the real world. The function (which, as we pointed out before, is called a ‘‘Cobb- Douglas’’ function) can be generalized a bit, as we show in Problem 2.10, but for most actual studies of consumer behavior, much more complicated functions are used.
the price a person pays for a good is not affected by how much of that good he or she buys. We assumed there were no special deals for someone who purchased many hamburgers or who opted for ‘‘super’’ sizes of soft drinks. In many cases, people do not face such simple budget constraints. Instead, they face a variety of inducements to buy larger quantities or complex bundling arrangements that give special deals only if other items are also bought. For example, the pricing of telephone service has become extremely complex, involving cut rates for more extensive long-distance usage, special deals for services such as voice mail or caller ID, and tie-in sales that offer favorable rates to customers who also buy Internet or cell phone service from the same vendor. Describing precisely the budget constraint faced by a consumer in such situations can sometimes be quite difficult. But a careful analysis of the properties of such complicated budget constraints and how they relate to the utility-maximizing model can be revealing in showing why people behave in the ways they do. Application 2.6: Loyalty Programs provides some illustrations.
Composite Goods
Another important way in which the simple two-good model in this chapter can be generalized is through the use of acomposite good. Such a good is constructed by combining spending on many individual items into one aggregated whole. One way such a good is used is to study the way people allocate their spending among such major items as ‘‘food’’ and ‘‘housing.’’ For example, in the next chapter, we show that spending on food tends to fall as people get richer, whereas spending on housing is, more or less, a constant fraction of income. Of course, these spending patterns are in reality made up of individual decisions about what kind of breakfast cereal to buy or whether to paint your house; but adding many things together can often help to illuminate important questions.
Probably the most common use of the composite good idea is in situations where we wish to study decisions to buy one specific item such as airline tickets or gasoline. In this case, a common procedure is to show the specific item of interest on the horizontal (X) axis and spending on ‘‘everything else’’ on the vertical (Y) axis.
This is the procedure we used in Application 2.3 and Application 2.4, and we use it many other times later in this book. Taking advantage of the composite good idea can greatly simplify many problems.
There are some technical issues that arise in using composite goods, though those do not detain us very long in this book. A first problem is how we are to measure a composite good. In our seemingly endless hamburger–soft drink exam- ples, the units of measurement were obvious. But the only way to add up all of the individual items that constitute ‘‘everything else’’ is to do so in dollars (or some other currency). Looking at dollars of spending on everything else will indeed prove to be a very useful graphical device. But one might have some lingering concerns that, because such adding up requires us to use the prices of individual items, we might get into some trouble when prices change. This then leads to a second problem with composite goods—what is the ‘‘price’’ of such a good. In most cases, there is no need to answer this question because we assume that the price of the composite good (goodY) does not change during our analysis. But, if we did
Composite good Combining expenditures on several different goods whose relative prices do not change into a single good for convenience in analysis.
A P P L I C A T I O N 2 . 6 Loyalty Programs
These days, everyone’s wallet is bulging with affinity cards. A quick check reveals that your authors regularly carry cards for Ace Hardware, Best Buy, Blockbuster, Circuit City (now bankrupt), Delta Airlines, and Dick’s Sporting Goods—and that is only the first four letters of the alphabet! These cards usually promise some sort of discount when you buy a lot of stuff. Why do firms push them?
Quantity Discounts and the Budget Constraint
The case of a quantity discount is illustrated in Figure 1. Here consumers who buy less thanXDpay full price and face the usual budget constraint. Purchases in excess ofXDentitle the buyer to a lower price (on the extra units), and this results in a flatter budget constraint beyond that point. The constraint, therefore, has a ‘‘kink’’ atXD. Effects of this kink on consumer choices are suggested by the indifference curveU1, which is tangent to the budget constraint at both pointAand pointB.
This person is indifferent between consuming relatively little ofXor a lot of it. A slightly larger quantity discount could tempt this consumer definitely to choose the larger amount.
Notice that such a choice entails not only consuming low-
price units of the good but also buying more of it at full price (up toXD) in order to get the discount.1
Frequent-Flier Programs
All major airlines sponsor frequent-flier programs. These enti- tle customers to accumulate mileage with the airline at reduced fares. Because unused-seat revenues are lost forever, the airlines utilize these programs to tempt consumers to travel more on their airlines. Any additional full-fare travel that the programs may generate provides extra profits for the airline.
One interesting side issue related to frequent-flier programs concerns business travel. When travelers have their fares reim- bursed by their employers they may have extra incentives to chalk-up frequent-flier miles. In such a case airlines may be especially eager to lure business travelers (who usually pay higher fares) with special offers such as ‘‘business class’’ service or airport-based clubs. Because a traveler pays the same zero- price no matter which airline is chosen, these extras may have a big influence on actual choices made. Of course travel departments of major companies recognize this and may adopt policies that seek to limit travelers’ choices.
Other Loyalty Programs
Most other loyalty programs work in the same way—credits accrued from prior purchases allow you to earn discounts on future ones. The effects of the programs on the sales of retailers may not be as significant as in the case of airlines, however, because many times customers may not under- stand how the discounts actually work. Retailers may also impose restrictions on discounts (i.e., they may expire after a year), so their actual value is more apparent that real.
Whether such programs really do breed consumer loyalty is much debated by marketing executives.
TOTHINKABOUT
1. How do the details of loyalty programs affect consumer purchasing decisions? What kinds of constraints do the programs you participate in impose? How do they affect your buying behavior?
2. Suppose frequent-flier coupons were transferable among people. How would this affect Figure 1 and, more generally, the overall viability of the program?
FIGURE 1Kinked Budget Constraint Resulting from a Quantity Discount
Quantity of Y per period
Quantity of X per period
0 XD
B U1
A
A quantity discount for purchases greater thanXDresults in a kinked budget constraint. This consumer is indifferent between consuming relatively littleX(pointA) or a lot ofX (pointB).
1For a more complete discussion of the kinds of pricing schemes that can be shown on a simple utility maximization graph, see J. S.
DeSalvo and M. Huq, ‘‘Introducing Nonlinear Pricing into Consumer Theory,’’Journal of Economic Education(Spring 2002):166–179.
wish to study changes in the price of a composite good, we would obviously have to define that price first.
In our treatment, therefore, we will not be much concerned with these technical problems associated with composite goods. If you are interested in the ways that some of the problems are solved, you may wish to do some reading on your own.10
SUMMARY
This chapter covers a lot of ground. In it we have seen how economists explain the kinds of choices people make and the ways in which those choices are con- strained by economic circumstances. The chapter has been rather tough going in places. The theory of choice is one of the most difficult parts of any study of micro- economics, and it is unfortunate that it usually comes at the very start of the course. But that placement clearly shows why the topic is so important. Practically every model of economic behavior starts with the tools introduced in this chapter.
The principal conclusions in this chapter are:
Economists use the term utility to refer to the satisfaction that people derive from their eco- nomic activities. Usually only a few of the things that affect utility are examined in any particular analysis. All other factors are assumed to be held constant, so that a person’s choices can be studied in a simplified setting.
Utility can be shown by an indifference curve map.
Each indifference curve identifies those bundles of goods that a person considers to be equally attrac- tive. Higher levels of utility are represented by higher indifference curve ‘‘contour’’ lines.
The slope of indifference curves shows how a person is willing to trade one good for another
while remaining equally well-off. The negative of this slope is called the ‘‘marginal rate of substitu- tion’’ (MRS), because it shows the degree to which an individual is willing to substitute one good for another in his or her consumption choices. The value of this trade-off depends on the amount of the two goods being consumed.
People are limited in what they can buy by their
‘‘budget constraints.’’ When a person is choosing between two goods, his or her budget constraint is usually a straight line because prices do not depend on how much is bought. The negative of the slope of this line represents the price ratio of the two goods—it shows what one of the goods is worth in terms of the other in the market- place.
If people are to obtain the maximum possible utility from their limited incomes, they should spend all the available funds and should choose a bundle of goods for which the MRS is equal to the price ratio of the two goods. Such a utility maximum is shown graphically by a tan- gency between the budget constraint and the highest indifference curve that this person’s income can buy.
REVIEW QUESTIONS
1. The notion of utility is an ‘‘ordinal’’ one for which it is assumed that people can rank combinations of goods as to their desirability, but that they cannot assign a unique numerical (cardinal) scale for the goods that quantifies ‘‘how much’’ one combina- tion is preferred to another. For each of the fol- lowing ranking systems, describe whether an
ordinal or cardinal ranking is being used: (a) mili- tary or academic ranks; (b) prices of vintage wines; (c) rankings of vintage wines by the French Wine Society; (d) press rankings of the ‘‘Top Ten’’
football teams; (e) results of the U.S. Open Golf Championships (in which players are ranked by the number of strokes they take); (f) results of the
10For an introduction, see W. Nicholson and C. Snyder,Microeconomic Theory: Basic Principles and Extensions, 10th ed. (Mason, OH: South-Western/Thomson Learning, 2008), Chapter 6.
U.S. Open Tennis Championships (which were conducted using a draw that matches players against one another until a final winner is found).
2. How might you draw an indifference curve map that illustrates the following ideas?
a. Margarine is just as good as the high-priced spread.
b. Things go better with Coke.
c. A day without wine is like a day without sun- shine.
d. Popcorn is addictive—the more you eat, the more you want.
e. It takes two to tango.
3. Inez reports that an extra banana would increase her utility by two units and an extra pear would increase her utility by six units. What is her MRS of bananas for pears—that is, how many bananas would she voluntarily give up to get an extra pear?
Would Philip (who reports that an extra banana yields 100 units of utility whereas an extra pear yields 400 units of utility) be willing to trade a pear to Inez at her voluntary MRS?
4. Oscar consumes two goods, wine and cheese. His weekly income is $500.
a. Describe Oscar’s budget constraints under the following conditions:
Wine costs $10/bottle, cheese costs $5/
pound;
Wine costs $10/bottle, cheese costs $10/
pound;
Wine costs $20/bottle, cheese costs $10/
pound;
Wine costs $20/bottle, cheese costs $10/
pound, but Oscar’s income increases to
$1,000/week.
b. What can you conclude by comparing the first and the last of these budget constraints?
5. While standing in line to buy popcorn at your favor- ite theater, you hear someone behind you say, ‘‘This popcorn isn’t worth its price—I’m not buying any.’’
How would you graph this person’s situation?
6. A careful reader of this book will have read foot- note 2 and footnote 5 in this chapter. Explain why these can be summarized by the commonsense idea that a person is maximizing his or her utility only if getting an extra dollar to spend would provide the same amount of extra utility no matter which good he or she chooses to spend it on.
(Hint: Suppose this condition were not true—is utility as large as possible?)
7. Most states require that you purchase automobile insurance when you buy a car. Use an indifference curve diagram to show that this mandate reduces utility for some people. What kinds of people are most likely to have their utility reduced by such a law? Why do you think that the government requires such insurance?
8. Two students studying microeconomics are trying to understand why the tangent condition studied in this chapter means utility is at a maximum.
Let’s listen:
Student A.If a person chooses a point on his or her budget constraint that is not tangent, it is clear that he or she can manage to get a higher utility by spending differently.
Student B.I don’t get it—how do you know he or she can do better instead of worse?
How can you help out Student B with a graph?
9. Suppose that an electric company charges consu- mers $.10 per kilowatt hour for electricity for the first 1,000 used in a month but $.15 for each extra kilowatt hour after that. Draw the budget con- straint for a consumer facing this price schedule, and discuss why many individuals may choose to consume exactly 1,000 kilowatt hours.
10. Suppose an individual consumes three items:
steak, lettuce, and tomatoes. If we were interested only in examining this person’s steak purchases, we might group lettuce and tomatoes into a single composite good called ‘‘salad.’’ Suppose also that this person always makes salad by combining two units of lettuce with one unit of tomato.
a. How would you define a unit of ‘‘salad’’ to show (along with steak) on a two-good graph?
b. How does the price of salad (PS) relate to the price of lettuce (PL) and the price of tomatoes (PT)?
c. What is this person’s budget constraint for steak and salad?
d. Would a doubling of the price of steak, the price of lettuce, the price of tomatoes, and this person’s income shift the budget constraint described in part c?
e. Suppose instead that the way in which this person made salad depended on the relative prices of lettuce and tomatoes. Now could you express this person’s choice problem as involving only two goods? Explain.
PROBLEMS
2.1 Suppose a person has $8.00 to spend only on apples and bananas. Apples cost $.40 each, and bana- nas cost $.10 each.
a. If this person buysonlyapples, how many can be bought?
b. If this person buysonly bananas, how many can be bought?
c. If the person were to buy 10 apples, how many bananas could be bought with the funds left over?
d. If the person consumes one less apple (that is, nine), how many more bananas could be bought? Is this rate of trade-off the same no matter how many apples are relinquished?
e. Write down the algebraic equation for this person’s budget constraint, and graph it show- ing the points mentioned in parts a through d (using graph paper might improve the accu- racy of your work).
2.2Suppose the person faced with the budget con- straint described in problem 2.1 has preferences for apples (A) and bananas (B) given by
Utility¼ ffiffiffiffiffiffiffiffiffiffiffi A·B p
a. IfA¼5 andB¼80, what will utility be?
b. IfA¼10, what value forB will provide the same utility as in part a?
c. IfA¼20, what value forB will provide the same utility as in parts a and b?
d. Graph the indifference curve implied by parts a through c.
e. Given the budget constraint from problem 2.1, which of the points identified in parts a through c can be bought by this person?
f. Show through some examples that every other way of allocating income provides less utility than does the point identified in part b. Graph this utility-maximizing situation.
2.3Paul derives utility only from CDs and DVDs. His utility function is
U¼ ffiffiffiffiffiffiffiffiffiffiffiffi C·D p
a. Sketch Paul’s indifference curves for U¼5, U¼10, andU¼20.
b. Suppose Paul has $200 to spend and that CDs cost $5 and DVDs cost $20. Draw Paul’s budget constraint on the same graph as his indifference curves.
c. Suppose Paul spends all of his income on DVDs. How many can he buy and what is his utility?
d. Show that Paul’s income will not permit him to reach theU¼20 indifference curve.
e. If Paul buys 5 DVDs, how many CDs can he buy? What is his utility?
f. Use a carefully drawn graph to show that the utility calculated in part e is the highest Paul can achieve with his $200.
2.4Sometimes it is convenient to think about the con- sumer’s problem in its ‘‘dual’’ form. This alternative approach asks how a person could achieve a given target level of utility at minimal cost.
a. Develop a graphical argument to show that this approach will yield the same choices for this consumer as would the utility maximiza- tion approach.
b. Returning to problem 2.3, assume that Paul’s target level of utility isU¼10. Calculate the costs of attaining this utility target for the fol- lowing bundles of goods:
i. C¼100,D¼1 ii. C¼50,D¼2 iii. C¼25,D¼4 iv. C¼20,D¼5 v. C¼10,D¼10 vi. C¼5,D¼20.
c. Which of the bundles in part b provides the least costly way of reaching theU¼10 target?
How does this compare to the utility-maximiz- ing solution found in problem 2.3?
2.5Ms. Caffeine enjoys coffee (C) and tea (T) accord- ing to the functionUðC;TÞ ¼3Cþ4T.
a. What does her utility function say about her MRS of coffee for tea? What do her indiffer- ence curves look like?
b. If coffee and tea cost $3 each and Ms. Caffeine has $12 to spend on these products, how much coffee and tea should she buy to maximize her utility?
c. Draw the graph of her indifference curve map and her budget constraint, and show that the utility-maximizing point occurs only on the T-axis where no coffee is bought.
d. Would this person buy any coffee if she had more money to spend?
e. How would her consumption change if the price of coffee fell to $2?