as percentage change in price– If this is the case, we regard the mirror-responsive demand as

UNITARY ELASTIC

Solution to Problem #1 (4)

• General formula for (Own) Price Elasticity of Demand:– (Change of quantity demanded / Total quantity demanded) / (Change

of price / Original Price)– Rearranging terms, we will get

• (Change in quantity demanded / Change in price) * (Original Price / Total quantity demanded)

• (1 / Slope of the demand curve) * (P / Q)

• Using the formula, we can derive price elasticity of demand at any point along the demand curve

Solution to Problem #1 (5)

• Point A– 1 / Slope of the demand curve 1 / (-100/100) = -1– Price is $100 and quantity demanded is 0– Price elasticity of demand = -1 * (100 / 0)– Price elasticity of demand = Infinity– The demand is perfectly elastic

• Point B– 1 / Slope of the demand curve = -1– Price is $75 and quantity demanded is 25– Price elasticity of demand = -1 * (75 / 25)– Price elasticity of demand = -3 (Or 3 in if we take absolute value)– As it is greater than 1, the demand is elastic

Solution to Problem #1 (6)

• Point C– 1 / Slope of the demand curve = -1– Price is $50 and quantity demanded is 50– Price elasticity of demand = -1 * (50 / 50)– Price elasticity of demand = -1 (Or 1 if we take the absolute value)– As it is exactly equal to 1, the demand is unitary elastic

• Point D– 1 / Slope of the demand curve = -1– Price is $25 and quantity demanded is 75– Price elasticity of demand = -1 * (25 / 75)– Price elasticity of demand = -1/3 (Or 1/3 if we take the absolute value)– As it is less than 1, the demand is inelastic

Solution to Problem #1 (7)

• Point E– 1 / Slope of the demand curve = -1– Price is $0 and quantity demanded is 100– Price elasticity of demand = -1 * (0 / 100)– Price elasticity of demand = 0 (Or 0 if we take the absolute value)– As it is exactly equal to 0, the price elasticity of demand is zero– The demand is perfectly inelastic- the quantity demanded does not

change regardless of the change in price

Problem #3, Chapter 4

• Suppose, while rummaging through your uncle’s closet, you found the original painting of Dogs Playing Poker, a valuable piece of art. You decided to set up a display in your uncle’s garage. The demand curve to see this valuable piece of art is as shown in the diagram. What price should you charge if your goal is to maximize your revenues from tickets sold? On a graph, show the inelastic and elastic regions of the demand curve. Quantity

(visitors/day)

6

12

Pric

e ($

/vis

it)

0

Solution to Problem #3 (1)

• Where is the source of revenue from displaying the artwork in your uncle’s garage?– Selling admission tickets to your uncle’s garage

• How much should you charge in order to maximize the revenue?– You should charge a price where the marginal revenue = marginal cost– However, no supply curve is given in this problem, and we can only

consider the demand curve alone

• How much should you charge then?– You should charge at the price where it is the midpoint of the demand

curve

Solution to Problem #3 (2)

• At the midpoint of a linear demand curve, the price elasticity of demand is unitary elastic (1)– Percentage of change in quantity demanded = Percentage of change

in price

• Left of the midpoint, the price elasticity of demand is elastic (>1)– Percentage of change in quantity demanded is greater than

Percentage of change in price– Increasing the price will lead to an decrease in quantity demanded,

and thus revenue will go down

Solution to Problem #3 (3)

• Right of the midpoint, the price elasticity of demand is inelastic (<1)– Percentage of change in quantity demanded is less than Percentage of

change in price– Decreasing the price will only lead to a slight increase in quantity

demanded, and thus revenue will go down

• At the midpoint,– Further change in price will cause total revenue fall– The optimal price is settled at the midpoint of a demand curve

• Therefore, you should charge $6 for each admission ticket where the total quantity demanded is 3

Solution to Problem #3 (4)

• Elastic region is located on the left of the midpoint• Inelastic region is located on the right of the midpoint

12

Price ($ per visit)

Quantity (Visitors per day)6

6

3

Inelastic region

Elastic region

Midpoint

Problem #5, Chapter 4

• Among the following groups- senior executives, junior executives, and students- which is likely to have the most and which is likely to have the least price-elastic demand for membership in the Association of Business Professionals?

Solution to Problem #5 (1)

• Senior executives are most likely to have a least price-elastic demand for membership in the Association of Business Professionals

• Senior executives have a higher income than junior executives, while junior executives have a higher income than students

• The membership shares only a small portion of the income earned by a typical senior executive– Change in price of the membership causes a small effect on senior

executive

Solution to Problem #5 (2)

• The membership shares a notable portion of the income earned by a typical junior executive– Change in price of the membership causes a notable effect on junior

executives• The membership shares a considerable portion of the income

earned by a typical student– Change in price of the membership causes a considerable effect on

students• In general, one earning high income is less likely to respond to

change in price dramatically as the price is actually a very small portion of one’s consumption budget

Solution to Problem #5 (3)

• Therefore, senior executives have a least price-elastic demand for the membership

• Which of the three groups has the most price-elastic demand for the membership?

• Students– They earning the lowest income among the groups will be

affected the most by the change in price of the membership as it takes a considerable portion of their income

– Hence, they will probably respond dramatically to change in the price of the membership

Problem #7, Chapter 4

• What are the respective price elasticities of supply at A and B on the supply curve shown in the accompanying figure?

0 9 12Quantity

Pric

e

4

6S

Change in price

Change in quantity

Solution to Problem #7 (1)

• Calculating price elasticity of supply is almost identical to calculating price elasticity of demand, except for the slope of the curve

• Price elasticity of supply refers to the percentage change of quantity supplied relative to the percentage change of price

• In other words, price elasticity of supply indicates how much will the quantity supplied change with respect to a 1% change in price

• Thus, it measures the responsiveness of quantity supplied to change in price

Solution to Problem #7 (2)

• Price elasticity of supply is always a positive index, as the supply curve is upward sloping

• When a price elasticity of supply is greater than one, that means percentage change in quantity supplied is greater than percentage change in price– If this is the case, we regard the highly responsive supply as ELASTIC

Solution to Problem #7 (3)

• When a price elasticity of supply is less than one, that means percentage change in quantity supplied is less than percentage change in price– If this is the case, we regard the weakly responsive supply as

INELASTIC

• When a price elasticity of supply is exactly equal to one, that means percentage change in quantity supplied is the same as percentage change in price– If this is the case, we regard the mirror-responsive supply as UNITARY

ELASTIC

Solution to Problem #7 (4)

• General formula for (Own) Price Elasticity of Supply:– (Change of quantity supplied / Total quantity supplied) / (Change of

price / Original Price)– Rearranging terms, we will get

• (Change in quantity supplied / Change in price) * (Original Price / Total quantity supplied)

• (1/ Slope of the supply curve) * (P / Q)

• Using the formula, we can derive price elasticity of supply at any point along the supply curve

Solution to Problem #7 (5)

• Point A– 1 / Slope of the supply curve = 1 / (2/3) = 3/2– Price is $4 and quantity supplied is 9– Price elasticity of supply = 3/2 * (4 / 9)– Price elasticity of supply = 2/3– As it is less than 1, the supply is inelastic

• Point B– 1 / Slope of the supply curve = 1 / (2/3) = 3/2– Price is $6 and quantity supplied is 12– Price elasticity of supply = 3/2 * (6 / 12)– Price elasticity of supply = 3/4– As it is less than 1, the supply is inelastic

Problem #9, Chapter 4

• At point A on the demand curve shown, by what percentage will a 1 percent increase in the price of the product affect the total expenditure on the product?

Quantity (units/week)P

rice

($/u

nit)

186

4

6

Solution to Problem #9 (1)

• In order to answer this question, we will need to compute the price elasticity of demand

• Applying the general formula, Price elasticity of demand = (1/ Slope of the demand curve) * (P/Q), we get

• Price elasticity of demand– The absolute value of the slope of this demand curve is 1/3 – Price is $4 and the quantity demanded is 6– Price elasticity of demand at point A = 3 * (4/6) = 2

Solution to Problem #9 (2)

• Based on the price elasticity of demand, we conclude that a 1-percent increase in price will cause a 2-percent decrease in quantity demanded for the product

• How much does the total expenditure change?• Total expenditure (TE) = Price (P) * Quantity (Q)• What will happen if the price increases by 1% and quantity

demanded decreases by 2%?• Initially, TE = P * Q• After the change in price, TE will become 1.01P * 0.98Q

Solution to Problem #9 (3)

• From the Total Expenditure function = 1.01P * 0.98Q, a 0.02 decrease in quantity demanded with a 0.01 increase in price of the product, will approximately lead to a 0.01 (1%) reduction in Total Expenditure.