# 27 Review and Practice

#### Summary

This chapter also 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.

In the market for goods and services, quantity supplied and quantity demanded are often relatively slow to react to changes in price in the short run, but react more substantially in the long run. As a result, demand and supply often (but not always) tend to be relatively inelastic in the short run and relatively elastic in the long run. The tax incidence depends on the relative price elasticity of supply and demand. When supply is more elastic than demand, buyers bear most of the tax burden, and when demand is more elastic than supply, producers bear most of the cost of the tax. Tax revenue is larger the more inelastic the demand and supply are.

### 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. If demand is inelastic, will shifts in supply have a larger effect on equilibrium price or on quantity?
5. Would you usually expect elasticity of demand or supply to be higher in the short run or in the long run? Why?
6. Transatlantic air travel in business class has an estimated elasticity of demand of 0.40 less than
transatlantic air travel in economy class, with an estimated price elasticity of 0.62. Why do you think this is the case?
7. Can you think of an industry (or product) with near infinite elasticity of supply in the short term? That is, what is an industry that could increase Qs almost without limit in response to an increase in the price?
8. Would you expect supply to play a more significant role in determining the price of a basic necessity like food or a luxury like perfume? Explain. Hint: Think about how the price elasticity of demand will differ between necessities and luxuries.
9. A city has built a bridge over a river and it decides to charge a toll to everyone who crosses. For one year, the city charges a variety of different tolls and records information on how many drivers cross the bridge. The city thus gathers information about elasticity of demand. If the city wishes to raise as much revenue as possible from the tolls, where will the city decide to charge a toll: in the inelastic portion of the demand curve, the elastic portion of the demand curve, or the unit elastic portion? Explain.
10. In a market where the supply curve is perfectly inelastic, how does an excise tax affect the price paid by consumers and the quantity bought and sold?
11. Normal goods are defined as having a positive income elasticity. We can divide normal goods into two types: Those whose income elasticity is less than one and those whose income elasticity is greater than one. Think about products that would fall into each category. Can you come up with a name for each category?
12. Suppose you could buy shoes one at a time, rather than in pairs. What do you predict the cross-price elasticity for left shoes and right shoes would be?
13. 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?
14. 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?
15. 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?
16. Suppose the income elasticity of the demand for beans is −0.8. Interpret this number.
17. 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.
18. Suppose the price elasticity of supply of tomatoes as measured on a given day in July is 0. Interpret this number.
19. 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?
20. 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

21. Consider the information in the table below that describes the demand for movie
rentals from your on-line supplier Instant Flicks.

 Price per movie (\$) Quantity demanded Total revenue Elasticity of demand 2 1200 3 1100 4 1000 5 900 6 800 7 700 8 600

a. Either on graph paper or a spreadsheet, map out the demand curve.
b. In column 3, insert the total revenue generated at each price.
c. At what price is total revenue maximized?
d.  In column 4, compute the elasticity of demand corresponding to each \$1 price reduction,
using the average price and quantity at each state.
e. Do you see a connection between your answers in parts (c) and (d)?

22. University fees in the State of Nirvana have been frozen in real terms for 10 years. During this period enrolments increased by 20 percent, reflecting an increase in demand. This means the supply curve is horizontal at a given price.
a. Draw a supply curve and two demand curves to represent the two equilibria described.
b. Can you estimate a price elasticity of demand for university education in this market?
c. In contrast, during the same time period fees in a neighboring state (where supply is also
horizontal) increased by 60 percent and enrolments increased by 15 percent. Illustrate this
situation in a diagram, where supply is again horizontal.

23. Waterson Power Corporation’s regulator has just allowed a rate increase from 9 to 11 cents per kilowatt hour of electricity. The short-run demand elasticity is -0.6 and the long-run demand elasticity is -1.2 at the current price.

a. What will be the percentage reduction in power demanded in the short run (use the midpoint
‘arc’ elasticity formula)?
b.  What will be the percentage reduction in power demanded in the long run?
c. Will revenues increase or decrease in the short and long runs?

24. Consider the own- and cross-price elasticity data in the table below.

 % change in price CDs Magazines Cappuccinos % change in quantity CDs -0.25 0.06 0.01 Magazines -0.13 -1.20 0.27 Cappuccinos 0.07 0.41 -0.85
1. For which of the goods is demand elastic and for which is it inelastic?
2. What is the effect of an increase in the price of CDs on the purchase of magazines and
cappuccinos? What does this suggest about the relationship between CDs and these other
commodities; are they substitutes or complements?
3. In graphical terms, if the price of CDs or the price of cappuccinos increases, illustrate how
the demand curve for magazines shifts.

25. A household’s income and restaurant visits are observed at different points in time. The table below describes the pattern.

 Income (\$) Restaurant Visits Income Elasticity of Demand 16,000 10 24,000 15 32,000 18 40,000 20 48,000 22 56,000 23 64,000 24
1. Construct a scatter diagram showing quantity on the vertical axis and income on the horizontal
axis.
2. Is there a positive or negative relationship between these variables?
3. Compute the income elasticity for each income increase, using midpoint values.
4. Are restaurant meals a normal or inferior good?

26. 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?

Refer to Figure 3.3 “Price Elasticities of Demand for a Linear Demand Curve” and answer questions 27-29

27.  Using the arc elasticity of demand formula, compute the price elasticity of demand between points B and C.

28 Using the arc elasticity of demand formula, compute the price elasticity of demand between points D and E.

29. How do the values of price elasticity of demand compare? Why are they the same or different?

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.” Answer questions 30 – 33

30. 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?

31. What do you think happened to total spending on frozen orange juice? Why?

32. 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.

33. Compute the price elasticity of demand between these two points.