Table 3.4 gathers a number of estimated income and price elasticities of demand.
As we shall see, these estimates often provide the starting place for analyzing how activities such as changes in taxes or import policy might affect various markets. In several later chapters, we use these numbers to illustrate such applications.
Although interested readers are urged to explore the original sources of these estimates to understand more details about them, in our discussion we just take note of a few regularities they exhibit. With regard to the price elasticity figures, most estimates suggest that product demands are relatively inelastic (between 0 and 1). For the groupings of commodities listed, substitution effects are not especially large, although they may be large within these categories. For example, substitu- tions between beer and other commodities may be relatively small, though substitutions among brands of beer may be substantial in response to price differ- ences. Still, all the estimates are less than 0, so there is clear evidence that people do respond to price changes for most goods.9
M i c r o Q u i z 3 . 9
Suppose that a set of consumers spend their incomes only on beer and pizza.
1. Explain why a fall in the price of beer will have an ambiguous effect on pizza pur- chases.
2. What can you say about the relationship between the price elasticity of demand for pizza, the income elasticity of demand for pizza, and the cross-price elasticity of the demand for pizza with respect to beer prices? (Hint: Remember the demand for pizza must be homogeneous.)
9Although the estimated price elasticities in Table 3.4 incorporate both substitution and income effects, they predominantly represent substitution effects. To see this, note that the price elasticity of demand (eQ,P) can be disaggregated into substitution and income effects by
eQ,P¼eSsiei
whereeSis the ‘‘substitution’’ price elasticity of demand representing the effect of a price change holding utility constant,siis the share of income spent on the good in question, andeiis the good’s income elasticity of demand.
Becausesiis small for most of the goods in Table 3.4,eQ,PandeShave values that are reasonably close.
As expected, the income elasticities in Table 3.4 are positive and are roughly centered about 1.0. Luxury goods, such as automobiles or transatlantic travel (eQ,I > 1), tend to be balanced by necessities, such as food or medical care (eQ,I< 1). Because none of the income elasticities is negative, it is clear that Giffen’s paradox must be very rare.
T A B L E 3 . 4
R e p r e s e n t a t i v e P r ic e a n d I n c o m e E l a s t i c it ie s o f D em a nd
PRICE ELASTICITY
INCOME ELASTICITY
Food 0.21 þ0.28
Medical services 0.18 þ0.22
Housing
Rental 0.18 þ1.00
Owner-occupied 1.20 þ1.20
Electricity 1.14 þ0.61
Automobiles 1.20 þ3.00
Beer 0.26 þ0.38
Wine 0.88 þ0.97
Marijuana 1.50 0.00
Cigarettes 0.35 þ0.50
Abortions 0.81 þ0.79
Transatlantic air travel 1.30 þ1.40
Imports 0.58 þ2.73
Money 0.40 þ1.00
Source:Food: H. Wold and L. Jureen,Demand Analysis(New York: John Wiley & Sons, Inc., 1953): 203. Medical Services: income elasticity from R. Andersen and L. Benham, ‘‘Factors Affecting the Relationship between Family Income and Medical Care Consumption’’ inEmpirical Studies in Health Economics, ed. (Baltimore: Johns Hopkins Press, 1970). Price elasticity from Manning et al., ‘‘Health Insurance and the Demand for Medical Care: Evidence from a Randomized Experiment,American Economic Review(June 1987): 251–277. Housing: income elasticities from F. de Leeuw, ‘‘The Demand for Housing,’’Review of Economics and Statistics(February 1971); price elasticities from H. S. Houthakker and L. D. Taylor,Consumer Demand in the United States(Cambridge, Mass.: Harvard University Press, 1970), 166–167. Electricity: R. F. Halvorsen, ‘‘Residential Demand for Electricity,’’ unpublished Ph.D. dissertation, Harvard University, December 1972. Automobiles: Gregory C. Chow,Demand for Automobiles in the United States(Amsterdam: North Holland Publishing Company, 1957). Beer and Wine: J. A. Johnson, E. H.
Oksanen, M. R. Veall, and D. Fritz, ‘‘Short-Run and Long-Run Elasticities for Canadian Consumption of Alcoholic Beverages,’’Review of Economics and Statistics(February 1992): 64–74. Marijuana: T. C. Misket and F. Vakil, ‘‘Some Estimates of Price and Expenditure Elasticities among UCLA Students,’’Review of Economics and Statistics (November 1972): 474–475. Cigarettes: F. Chalemaker, ‘‘Rational Addictive Behavior and Cigarette Smoking,’’
Journal of Political Economy(August 1991): 722–742. Abortions: M. J. Medoff, ‘‘An Economic Analysis of the Demand for Abortions,’’Economic Inquiry(April 1988): 253–259. Transatlantic air travel: J. M. Cigliano, ‘‘Price and Income Elasticities for Airline Travel,’’Business Economics(September 1980): 17–21. Imports: M. D. Chinn, ‘‘Beware of Econometricians Bearing Estimates,’’Journal of Policy Analysis and Management(Fall 1991): 546–567. Money:
‘‘Long-Run Income and Interest Elasticities of Money Demand in the United States,’’Review of Economics and Statistics(November 1991): 665–674. Price elasticity refers to interest rate elasticity.
SUMMARY
In this chapter, we showed how to construct the market demand curve for a product—a basic building block in the theory of price determination. Because market demand is composed on the reactions of many consu- mers, we began this study with a description of how individuals react to price changes. The resulting analy- sis of substitution and income effects is one of the most important discoveries of economic theory. This theory provides a fairly complete description of why indivi- dual demand curves slope downward, and this leads directly to the familiar downward sloping market demand curve. Because this derivation is fairly lengthy and complicated, there are quite a few things to keep in mind:
Proportionate changes in all prices and income do not affect individuals’ economic choices because these do not shift the budget constraint.
A change in a good’s price will create substitution and income effects. For normal goods, these work in the same direction—a fall in price will cause more to be demanded, and a rise in a price will cause less to be demanded.
A change in the price of one good will usually affect the demand for other goods as well. That is, it will shift the other good’s demand curve. If the two goods are complements, a rise in the price of one will shift the other’s demand curve inward.
If the goods are substitutes, a rise in the price of one will shift the other’s demand curve outward.
Consumer surplus measures the area below a demand curve and above market price. This area
shows what people would be willing to pay for the right to consume a good at its current market price.
Market demand curves are the horizontal sum of all individuals’ demand curves. This curve slopes downward because individual demand curves slope downward. Factors that shift individual demand curves (such as changes in income or in the price of another good) will also shift market demand curves.
The price elasticity of demand provides a con- venient way of measuring the extent to which market demand responds to price changes—it measures the percentage change in quantity dem- anded (along a given demand curve) in response to a 1 percent change in price.
There is a close relationship between the price elasticity of demand and changes in total spending on a good. If demand is inelastic (0 >eQ,P>1), a rise in price will increase total spending, whereas a fall in price will reduce it. Alternatively, if demand is elastic (eQ,P<1), a rise in price will reduce total spending, but a fall in price will in fact increase total spending because of the extra sales gener- ated.
The price elasticity of demand is not necessarily constant along a demand curve, so some care must be taken when prices change by significant amounts.
REVIEW QUESTIONS
1. Monica always buys one unit of food together with three units of housing, no matter what the prices of these two goods. If food and housing start with equal prices, decide whether the follow- ing events would make her better off or worse off or leave her welfare unchanged.
a. The prices of food and housing increase by 50 percent, with Monica’s income unchanged.
b. The prices of food and housing increase by 50 percent, and Monica’s income increases by 50 percent.
c. The price of food increases by 50 percent, the price of housing remains unchanged, and Monica’s income increases by 25 percent.
d. The price of food remains unchanged, the price of housing increases by 50 percent, and Mon- ica’s income increases by 25 percent.
e. How might your answers to part c and part d change if Monica were willing to alter her mix of food and housing in response to price changes?
2. When there are only two goods, the assumption of a diminishing MRS requires that substitution effects have price and quantity move in opposite directions for any good. Explain why this is so. Do you think the result holds when there are more than two goods?
3. George has rather special preferences for DVD rentals. As his income rises, he will increase his
rentals until he reaches a total of seven per week.
After he is regularly renting seven DVDs per week, however, further increases in his income do not cause him to rent any more DVDs.
a. Provide a simple sketch of George’s indiffer- ence curve map.
b. Explain how George will respond to a fall in the price of DVD rentals.
4. Is the following statement true or false? Explain.
‘‘Every Giffen good must be inferior, but not every inferior good exhibits the Giffen paradox.’’
5. Explain whether the following events would result in a move along an individual’s demand curve for popcorn or in a shift of the curve. If the curve would shift, in what direction?
a. An increase in the individual’s income b. A decline in popcorn prices
c. An increase in prices for pretzels
d. A reduction in the amount of butter included in a box of popcorn
e. The presence of long waiting lines to buy pop- corn
f. A sales tax on all popcorn purchases
6. In the construction of the market demand curve shown in Figure 3.12, why is a horizontal line drawn at the prevailing price,Px? What does this assume about the price facing each person? How are people assumed to react to this price?
7. ‘‘Gaining extra revenue is easy for any producer—
all it has to do is raise the price of its product.’’ Do
you agree? Explain when this would be true and when it would not be true.
8. Suppose that the market demand curve for pasta is a straight line of the formQ¼30050Pwhere Qis the quantity of pasta bought in thousands of boxes per week and P is the price per box (in dollars).
a. At what price does the demand for pasta go to 0? Develop a numerical example to show that the demand for pasta is elastic at this point.
b. How much pasta is demanded at a price of $0?
Develop a numerical example to show that demand is inelastic at this point.
c. How much pasta is demanded at a price of $3?
Develop a numerical example that suggests that total spending on pasta is as large as pos- sible at this price.
9. J. Trueblue always spends one-third of his income on American flags. What is the income elasticity of his demand for such flags? What is the price elas- ticity of his demand for flags?
10. Table 3.4 reports an estimated price elasticity of demand for electricity of1.14. Explain what this means with a numerical example. Does this num- ber seem large? Do you think this is a short- or long-term elasticity estimate? How might this esti- mate be important for owners of electric utilities or for bodies that regulate them?
PROBLEMS
3.1Elizabeth M. Suburbs makes $200 a week at her summer job and spends her entire weekly income on new running shoes and designer jeans, because these are the only two items that provide utility to her. Furthermore, Elizabeth insists that for every pair of jeans she buys, she must also buy a pair of shoes (without the shoes, the new jeans are worthless). Therefore, she buys the same number of pairs of shoes and jeans in any given week.
a. If jeans cost $20 and shoes cost $20, how many will Elizabeth buy of each?
b. Suppose that the price of jeans rises to $30 a pair. How many shoes and jeans will she buy?
c. Show your results by graphing the budget con- straints from part a and part b. Also draw Elizabeth’s indifference curves.
d. To what effect (income or substitution) do you attribute the change in utility levels between part a and part b?
e. Now we look at Elizabeth’s demand curve for jeans. First, calculate how many pairs of jeans she will choose to buy if jeans prices are $30,
$20, $10, or $5.
f. Use the information from part e to graph Ms. Suburbs’s demand curve for jeans.
g. Suppose that her income rises to $300. Graph her demand curve for jeans in this new situa- tion.
h. Suppose that the price of running shoes rises to
$30 per pair. How will this affect the demand curves drawn in part b and part c?
3.2Currently, Paula is maximizing utility by purchas- ing 5 TV dinners (T) and 4 Lean Cuisine meals (L) each week.
a. Graph Paula’s initial utility-maximizing choice.
b. Suppose that the price ofTrises by $1 and the price ofLfalls by $1.25. Can Paula still afford
to buy her initial consumption choices? What do you know about her new budget constraint?
c. Use your graph to show why Paula will choose to consume moreLand lessTgiven her new budget constraint. How do you know that her utility will increase?
d. Some economists define the ‘‘substitution effect’’ of a price change to be the kind of change shown in part c. That is, the effect represents the change in consumption when the budget constraint rotates aboutthe initial consumption bundle. Precisely how does this notion of a substitution effect differ from the one defined in the text?
e. If the substitution effect were defined as in part d, how would you define ‘‘the income effect’’ in order to get a complete analysis of how a per- son responds to a price change?
3.3David gets $3 per month as an allowance to spend any way he pleases. Because he likes only peanut butter and jelly sandwiches, he spends the entire amount on peanut butter (at $.05 per ounce) and jelly (at $.10 per ounce). Bread is provided free of charge by a concerned neighbor. David is a picky eater and makes his sand- wiches with exactly 1 ounce of jelly and 2 ounces of peanut butter. He is set in his ways and will never change these proportions.
a. How much peanut butter and jelly will David buy with his $3 allowance in a week?
b. Suppose the price of jelly were to rise to $.15 per ounce. How much of each commodity would be bought?
c. By how much should David’s allowance be increased to compensate for the rise in the price of jelly in part b?
d. Graph your results of part a through part c.
e. In what sense does this problem involve only a single commodity—peanut butter and jelly sandwiches? Graph the demand curve for this single commodity.
f. Discuss the results of this problem in terms of the income and substitution effects involved in the demand for jelly.
3.4Irene’s demand for pizza is given by:
Q¼0:3I P
where Q is the weekly quantity of pizza bought (in slices),Iis weekly income, andPis the price of pizza.
Using this demand function, answer the following:
a. Is this function homogeneous inIandP?
b. Graph this function for the caseI¼200.
c. One problem in using this function to study consumer surplus is that Q never reaches zero, no matter how highPis. Hence, suppose that the function holds only forP10 and that Q¼0 forP> 10. How should your graph in part b be adjusted to fit this assumption?
d. With this demand function (andI¼200), it can be shown that the area of consumer surplus is approximately CS¼1986P60 lnðPÞ, where ‘‘ln(P)’’ refers to the natural logarithm ofP. Show that ifP¼10,CS¼0.
e. SupposeP¼3. How much pizza is demanded, and how much consumer surplus does Irene receive? Give an economic interpretation to this magnitude.
f. IfP were to increase to 4, how much would Irene demand and what would her consumer surplus be? Give an economic interpretation to why the value ofCShas fallen.
3.5The demand curves we studied in this chapter were constructed holding a person’s nominal income constant—hence, changes in prices introduced changes in real income (that is, utility). Another way to draw a demand curve is to hold utility constant as prices change. That is, the person is ‘‘compensated’’ for any effects that the prices have on his or her utility. Such compensated demand curvesillustrate only substitution effects, not income effects. Using this idea, show that:
a. For any initial utility-maximizing position, the regular demand curve and the compensated de- mand curve pass through the same price/quan- tity point.
b. The compensated demand curve is generally steeper than the regular demand curve.
c. Any regular demand curve intersects many dif- ferent compensated demand curves.
d. If Irving consumes only pizza and chianti in fixed proportions of one slice of pizza to one glass of chianti, his regular demand curve for pizza will be downward sloping but his com- pensated demand curve(s) will be vertical.
3.6The residents of Uurp consume only pork chops (X) and Coca-Cola (Y). The utility function for the typical resident of Uurp is given by
Utility¼UðX,YÞ ¼ ffiffiffiffiffiffiffiffiffiffiffi XY p
In 2009, the price of pork chops in Uurp was $1 each;
Cokes were also $1 each. The typical resident consumed 40 pork chops and 40 Cokes (saving is
impossible in Uurp). In 2010, swine fever hit Uurp and pork chop prices rose to $4; the Coke price remained unchanged. At these new prices, the typical Uurp resi- dent consumed 20 pork chops and 80 Cokes.
a. Show that utility for the typical Uurp resident was unchanged between the 2 years.
b. Show that using 2009 prices would show an increase in real income between the 2 years.
c. Show that using 2010 prices would show a decrease in real income between the years.
d. What do you conclude about the ability of these indexes to measure changes in real income?
3.7Suppose that the demand curve for garbanzo beans is given by
Q¼20P
whereQis thousands of pounds of beans bought per week andPis the price in dollars per pound.
a. How many beans will be bought atP¼0?
b. At what price does the quantity demanded of beans become 0?
c. Calculate total expenditures (PÆQ) for beans of each whole dollar price between the prices identified in part a and part b.
d. What price for beans yields the highest total expenditures?
e. Suppose the demand for beans shifted to Q¼402P. How would your answers to part a through part d change? Explain the dif- ferences intuitively and with a graph.
3.8Tom, Dick, and Harry constitute the entire market for scrod. Tom’s demand curve is given by
Q1¼1002P
forP50. ForP> 50,Q1¼0. Dick’s demand curve is given by
Q2¼1604P
forP40. ForP> 40,Q2¼0. Harry’s demand curve is given by
Q3¼1505P
forP30. ForP> 30,Q3¼0. Using this information, answer the following:
a. How much scrod is demanded by each person atP¼50? AtP¼35? AtP¼25? AtP¼10?
And atP¼0?
b. What is the total market demand for scrod at each of the prices specified in part a?
c. Graph each individual’s demand curve.
d. Use the individual demand curves and the results of part b to construct the total market demand for scrod.
3.9In Chapter 3 we introduced the concept of consu- mer surplus as measured by the area above market price and below an individual’s demand for a good.
This problem asks you to think about that concept for the market as a whole.
a. Consumer surplus in the market as a whole is simply the sum of the consumer surplus received by each individual consumer. Use Fig- ure 3.12 to explain why this total consumer surplus is also given by the area under the marketdemand curve and above the current price.
b. Use a graph to show that the loss of consumer surplus resulting from a given price rise is greater with an inelastic demand curve than with an elastic one. Explain your result intui- tively. (Hint: What is the primary reason a demand curve is elastic?)
c. How would you evaluate the following asser- tion: ‘‘The welfare loss from any price increase can be readily measured by the increased spending on a good made necessary by that price increase.’’
3.10Consider the linear demand curve shown in the following figure. There is a geometric way of calculat- ing the price elasticity of demand for this curve at any arbitrary point (say pointE). To do so, first write the algebraic form of this demand curve asQ¼aþbP.
a. With this demand function, what is the value of Pfor whichQ¼0?
Price
P*
Y D
X
Quantity per week
0 Q* D
E