ELASTICITY

 ELASTICITY

Ragan Chapter 4

Elasticity and Slope

Elasticity is related to slope

1. Consider an example where the demand for apples (in kilograms) depends on the price (in dollars). Graph the

demand curves D0 = 12 – 2p and D1 = 15 – 3p.

a. At p = 3 the slope of D0 is equal to __________ and the slope of D1 is equal to __________ kilograms per

dollar.

b. At p = 3, the own-price elasticity of demands are η0XX = ________ and η1XX = __________.

2. List 3 factors that lead to an inelastic (steep) demand curve. (p. 80)

Quantity

Price

Elasticity and Expenditure

3. Discuss the relationship between Elasticity and Expenditure E = p x Q [Figure 4-5] at Mississauga Transit.

Illustrate using D = 12 – 2p

Quantity

Price

Elasticity and a change in determinants

4. Elasticity and a change in determinants

a. Elasticity of demand is important when shifting the supply curve [Figure 4-1]

b. Elasticity of supply is important when shifting the demand curve.

Supply Shift Demand Shift

5. Example Question [Worksheet 2-3] Due to bad weather, farmers did not get a good harvest of potatoes. This

caused a decrease in the supply of potatoes. Potatoes are a key input to French fries. French fries and

hamburgers are complements in consumption.

a. Provide Supply and Demand diagrams showing the market for French fries and the market for

hamburgers that illustrate how bad harvest of potatoes affects the markets.

b. Illustrate the combination of elasticities that would result in the largest change in the price of

Hamburgers.

Potatoes French Fries Hamburgers

Elasticity varies along a linear demand curve

6. Illustrate DX = 16 – 2pX + 4pY where pY = 1 and SX = 2pX – 2w where w = 2

a. In the range from pX = 5 to pX = 7 the own-price elasticity of supply is equal to __________ (Figure 4-6)

b. In the range from pX = 5 to pX = 7 the own-price elasticity of demand is equal to __________

c. In the range from pX = 7 to pX = 9 the own-price elasticity of demand is equal to __________

d. (Figure 4-2). Note that buyers become more elastic as price rises along a linear demand curve

Quantity

Price

Elasticity changes when demand shifts

7. Illustrate DX = 16 – 2pX + 4pY where pY = 1 and SX = 2pX – 2w where w = 2. Now pY = 3. In the range pX = 5 to pX = 7

the own-price elasticity of demand is equal to __________. What has happened to the price sensitivity of buyers

when the demand curve shifts to the right?

Quantity

Price

Cross Price Elasticity

8. Illustrate DX = 16 – 2pX + 4pY where pY = 1 and SX = 2pX – 2w where w = 2. Now pY = 3In the range from pY = 1 to

pY = 3 the cross-price elasticity of demand is equal to __________

Quantity

Price

Income Elasticity

9. Demand and supply are S = 2p – 40 and D = 40 – 2p + m where income is initially m = 40. Now income increases

to m1 = 80.

Calculate the income elasticity of demand

Is this good a necessity?

Income Elasticity

9. Demand and supply are S = 2p – 40 and D = 40 – 2p + m where income is initially m = 40. Now income increases

to m1 = 80.

Calculate the income elasticity of demand

Is this good a necessity?

Review Questions

1. Prices are determined by demand D = 80 – 2p and supply S = 2p – 20. Calculate the price at which demand is unit

elastic. Provide a Supply and Demand Diagram to illustrate this calculation.

2. The demand for good X depends on income: D = 3 – p + m. The supply for good X is S = p. Income changes from

m = 1 to m = 3. Calculate the income elasticity of demand for good x at the original equilibrium price. Provide a

supply and demand diagram to illustrate this calculation.

Review Questions

1. Prices are determined by demand D = 80 – 2p and supply S = 2p – 20. Calculate the price at which demand is unit

elastic. Provide a Supply and Demand Diagram to illustrate this calculation.

2. The demand for good X depends on income: D = 3 – p + m. The supply for good X is S = p. Income changes from

m = 1 to m = 3. Calculate the income elasticity of demand for good x at the original equilibrium price. Provide a

supply and demand diagram to illustrate this calculation.

3. Prices are determined by demand D = 80 – p and supply S = p – 20. Expenditure is at a maximum when price is

equal to ______. Provide a Supply and Demand Diagram to illustrate this calculation.

4. The demand for good X depends on the price of good Y: DX = 5 – pX + pY . The supply for good X is SX = pX . The

price of good Y changes from pY = 1 to pY = 3. Calculate the cross-price elasticity of demand for good X at the

original equilibrium price. Provide a Supply and Demand Diagram to illustrate this calculation.

5. Suppose that the quantity demanded rises from 90 units to 110 units when the price falls from $1.20 to 80 cents

per unit. The price elasticity of demand for this product is equal to

6. A perfectly vertical demand curve shows that the own-price elasticity of demand is

a. Infinite.

b. Zero. ✓

c. Less than one.

d. Unity.

7. A perfectly horizontal demand curve shows that the own-price elasticity of demand is

a. Infinite. ✓

b. Zero.

c. Less than one.

d. Unity.

8. As the price of some product increases from $4.00 to $5.00 per unit the quantity supplied rises from 500 to 1000

units per month. The price elasticity of supply for this product is

9. When the price of good X rose from $3 to $5 quantities demanded for good X decreased from 55 to 45 and the

demand for good Y increased from 80 to 120. The cross-price elasticity of demand for good Y is equal to

10. When the price of good X increased from $1.00 to $1.50, sellers of this product increased the quantity supplied

from 30 to 50 units. In this range, the price elasticity of supply is equal to,

11. Quantity demanded rises from 40 units to 60 units per month when the price falls from $1.05 to 95 cents per

unit. The price elasticity of demand for this product is

12. An upward-sloping straight-line supply curve through the origin has an elasticity of

a. One. ✓

b. Zero.

c. Infinity.

13. With a downward-sloping straight-line demand curve, price elasticity of demand is

a. Increasing to the midpoint of the curve and then decreasing.

b. Decreasing continuously with price increases.

c. Rising continuously with price increases. ✓

d. Constant everywhere on it.

14. The income elasticity of demand for a luxury good is

a. Greater than 1. ✓

b. Equal to 1.

c. Equal to 0.

d. Negative.

15. The demand curve is D = 160 – 2p. Total expenditures on this good are at a maximum when sellers charge a

price of

16. Good W has an income elasticity of –2.00. Good X has an income elasticity of 0. Good Y has an income elasticity

of 0.6. Good Z has an income elasticity of 1.20. Which good is a necessity.

a. Good Y ✓

17. The demand for Good A is given by D = 240 – 20p and supply is S = 20p. Between prices of 2 and 6 the own-price

elasticity of demand is equal to

18. Sellers who offer price reductions to their customers will realize an increase in revenue if

a. the elasticity of supply is greater than 1

b. the elasticity of demand is greater than 1 ✓

c. the elasticity of demand is less than 1

d. the elasticity of supply is less than 1

19. Buyers of Good X expect the price will rise tomorrow. Good X is a complement in production for Good Y. Today’s

equilibrium price of Good Y will have the biggest change if:

a. Supply of X is inelastic, and Demand for Y is elastic

b. Supply of X is inelastic, and Demand for Y is inelastic ✓

c. Supply of X is elastic, and Demand for Y is elastic

d. Supply of X is inelastic, and Demand for Y elastic

20. The income elasticity of demand for a necessity good is

21. When sellers expect the price to fall the supply curve will shift ______ and the elasticity of supply will ______.

a. Right, increase.

b. Left, decrease.

c. Left, increase. ✓

d. Right, decrease.

22. When sellers expect the price to rise the supply curve will shift ______ and the elasticity of supply will ______.

a. Right, increase.

b. Left, increase.

c. Left, decrease.

d. Right, decrease. ✓

23. Suppose that the quantity demanded of skipping ropes rises from 1200 to 800 units when the price falls from

$1.25 to $0.75 per unit. The price elasticity of demand for this product is

24. An economics student working as a barista at Second Cup records the following information

a. The own price elasticity of demand for coffee is equal to __________

b. The cross-price elasticity of demand for coffee is equal to __________

c. The income elasticity of demand for coffee is equal to __________

25. Due to bad weather, farmers did not get a good harvest of potatoes. This caused a decrease in the supply of

potatoes. Potatoes are a key input to French fries. French fries and hamburgers are complements in

consumption.

a. Provide Supply and Demand diagrams showing the market for French fries and the market for

hamburgers that illustrate how bad harvest of potatoes affects the markets.

b. Illustrate the combination of elasticities that would result in the largest change in the price of

Hamburgers.

26. Changes to Ontario laws allow 12-year-olds to buy beer. The minimum age for wine is unchanged.

a. Provide a labelled Supply and Demand diagram that shows how a reduction in the minimum age to buy

beer will affect equilibrium price and quantities in the market for beer.

b. Provide a second Supply and Demand diagram that shows how this shock in the market for beer will

affect the equilibrium price and quantity of wine.

c. Clearly illustrate the combination of elasticities that will result in the largest change in the price of wine.

26. Changes to Ontario laws allow 12-year-olds to buy beer. The minimum age for wine is unchanged.

a. Provide a labelled Supply and Demand diagram that shows how a reduction in the minimum age to buy

beer will affect equilibrium price and quantities in the market for beer.

b. Provide a second Supply and Demand diagram that shows how this shock in the market for beer will

affect the equilibrium price and quantity of wine.

c. Clearly illustrate the combination of elasticities that will result in the largest change in the price of wine.

27. Hamburgers and Catsup are complements in consumption. Hamburgers and Salmon are substitutes in consumption.

During November, the B.C. Salmon migration occurs. Fishermen catch unusually large quantities of the fish.

a. Explain how an increase in supply in the fish industry is likely to affect the equilibrium price of catsup.

When the supply of salmon rises the price of salmon will fall. This will cause a reduction in the demand for hamburgers. The

lower price of hamburgers will cause an increase in the demand for catsup and an increase in the price of catsup.

b. Which combination of elasticities will result in the largest increase in the price of catsup?

The price of salmon will change most dramatically when the demand for salmon is inelastic. The price of hamburgers will fall

most when the supply of hamburgers in inelastic. The price of catsup will rise by the most when the supply of catsup is inelastic.

28. Equilibrium prices and quantities are determined by demand D1 = 200 – 2p1 and supply S1 = 2p1 – 40 in the market for

Good 1 and by D2 = 240 – 2p2 and supply S2 = 2p2 – p1 – 20 in the market for Good 2.

a. Provide a diagram showing the equilibrium price and quantity in the market for Good 1 and a second diagram

showing the equilibrium price and quantity in the market for Good 2.

b. Next month the government will introduce a t = 40 per unit tax in the market for Good 1 (not Good 2). Update

your diagrams to show and quantify how prices and quantities will be affected in both markets.

c. Illustrate (do not calculate) how the price of Good 2 would be affected if the demand curve in Market 1 was less

elastic.

29. Consider a market where Demand is D = 450 – 10p and Supply is S = 10p – 50.

a. The equilibrium price is equal to _________

𝑝 ∗ = 450 + 50

20 = 25, 𝑞 = 200

b. At equilibrium, the own-price elasticity of demand is equal to __________

c. At equilibrium, the own-price elasticity of supply is equal to __________

𝜂""

d. At equilibrium, consumer surplus is equal to __________

𝐶𝑆 = (45 − 25) × 200

2 = 2000

e. At equilibrium, producer surplus is equal to __________

𝑃𝑆 = (25 − 5) × 200

2 = 2000

30. Equilibrium prices and quantities are determined by demand D1 = 200 – 2p1 and supply S1 = 2p1 – 40 in the market for

Good 1 and by D2 = 240 – 2p2 and supply S2 = 2p2 – p1 – 20 in the market for Good 2.

a. Provide a diagram showing the equilibrium price and quantity in the market for Good 1 and a second diagram

showing the equilibrium price and quantity in the market for Good 2.

b. Next month the government will introduce a t = 40 per unit tax in the market for Good 1 (not Good 2). Update

your diagrams to show and quantify how prices and quantities will be affected in both markets.

c. Illustrate (do not calculate) how the price of Good 2 would be affected demand curve in Market 1 was less elastic.