# 5.4: Review and Practice

#### Summary

This chapter introduced a new tool: the concept of elasticity. Elasticity is a measure of the degree to which a dependent variable responds to a change in an independent variable. It is the percentage change in the dependent variable divided by the percentage change in the independent variable, all other things unchanged.

The most widely used elasticity measure is the price elasticity of demand, which reflects the responsiveness of quantity demanded to changes in price. Demand is said to be price elastic if the absolute value of the price elasticity of demand is greater than 1, unit price elastic if it is equal to 1, and price inelastic if it is less than 1. The price elasticity of demand is useful in forecasting the response of quantity demanded to price changes; it is also useful for predicting the impact a price change will have on total revenue. Total revenue moves in the direction of the quantity change if demand is price elastic, it moves in the direction of the price change if demand is price inelastic, and it does not change if demand is unit price elastic. The most important determinants of the price elasticity of demand are the availability of substitutes, the importance of the item in household budgets, and time.

Two other elasticity measures commonly used in conjunction with demand are income elasticity and cross price elasticity. The signs of these elasticity measures play important roles. A positive income elasticity tells us that a good is normal; a negative income elasticity tells us the good is inferior. A positive cross price elasticity tells us that two goods are substitutes; a negative cross price elasticity tells us they are complements.

Elasticity of supply measures the responsiveness of quantity supplied to changes in price. The value of price elasticity of supply is generally positive. Supply is classified as being price elastic, unit price elastic, or price inelastic if price elasticity is greater than 1, equal to 1, or less than 1, respectively. The length of time over which supply is being considered is an important determinant of the price elasticity of supply.

### Concept Problems

1. Explain why the price elasticity of demand is generally a negative number, except in the cases where the demand curve is perfectly elastic or perfectly inelastic. What would be implied by a positive price elasticity of demand?
2. Explain why the sign (positive or negative) of the cross price elasticity of demand is important.
3. Explain why the sign (positive or negative) of the income elasticity of demand is important.
4. Economists Dale Heien and Cathy Roheim Wessells found that the price elasticity of demand for fresh milk is −0.63 and the price elasticity of demand for cottage cheese is −1.1 (Heien, D. M. and Wessels, C. R., 1998). Why do you think the elasticity estimates differ?
5. The price elasticity of demand for health care has been estimated to be −0.2. Characterize this demand as price elastic, unit price elastic, or price inelastic. The text argues that the greater the importance of an item in consumer budgets, the greater its elasticity. Health-care costs account for a relatively large share of household budgets. How could the price elasticity of demand for health care be such a small number?
6. Suppose you are able to organize an alliance that includes all farmers. They agree to follow the group’s instructions with respect to the quantity of agricultural products they produce. What might the group seek to do? Why?
7. Suppose you are the chief executive officer of a firm, and you have been planning to reduce your prices. Your marketing manager reports that the price elasticity of demand for your product is −0.65. How will this news affect your plans?
8. Suppose the income elasticity of the demand for beans is −0.8. Interpret this number.
9. Transportation economists generally agree that the cross price elasticity of demand for automobile use with respect to the price of bus fares is about 0. Explain what this number means.
10. Suppose the price elasticity of supply of tomatoes as measured on a given day in July is 0. Interpret this number.
11. The price elasticity of supply for child-care workers was reported to be quite high, about 2. What will happen to the wages of child-care workers as demand for them increases, compared to what would happen if the measured price elasticity of supply were lower?
12. The Case in Point on cigarette taxes and teen smoking suggests that a higher tax on cigarettes would reduce teen smoking and premature deaths. Should cigarette taxes therefore be raised?

### Numerical Problems

1. Economist David Romer found that in introductory economics classes a 10% increase in class attendance is associated with a 4% increase in course grade (Romer, D., 1993). What is the elasticity of course grade with respect to class attendance?
2. Refer to Figure 5.2 “Price Elasticities of Demand for a Linear Demand Curve” and

1. Using the arc elasticity of demand formula, compute the price elasticity of demand between points B and C.
2. Using the arc elasticity of demand formula, compute the price elasticity of demand between points D and E.
3. How do the values of price elasticity of demand compare? Why are they the same or different?
4. Compute the slope of the demand curve between points B and C.
5. Computer the slope of the demand curve between points D and E.
6. How do the slopes compare? Why are they the same or different?
3. Consider the following quote from The Wall Street Journal: “A bumper crop of oranges in Florida last year drove down orange prices. As juice marketers’ costs fell, they cut prices by as much as 15%. That was enough to tempt some value-oriented customers: unit volume of frozen juices actually rose about 6% during the quarter.”

1. Given these numbers, and assuming there were no changes in demand shifters for frozen orange juice, what was the price elasticity of demand for frozen orange juice?
2. What do you think happened to total spending on frozen orange juice? Why?
4. Suppose you are the manager of a restaurant that serves an average of 400 meals per day at an average price per meal of $20. On the basis of a survey, you have determined that reducing the price of an average meal to$18 would increase the quantity demanded to 450 per day.

1. Compute the price elasticity of demand between these two points.
2. Would you expect total revenues to rise or fall? Explain.
3. Suppose you have reduced the average price of a meal to $18 and are considering a further reduction to$16. Another survey shows that the quantity demanded of meals will increase from 450 to 500 per day. Compute the price elasticity of demand between these two points.
4. Would you expect total revenue to rise or fall as a result of this second price reduction? Explain.
5. Compute total revenue at the three meal prices. Do these totals confirm your answers in (b) and (d) above?
5. The text notes that, for any linear demand curve, demand is price elastic in the upper half and price inelastic in the lower half. Consider the following demand curves:

Figure 5.13

The table gives the prices and quantities corresponding to each of the points shown on the two demand curves.

Demand curve D1 [Panel (a)] Demand curve D2 [Panel (b)]
Price Quantity Price Quantity
A 80 2 E 8 20
B 70 3 F 7 30
C 30 7 G 3 70
D 20 8 H 2 80
1. Compute the price elasticity of demand between points A and B and between points C and D on demand curve D1 in Panel (a). Are your results consistent with the notion that a linear demand curve is price elastic in its upper half and price inelastic in its lower half?
2. Compute the price elasticity of demand between points E and F and between points G and H on demand curve D2 in Panel (b). Are your results consistent with the notion that a linear demand curve is price elastic in its upper half and price inelastic in its lower half?
3. Compare total spending at points A and B on D1 in Panel (a). Is your result consistent with your finding about the price elasticity of demand between those two points?
4. Compare total spending at points C and D on D1 in Panel (a). Is your result consistent with your finding about the price elasticity of demand between those two points?
5. Compare total spending at points E and F on D2 in Panel (b). Is your result consistent with your finding about the price elasticity of demand between those two points?
6. Compare total spending at points G and H on D2 in Panel (b). Is your result consistent with your finding about the price elasticity of demand between those two points?
6. Suppose Janice buys the following amounts of various food items depending on her weekly income:

Weekly Income Hamburgers Pizza Ice Cream Sundaes
$500 3 3 2$750 4 2 2
1. Compute Janice’s income elasticity of demand for hamburgers.
2. Compute Janice’s income elasticity of demand for pizza.
3. Compute Janice’s income elasticity of demand for ice cream sundaes.
4. Classify each good as normal or inferior.
7. Suppose the following table describes Jocelyn’s weekly snack purchases, which vary depending on the price of a bag of chips:

Price of bag of chips Bags of chips Containers of salsa Bags of pretzels Cans of soda
$1.00 2 3 1 4$1.50 1 2 2 4
1. Compute the cross price elasticity of salsa with respect to the price of a bag of chips.
2. Compute the cross price elasticity of pretzels with respect to the price of a bag of chips.
3. Compute the cross price elasticity of soda with respect to the price of a bag of chips.
4. Are chips and salsa substitutes or complements? How do you know?
5. Are chips and pretzels substitutes or complements? How do you know?
6. Are chips and soda substitutes or complements? How do you know?
8. The table below describes the supply curve for light bulbs:

Price per light bulb Quantity supplied per day
$1.00 500 1.50 3,000 2.00 4,000 2.50 4,500 3.00 4,500 Compute the price elasticity of supply and determine whether supply is price elastic, price inelastic, perfectly elastic, perfectly inelastic, or unit elastic: 1. when the price of a light bulb increases from$1.00 to $1.50. 2. when the price of a light bulb increases from$1.50 to $2.00. 3. when the price of a light bulb increases from$2.00 to $2.50. 4. when the price of a light bulb increases from$2.50 to \$3.00.

## References

Heien, D. M., and Cathy Roheim Wessels, “The Demand for Dairy Products: Structure, Prediction, and Decomposition,” American Journal of Agricultural Economics 70:2 (May 1988): 219–228.

Romer, D., “Do Students Go to Class? Should They?” Journal of Economic Perspectives 7:3 (Summer 1993): 167–174.