Elasticity

J. Zachary Klingensmith

4 Elasticity

4.1 elasticity of demand

Review Activities

Directions: Determine whether the demand in the following situations is elastic, inelastic, or unit-elastic. NOTE: Use the theory to determine what is true in general. There is no way to truly know whether the demand is elastic, inelastic, or unit-elastic without quantitative data.

Problems

Problem 4.1.1: When the price of the Game Station Pro increased from $200 to $225, the number of units sold per month decreased from 200 to 150. Calculate the elasticity of demand. Is the good’s demand elastic, inelastic, or unit elastic?

Answer: -2.42, elastic

Problem 4.1.2: Big Al decreased the price of the Super Burger from $3 to $2. During that time, the sale of the burger increased from 30 per day to 35 per day. Calculate the elasticity of demand. Is the good’s demand elastic, inelastic, or unit elastic?

Answer: -0.38, Inelastic

Problem 4.1.3: Morton’s increases the price of salt from $2 per pound to $3 per pound. After the price increase, the sales of the salt decreased from 3,000 pounds per day to 2,000 pounds per day. Calculate the elasticity of demand. Is the good’s demand elastic, inelastic, or unit elastic?

Answer: -1, Unit-elastic

Problem 4.1.4: Consider problems 4.1.1-4.1.3. If the goal is to increase revenue, what should be done with each goods’ price (if anything)?

Answer: Lower price; raise price; no change

Problem 4.1.5: When the price of a donut increases from $1.00 to $1.35, the number sold each day fell from 200 to 180. Calculate the price elasticity of demand. Is the demand elastic, inelastic, or unit-elastic? When the donut store again increased their prices, this time from $1. 35 to $1.50, the number sold each day fell from 180 to 130. Calculate the price elasticity of demand. Is the demand elastic, inelastic, or unit-elastic? What happens to their revenue after each price change?

Answer: -0.35, inelastic, revenue increases from $200 to $243 (as expected); -3.06, elastic, revenue decreases from $243 to $195 (as expected)

Problem 4.1.6: When the price of a movie rental was reduced from $5 to $4, the number of rentals per night increased from 200/night to 300/night. When the price was reduced again, this time from $4 to $3, the number of rentals per night increased from 300/night to 350/night. Calculate the elasticity at each price change. In addition, calculate the change in revenue associated with each price change. Does this match the theory?

Answer: -1.8, elastic, revenue increases from $1,000 to $1,200; -0.53, inelastic, revenue falls from $1,200 to $1,050; both results match the theory

External Resources

Khan Academy: Introduction to Elasticity

Khan Academy: Determinants of Elasticity of Demand

Khan Academy: Perfect Elasticity and Perfect Inelasticity

Khan Academy: Elasticity and Revenue

4.2 passing costs to consumers

Review Activities

Problems

Problem 4.2.1: When the price of toy cars decreased in price from $8 to $7, the quantity supplied of toy cars decreased from 30,000 to 25,000. Calculate the elasticity of supply. Is the supply elastic, inelastic, or unit-elastic?

Answer: 1.36, elastic

Problem 4.2.2: Suppose that a $2.00 tax is placed on tickets to a soccer stadium. Tickets typically cost $50.00. The elasticity of supply for the tickets is 0.72 and the elasticity of demand is -1.17. Further, the tax will be paid by the stadium. How will the tax burden be split? What will the new price of the ticket be? How much will the stadium earn from the sale of a ticket?

Answer: $0.76 by the consumer, $1.24 by the stadium; Ticket will now cost $50.76 but the stadium will only earn $48.76.

Problem 4.2.3: A $30.00 tax is placed on the purchase of every new tire. The tax will be paid by the consumer and the average tire costs $80.00. The elasticity of demand is -0.35 and the elasticity of supply is 1.45. How will the tax burden be split? What will the new price of a tire be?

Answer: $24.17 paid by consumer, $5.83 paid by supplier; New price of tire will be $104.17 but the supplier will only earn $74.17.

Problem 4.2.4: A $0.50 tax is placed on cups of Pepsi and other colas. A cup of Pepsi typically costs $1.50. The tax will be paid by the consumer. The elasticity of demand is -1.35 and the elasticity of supply is 1.05. How will the tax burden be split? What will the new price of a cup of Pepsi be?

Answer: $0.22 paid by consumer, $0.28 paid by store; New price of soda is $1.72 but the store will only earn $1.22.

External Resources

Khan Academy: Price Elasticity of Supply

Khan Academy: Elasticity of Supply II

Khan Academy: Determinants of Elasticity of Supply

4.3 other demand elasticities

Review Activities

Problems

Problem 4.3.1: When Leslie’s income increased from $30,000 to $40,000, her demand for waffles increases from 10 per week to 20 per week. Calculate the income elasticity. Is the good considered a normal good or an inferior good? If the good is a normal good, is it a necessity or a luxury/superior good?

Answer: 2.33, normal, luxury

Problem 4.3.2: Philippe saw his weekly pay drop from $900/week to $800/week. After the decrease in pay, his weekly consumption of tea increased from 2 cups per day to 3 cups per day. Calculate the income elasticity. Is the good considered a normal good or an inferior good? If the good is a normal good, is it a necessity or a luxury/superior good?

Answer: -3.4, inferior

Problem 4.3.3: When Rozan’s income increased from $52,000/year to $53,500/year, her consumption of wine increased from 3 glasses per week to 5 glasses per week. Calculate the income elasticity of demand. Is wine a normal or inferior good for Rozan? If the good is a normal good, is it a necessity or a luxury/superior good?

Answer: 17.58, normal, luxury

Problem 4.3.4: When Feng’s income increases from $1,000 per week to $1,050 per week, his consumption of peanut butter and jelly sandwiches falls from 6/week to 4/week. Calculate the income elasticity. Is a peanut butter and jelly sandwich a normal or inferior good? If the good is a normal good, is it a necessity or a luxury/superior good?

Answer: -8.20, inferior

Problem 4.3.5: When Xiao’s income increases from $800 per week to $900 per week, his household consumption of water increases from 1,500 gallons per month to 1,600 gallons per month. Is water a normal or inferior good? If the good is a normal good, is it a necessity or a luxury/superior good?

Answer: 0.55, normal, necessity

Problem 4.3.6: When the price of widgets increased from $5 to $7, the demand for tinker toys fell from 300 to 200. Calculate the cross-price elasticity of the good. Are the two goods complements, substitutes, or (relatively) unrelated?

Answer: -1.20, complements

Problem 4.3.7: When the price of Product X decreased from $10 to $8, the demand for Product Y fell from 100 to 50. Calculate the cross-price elasticity of the good. Are the two goods complements, substitutes, or (relatively) unrelated?

Answer: 3.00, substitutes

Problem 4.3.8: When the price of xykak increases from $2 to $6, the demand for gijo increases from 1,000 to 1,010. Calculate the cross-price elasticity of the good. Are the two goods complements, substitutes, or (relatively) unrelated?

Answer: 0.01, unrelated

Problem 4.3.9: When the price of apples increases from $2 to $3 per pound, the quantity demanded of apples falls from 1,000 pounds per month to 900 pounds per month. At the same time, the quantity demanded of pears increases from 500 pounds per month to 700 pounds per month. Finally, a few months later, an economic expansion occurs which causes the average wage rate to increase from $10.00 per hour to $11.00 per hour. This causes the quantity demanded of apples to increase from 900 pounds per month to 1,100 pounds per month.

Calculate the price elasticity of demand for apples. Is the demand for applies elastic, inelastic, or unit-elastic?
Calculate the income elasticity. Are apples considered to be normal or inferior? If the good is a normal good, is it a necessity or a luxury/superior good?
Calculate the cross-price elasticity between apples and pears. Are apples and pears substitutes, complements, or (relatively) unrelated?

Answers: -0.26, inelastic; 2.1, normal, luxury; 0.83, substitutes

Problem 4.3.10: As the price of gasoline increases from $3 to $4 per gallon, a country decreases its consumption of gasoline from 100 million gallons to 90 million gallons. Due to the price increase, the demand for the Nissan Leaf car increases from 10 thousand to 15 thousand. Finally, over the next several months, the country enters into a recession in which the average income falls from $50 thousand per year to $40 thousand per year. During this time, the consumption of gasoline decreases from 90 million gallons to 60 million gallons.

Calculate the price elasticity of demand for gasoline. Is the demand for gasoline elastic, inelastic, or unit-elastic?
Calculate the income elasticity for gasoline. Is gasoline a normal good or inferior good? If the good is a normal good, is it a necessity or a luxury/superior good?
Calculate the cross-price elasticity between gasoline and the Nissan Leaf. Are gasoline and the Nissan Leaf complements or substitutes?

Answers: -0.37, inelastic; 1.8, normal, luxury; 1.4, substitutes