CHAPTER 5 ELASTICITY PROBLEM SET 1.

a. When the price of gasoline rises from $2 per gallon to $3 per gallon, the price elasticity of demand for gasoline over 1 month is 0.26. $3 − $2 $1 % change in price = = = 0.4 or 40% ⎛ $3 + $2 ⎞ $2.5 ⎜ ⎟ ⎝ 2 ⎠ 400 − 360 40 % change in quantity = = = 0.105 or 10.5% ⎛ 400 + 360 ⎞ 380 ⎜ ⎟ 2 ⎝ ⎠ %ΔQ 10.5% E= = = 0.26 %ΔP 40% b. When the price of gasoline rises from $2 per gallon to $3 per gallon, the price elasticity of demand for gasoline over 1 month is 0.40.

% change in quantity =

E=

400 − 340 60 = = 0.162 or 16.2% ⎛ 400 + 340 ⎞ 370 ⎜ ⎟ 2 ⎝ ⎠

%ΔQ 16.2% = = 0.40 %ΔP 40%

b. When the price of gasoline rises from $2 per gallon to $3 per gallon, the price elasticity of demand for gasoline over 1 month is 0.56.

% change in quantity =

E= 2.

400 − 320 80 = = 0.222 or 22.2% ⎛ 400 + 320 ⎞ 360 ⎜ ⎟ 2 ⎝ ⎠

%ΔQ 22.2% = = 0.56 %ΔP 40%

Long-run elasticity of demand for cigarettes is larger than the short-run elasticity and this is what we would expect. In general, our demand for goods becomes more elastic over time and cigarettes are no exception. In the short-run, when the price of cigarettes rises, smokers may decrease their cigarette consumption only slightly because smoking is addictive. But over time, they could transition to smoking significantly fewer cigarettes per day or even quit smoking altogether.

3.

We would use income elasticity to determine if “tooth extraction” is an inferior good. If income elasticity of “tooth extraction” is negative, then we would conclude that it is an inferior good. Alternatively, if it is positive, we would conclude that it is a normal good.

4.

For the poor, expenditure on Kellogg’s cornflakes is likely a higher share of their budget, than for the rich. When spending on a good makes up a larger proportion of families’ budgets, the demand tends to be more elastic, so the poor would have elasticity of 4.05 and the rich 2.93.

5.

a. This is a straight line demand curve since for every $0.50 increase in price, the quantity of bottles demanded falls by the same amount (100 units). b. Demand is inelastic for this price change. 500 − 400 1 − 1.50 ÷ ⎛ 500 + 400 ⎞ ⎛ 1 + 1.50 ⎞ ⎜ ⎟ ⎜ ⎟ 2 ⎝ ⎠ ⎝ 2 ⎠ 100 0.50 = ÷ 450 1.25 = 0.55 E=

c. Demand is elastic for this price change. 200 − 100 2.50 − 3 ÷ ⎛ 200 + 100 ⎞ ⎛ 2.50 + 3 ⎞ ⎜ ⎟ ⎜ ⎟ 2 ⎝ ⎠ ⎝ 2 ⎠ 100 0.50 = ÷ 150 2.75 = 3.66 d. As we slide down the demand curve, the price elasticity of demand changes from 3.66 to 0.55, that is, demand becomes less elastic. E=

e. P 1.00 1.50 2.00

Qd 500 400 300

Total Revenue 500 600 600

2.50 3.00

200 100

500 300

f. From the table in part e, we can confirm that an increase in price in the inelastic range (from $1 to $1.50) led to an increase in total revenue from $500 to $600, while an increase in price in the elastic range (from $2.50 to $3.00) led to a decrease in total revenue (from $500 to $300). 6.

For the demand curve to be unit elastic, there would have to be no change in revenue as a result of a price change. In the initial situation, 110 units are sold at a price of $9 per unit, so revenue is $9 x 110 = $990. If demand is unit elastic, and the price rises to $11 per unit, a constant revenue implies that the new quantity demanded would have to be $990/$11 = 90 units. Now we know two points on the demand curves. To find other points, try to come up with price quantity combinations such that p x q = $990. Once you’ve found one or two more, plot them and connect them to find that the demand curve must be curved. Price Per Unit ($)

$11 $9

D 7.

Given that the short-run elasticity of demand is 0.35, a 25 percent increase fares Quantity perinyear 90 110 would lead to a 25 x 0.35 = 8.75 percent decrease in ridership. Since New Yorker’s take about 2 billion trips per year, an 8.75% decrease would amount to (1-0.0875)*2 billion = 1.825 billion trips per year (a decrease of 175 million trips per year). The new revenue would be 1.825 billion*$2.5 = 4.5625 billion. Since demand is inelastic, a rise in price lead to an increase in revenue, as expected. Furthermore, since demand is more inelastic in the short run than in the long run, we observe that the revenue increase in the short run (4.5625 billion – 4 billion = 562.5 million) is higher than the revenue increase in the long run, calculated in the chapter.

8.

We learned that about 25 percent of the world’s oil is produced in the Persian Gulf. If half the Gulf’s capacity was wiped out, that would amount to a 12.5 percent drop in production. In the long run, with a long-run demand elasticity of 0.45, the price would have to rise by 12.5/0.45 = 27.78 percent. From an initial price of $60 per barrel, the price would rise by 0.2778 x 60 = $16.67 per barrel to a new price of $76.67 per barrel. (Note that here we did not use the midpoint rule when we increased the price by a certain percentage. If we used the midpoint rule the resulting price would be $79.36 per barrel)

9.

a. It is not a straight line demand curve since quantity demanded does not fall by the same amounts following repeated price rises by a fixed amount. c. Demand is elastic for this price change. 230 − 150 11 − 10 ÷ ⎛ 230 + 150 ⎞ ⎛ 11 + 10 ⎞ ⎜ ⎟ ⎜ ⎟ 2 ⎝ ⎠ ⎝ 2 ⎠ 80 1 = ÷ 190 9.5 =4 E=

c. Demand is elastic for this price change. 90 − 40 13 − 12 ÷ ⎛ 90 + 40 ⎞ ⎛ 13 + 12 ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ 2 ⎠ ⎝ 2 ⎠ 50 1 = ÷ 65 12.5 = 9.61 E=

10. a. The demand for pork is more elastic than the demand for cigarettes because the estimated elasticity for pork is greater than the highest estimated elasticity for cigarettes, i.e. 0.78 > 0.7. This is because there are more substitutes for pork (e.g., beef, chicken) than there are for cigarettes. b. If the price of milk rises by 5 percent, then the quantity of milk demanded will fall by 2.7 percent (5 × 0.54). 11. a. More elastic. b. Quantity demanded will fall by 2,190 bottles. To find this answer, first use the mid-point rule to calculate that the price of Pepsi increased by 10%. Then, substitute this value and the value of the price elasticity of demand into the equation for price elasticity of demand, and solve for the change in quantity demanded: 2.08 = x ÷ 10% x = 20.8%. Hence, the quantity of Pepsi demanded falls by 20.8% due to a price increase of

10%. c. The price of ground beef will have to increase by 4.9%. Find this by substituting what is known into the equation for price elasticity of demand and solving for x: 1.02 = 5% ÷ x x = 4.9% 12.

a. They should increase their price to $30/hour. Given that the price elasticity of demand for their service is 0.5 (i.e. it is inelastic), their revenue will increase when they increase their price to $30/hour because the increase in their price will be larger (in percentage terms) than the decrease in their demand. (Also note: They will be doing less moving at a higher price, so their other costs will go down as well, and they will enjoy more leisure.) b. Demand is likely to become more elastic. The availability of substitutes is one of the primary determinants of price elasticity of demand. Increased competition from companies providing essentially the same service will make demand for “Three Guys” services more sensitive to changes in price, hence, more elastic.

MORE CHALLENGING QUESTION 13.

Either the supply of PCs in Europe is perfectly inelastic, or the demand for PCs in Europe is perfectly elastic. Neither of these statements is likely to be true, or even close to true.

EXPERIENTIAL EXERCISES Cross-price elasticities are important in the computer industry. Read the “Personal Technology” column in Thursday’s Wall Street Journal and find a story that describes a hardware or software product. Make a list of other products that you think would be substitutes (positive cross-price elasticity) for the product in the article. Arrange the items in your list from very close substitutes (very large cross-price elasticity) to more distant substitutes (smaller cross-price elasticity). For each item on the list, make your best guess about the numerical value of the elasticity. Using the guess, what would happen if the price of each item on your list rose by 10%? When you’ve finished, follow the same steps for a list of complements to the product in question. In this case, the cross-price elasticities will be negative.