CHECKPOINT 5.1 Price Elasticity of Demand
.1a. The percentage change in price is 8 percent. The midpoint method shows ⎛$26−$24 ⎞ the percentage is ⎜($24 + $26) ÷ 2)⎟×100. ⎝⎠
.1b. The percentage change in quantity is 4 percent. The midpoint method
⎛196 million − 204 million ⎞shows the percentage is ⎜(204 million + 196 million) ÷ 2)⎟×100.
1c. The demand for Internet services is inelastic because the percentage change in quantity demanded is less than the percentage change in price.
.1d. The demand for AOL service is more elastic than the demand for Internet service because more substitutes exist for AOL service in particular than for Internet service in general. AOL service is a more narrowly defined service.
.1e. Thepriceelasticityofdemand=(4percent)÷(8percent)=0.5.
.1f. The initial total revenue is $24 a month × 204 million subscribers, which is $4,896 million a month. The new total revenue is $26 a month × 196 million subscribers, which is $5,096 million a month. So total revenue increases by $5,096 million a month − $4,896 million a month, which is $200 million a month.
.1g. The price elasticity of demand is useful because it allows us to make precise predictions about how much demanders change the quantity they demand when the price changes. For instance, if the price elasticity of demand for AOL is 0.5, then AOL can determine that a 10 percent increase in the price of their service will decrease the quantity that people demand by 5 percent.
.1h. The demand for Internet service is unit elastic at a price higher than $25 a month. At $25 a month, the elasticity equals 0.5. As we move up along a linear demand curve, the price elasticity of demand increases. So the de‐mand for Internet service is unit elastic at the midpoint of the demand curve, which is at a price greater than $25 a month.
?CHECKPOINT 5.2 Price Elasticity of Supply
.1a. The supply of asparagus is elastic. The percentage change in the quantity supplied is greater than the percentage change in the price.
.1b. The supply of asparagus over this large price range is elastic because there is the possibility of plowing the crop under and producing nothing. Once harvested, asparagus is not very storable, which makes supply more inelas‐ tic.
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Chapter 5 . Elasticities of Demand and Supply 137 1c. The percentage change in the quantity supplied of asparagus is
⎛2,000−0 ⎞ ⎜(2,000 + 0) ÷ 2)⎟×100, which is 200 percent. The percentage change in the
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⎛$45 acrate−$15acrate ⎞ priceofasparagusis⎜($45acrate+$15acrate)÷2)⎟×100, whichis100per‐
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cent. So the price elasticity of supply = (200 percent) ÷ (100 percent) = 2.0.
1d. As time passes, the elasticity of supply increases. After all the technologi‐cally possible ways of adjusting production have been exploited, the supply of asparagus becomes extremely elastic.
2. The percentage change in the price of roses is ($40) ÷ ($60) × 100 = 66.7 per‐ cent. The percentage change in the quantity of roses supplied is (18 million bunches) ÷ (15 million bunches) × 100 = 120 percent. So the price elasticity of supply equals (120 percent) ÷ (66.7 percent), which is 1.80.
?CHECKPOINT 5.3 Cross Elasticity and Income Elasticity
.1a. Cola and pizza are complements because they are goods that are consumed together. More rigorously, the cross elasticity of demand for the two is negative (when the price of a pizza falls, the quantity of cola demanded in‐ creases) which means the two are complement.
.1b. The cross elasticity of demand for cola with respect to pizza equals the per‐centage change in the quantity of cola divided by the percentage change in the price of a pizza. The percentage change in the quantity of cola equals
⎛250 an hour − 150 an hour ⎞ ⎜(150 an hour + 250 an hour) ÷ 2)⎟×100, which is 50 percent. The percentage
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⎛ $7 a pizza − $9 a pizza ⎞ change in the price of a pizza is ⎜($9 a pizza + $7 a pizza) ÷ 2)⎟×100, which
⎝⎠ is −25 percent. So the cross elasticity of demand for cola with respect to
pizza is (50 percent) ÷(−25 percent), which is −2.00. 1c. Pizza and burgers are substitutes. A burger can be consumed in place of a
pizza. More rigorously, the cross elasticity of demand for the two is positive (when in the price of pizza falls, the quantity of burgers demanded de‐ creases) which means the two are substitutes.
1d. The cross elasticity of demand for burgers with respect to pizza equals the percentage change in the quantity of burgers divided by the percentage change in the price of a pizza. Part (a) shows that the percentage change in the price of pizza is −25 percent. The percentage change in the quantity of
⎛100 an hour − 200 an hour ⎞ burgers is ⎜(200 an hour + 100 an hour) ÷ 2)⎟×100, which is −66.67 percent.
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138 Part 2 . A CLOSER LOOK AT MARKETS
So the cross elasticity of demand for burgers with respect to pizza is (–66.67
percent) ÷ (−25 percent), which is 2.67. 1e. The owner can determine how the quantities of burgers and cola he or she
sells will change if the price of a nearby pizza place changes the price of its pizza.
.2a. Frozen fish cakes are an inferior good because as income in Miami in‐ creases, the quantity demanded decreases. The income elasticity is negative and the negative elasticity indicates that frozen fish cakes are an inferior good.
.2b. The income elasticity of demand for frozen fish cakes is (−5 percent) ÷ (10 percent) = −0.50.
.2c. Theincomeelasticityofdemandforfreshfishis(15percent)÷(10percent)= 1.50.
.2d. The owner of a fresh fish shop can use these two elasticities to predict how sales of fresh and frozen fish change when people’s income change. For in‐ stance, if the economy in Miami goes into a recession so that people’s in‐ comes generally fall, the owner can predict that the quantity of frozen fish demanded will increase and the quantity of fresh fish demanded will de‐ crease. As a result, the owner can stock more frozen fish and less fresh fish.