CHAPTER C1. CONSUMER BEHAVIOR AND DEMAND


Topics covered in this chapter:

1. patterns of consumer behavior

2. expected vs. certain values of choices

3. comparison of actual outcomes to expected values

4. the behavior of the utility function

5. qualifications to the principle of diminishing marginal utility

6. managerial implications of utility relationships

7. the meaning of the law of demand

8. the utility basis of the demand curve

9. treatment of demand determinants in specifying demand relationships

10. the distinction between change of demand and change of quantity demanded

11. demand shift as a demand surface phenomenon

12. managerial implications of the distinction between normal and

inferior goods

13. managerial implications of substitutable and complementary goods

14. the relationships among total, average, and marginal revenues

15. the significance of marginal revenue as a decision criterion


CHAPTER C1. CONSUMER BEHAVIOR AND DEMAND


Chapter C3 begins with the assertion that production is the central function of the organized business enterprise. Production is undertaken in the hope of relieving the economic problem of scarcity. But a rational decision to produce any particular good or service is predicated upon the existence of a social phenomenon: an adequate demand by other members of society for the fruits of the productive effort. This chapter focuses upon the managerial problem of identifying the characteristics of the demand that may be tapped by the productive enterprise, and the possibility of manipulating (creating, increasing, altering) that demand in the interest of the enterprise. We begin with a consideration of the principles of consumer behavior.


Consumer Behavior

In Chapter A2 we noted the possibility that people may act without engaging in any prior, deliberate decision making. Indeed, there is reason to believe that human beings often engage in such conditioned responses. Such responses often occur in circumstances where the decision maker has compiled a great deal of past experience with similar conditions, and where the consequences of choosing among alternative courses of action are essentially trivial. We must also admit the existence of capricious actions taken by people who give little or no consideration to the consequences, even when the alternative outcomes are likely to be non-trivial. Each of us probably engages in conditioned response behavior much of the time, and everyone occasionally indulges in the capricious action. While capricious behavior can not be modeled, conditioned-response behavior may be treated with a default forecasting model, i.e., that tomorrow will be like today because today is like yesterday.

We now turn attention to the phenomenon of deliberate, rational decision making on the part of the consumer. We must acknowledge two possibilities with respect to the information upon which the consumer must predicate the decision: the consumer either has perfect information about the possible alternatives to be purchased, or the consumer has some information but lacks knowledge of much that is relevant to the decision context. The task of analyzing consumer behavior would be greatly facilitated if consumers always have all needed information, but, unfortunately, the world is much different from this ideal situation. We must therefore employ the concept of the expected value of the possible outcomes from the consumer's choice as introduced in Chapter A2. The expected value of a particular consumer choice is the probability-weighted average of all of the possible outcomes resulting from the choice. In the event that the probability of occurrence of one of the possible outcomes is 100 percent, then the expected value becomes the certain value of the choice. Treating certain value as a special case of expected value, we shall make all subsequent references in this regard to expected value.

The time-honored term that economists have used to refer to the expected value of the outcome of a consumer choice is "utility." Utility, or satisfaction, is an amalgam of a wide range of the consumer's attitudes with respect to the results of the choice. Its dimensions include the extent to which the choice is perceived to meet a particular need, and may extend to such nebulous concepts as the pleasure or enjoyment derived from the outcome of the choice. We must also acknowledge the possibility that the outcome of a consumer choice may be negative in the sense that the perceived need was not met by the choice, or that the choice resulted in displeasure or pain (emotional as well as physical).

In the cases of so-called "big ticket" items that are typically purchased in discrete quantities of ones (e.g., houses, cars, boats, cameras, stereo systems, mink coats, etc.), the consumer's choice usually is of the all-or-nothing variety, i.e., whether or not to make the acquisition. Before the acquisition, the consumer can only estimate the expected value of the choice to acquire the item. Only after the fact of the acquisition (often, long after the fact) can a comparison of the actual outcome be made to the estimate of the expected value made before the acquisition. The rational decision criterion is whether the expected value of the choice to acquire is greater than the cost of the acquisition. The consumer's decision can be judged to be good or bad only in the retrospective comparison of the actual value of the outcome to the acquisition cost. Intelligent consumers will compile a stock of experience concerning preacquisition estimates of expected values compared to post-acquisition realized values. Sellers wishing to manipulate the prospective consumer's demands for their products may attempt to pursue strategies to get the consumers to over-estimate their expected values of the outcomes, or to ignore their accumulated experiences with ex-post realized values relative to ex-ante estimated values.

An even larger proportion of the consumer's choices is not all-or-nothing, but rather more-or-less choices. In these cases, the consumer, after deciding that some of the good or service is needed, must also decide how much to acquire. All of the principles described above apply to the fundamental decision to acquire any of the good or service. But the quantity question requires recognition of an additional decision criterion. Economists have deduced from a great deal of personal and collective experience that consumers, in acquiring successive additional units of most goods or services, tend to realize declining amounts of additional value (i.e., utility or satisfaction). This phenomenon is referred to the in the economics literature as the "principle of diminishing marginal utility."

Economists recognize that the consumer may experience an initial surge of realized value from consuming the first few units of the good or service, but they have also become convinced of the certainty of eventual diminishing marginal utility for most goods. The qualification is in regard to goods (alcohol, drugs) or activities (hobbies, sex) that may be addictive or compulsive. Although there is much that is yet unknown in regard to addictive behavior, it may be hypothesized that the consumer realizes increasing marginal utility when consuming successive units of goods that are objects of addiction.

Figure C1-1 illustrates what economists think that a so-called total utility (TU) function and its derived marginal utility (MU) function might look like for a normal good, assuming all other factors constant. The underlying functional relationship can be given by

(1) TUx = f(Qx/ ... ),

i.e., the total utility realized in consuming good x is determined by the quantity of x consumed, given all other factors. The graph of the TU function can be perceived to be a two-dimensional section through a three-dimensional utility surface (illustrated in the Appendix to this Chapter). As it is illustrated in panel (a) of Figure C1-1, the TU curve is concave upward initially, over the range from the origin to Q1. This is the initial consumption range over which the consumer may experience the surge of utility rising at an increasing rate. But beyond Q1, and up to quantity Q2, total utility increases at a decreasing rate. The key concept here is the decreasing rate of increase of total utility. It is apparent that the total amount of utility realized in the consumption of commodity x reaches a maximum at quantity Q2. Successive units consumed beyond Q2 actually yield negative satisfactions, so the total amount of utility decreases. The MU curve is derived from the TU curve according to the principles outlined in Chapter B2. We can observe that over the quantity range for which TU is increasing at an increasing rate, from the origin to Q1, MU rises, reaching a peak at Q1. Over the quantity range for which TU is increasing at a decreasing rate, MU falls, reaching a value of zero at Q2 the quantity at which TU is maximum. The quantity range between Q1 and Q2 is described as the range of diminishing marginal utility. And it is this range that economists think represents the usual circumstances under which consumers make most of their choices. The reader is now invited to speculate on the likely appearances of the TU and MU curves for a commodity that is an object of addiction or compulsive consumption.

In the case of a non-addictive good or activity, the rational decision criterion is to continue to consume more of the good, even while realizing declining additional utility, until the marginal value realized in consumption is no longer greater than the marginal cost of the acquisition. In order to make such a comparison, the marginal cost of acquisition must be perceived in units comparable to those in which satisfactions are measured. One way to do this is to regard the acquisition cost in terms of dissatisfaction or disutility at having to part with purchasing power to make the acquisition. If the marginal utility does indeed decline, a point at which additional consumption should cease will be reached. In Figure C1-1, curve MD (marginal disutility) represents the marginal cost of acquiring additional units of the commodity (constant as illustrated). The consumer should push consumption to Q3, beyond which the marginal utility falls below the marginal disutility realized in acquisition.

In the case of a good or activity that is an object of addiction, since the marginal utility always increases as successive units are consumed, no consumption-limiting criterion is ever reached unless the marginal disutility rises to exceed the increasing marginal utility. Even then, it cannot be assumed that the addictive subject can engage in rational choice. An enterprise wishing to promote the sale of its product or service may pursue a strategy designed to induce the consumer to suffer the illusion that marginal utility declines at a slower rate than it does in reality, or to believe that marginal utility only increases as with an addictive good or activity. In either case, the naive or unwary consumer may be induced to consume larger quantities than he might with more rational consideration. Intelligent consumers can be expected to add to their stocks of experience such comparisons between ex-ante estimates of expected values of satisfactions and ex-post realizations of actual satisfactions. The manager should be aware that intelligent, experienced, and mature consumers are likely to be more resistant to efforts at manipulation of their preferences. The obverse of this principle is that less-experienced consumers (especially children and adolescents) or less-capable adult consumers may be more amenable to preference manipulation. This possibility should raise ethical "red flags" in the minds of conscientious managers.

Perhaps a less controversial approach to promoting sales of the product is for the enterprise to try to change one or more of the non-quantity determinants of utility, which to this point have remained unspecified and assumed constant. One of those surely is the consumer's taste for the good or service. An effective promotional strategy may improve the image of the good or service, thereby making it more desirable to the consumer. This will cause the TU curve, and with it the MU curve, to shift upward and to the right. The reader is invited to envision a modification to Figure C1-1 to illustrate this phenomenon. The shifted MU curve should intersect the MD curve at a quantity larger than Q3, thus achieving the seller's objective.


The Theory Of Demand

Demand is the desire for a good or service, together with the purchasing power to make the desire effective, both backed by the willingness of the consumer to part with the purchasing power. The demand curve is a graphic representation of the path along which the consumer would rationally choose to purchase quantities of the good or service at various prices. The so-called Law of Demand is the hypothesis that consumers will buy ever greater quantities of the good or service at progressively lower prices, i.e., acquisition costs. The fundamental behavioral principle underlying the concept of the demand curve is the shape of the marginal utility curve over the range of diminishing marginal utility. The connection between demand and utility is that the seller must offer the consumer some inducement to purchase more of the good once his marginal utility has fallen to the level of the disutility realized in acquiring the last unit. The obvious inducement is a lower price or acquisition cost. Consumers can be expected to purchase more at lower prices. The inverse is also expected: consumers will purchase smaller quantities at higher prices.

In addition to the marginal utility principle, economists offer two other explanations for the law of demand, the income and substitution effects. The substitution effect occurs when an increase in its price leads consumers to shift their purchases away from the good or service and to its substitutes--hence the inverse relationship between the own-price of the good or service and its quantity demanded. A downward change in the price of an item leads to an increase in quantity demanded as consumers shift their purchases away from substitutes and toward the item.

The income effect of a price change results from recognition that the consumer is faced with a range of choices. For example, when the price of an item falls, the consumer can purchase more of the item itself, or more of other items that he consumes, or retain unspent purchasing power. The decrease in the price of the item then results in an implicit increase of his income. Conversely, an increase in the price of the item means that the consumer must purchase less of item, less of other items that he normally purchases, or spend more than he has spent in the past. In either case, an inverse relationship between the price of the item and the quantity consumed of it is a consequence.

Demand Curves and Demand Surfaces. To this point we have spoken of demand in regard to the quantities of an item that might be purchased by a single consumer. But demand can also be regarded as a collective concept, i.e., as the summation of the quantities of an item that would be purchased by a collection of consumers over the range of possible prices. The collection of consumers may include all who are "in the market" for the particular item, but it may be more narrowly construed to those who are likely to purchase the item from a particular seller. In the former case we can speak of market demand, and in the latter case the demand faced by the particular seller, i.e., the firm's demand. Whether that for an individual consumer or some collection of consumers, the functional notation representation of the demand relationship may be given by

(2) Qx = f( Px / ... ),

i.e., the quantity demanded of a good or service is determined by the price of the good or service, given all other determinants. The functional relationship, f, is presumed to be inverse for the relationship between quantity and price. This inverse relationship, i.e., the Law of Demand, can be illustrated by drawing a demand curve on a set of coordinate axes for price and quantity as in Figure C1-2. The downward (left to right) slope of the demand curve is a manifestation of the principle of diminishing marginal utility.

We have drawn the demand curve in Figure C1-2 as a straight line with a negative slope. The equation for such a linear demand curve can be given in slope-intercept form as

(3) Qx = c + d(Px),

where c is the quantity-axis intercept, and d is the (assumed negative) slope of the demand curve. The linearity of this demand curve is assumed only for purposes of simplicity. In reality, a demand curve may exhibit any degree of curvature, and it may be concave upward or downward. Even if a straight line can approximate the price-quantity relationship, the linear demand curve may exhibit a range of slopes, from nearly horizontal at one extreme, to almost vertical at the other. And even these extremes are not effective limits on the possible slopes that demand curves may take. If the income effect of a price change of an inferior good were great enough to outweigh the substitution effect, the demand curve would slope upward from left to right in apparent contradiction to the law of demand.

If the demand curve illustrated in Figure C1-2 can be presumed to be a realistic representation of a real demand relationship for good x, then a decrease of the price from P1 to P2 can be expected to lead to an increase in the consumer's purchases of x from Q1 to Q2. Economists refer to such a movement from one point to another along a fixed-locus demand curve as a "change of quantity demanded." Such a change of quantity demanded is attributable exclusively to a change in the price of the good, given all other determinants.

The demand for any good or service is actually determined by many factors in addition to the price of the good or service. In fact, for some items the price may be one of the lesser-significant determinants of its demand. A more general specification of a demand curve may be given by

(4) Qx = f( Px, I, T, B, ... , Py, Pz, ... ),

where I is the income of the consumer, T stands for "tastes and preferences" (the same tastes and preferences referred to above as determinants of utility), B is the consumer's current level of indebtedness, Py is the price of a relevant substitute good, and Pz is the price of a related complement good. The ellipsis symbols ( ... ) between B and Py suggest that there are other non-price demand determinants that have not yet been specified (or even identified). Those following Pz allow for prices of yet other substitute and complement goods.

There is nothing particularly significant about the order in which the determinants of demand are listed on the right side of the equation. The order of the listing can be changed at will, and any one of them can be moved to the head of the queue as required. The price of the good itself (i.e., the good's "own price") is typically listed in the first position because, historically, the attention of economists turned to this determinant first. Also, in the cases of most goods and services, the own price may indeed be the most important or significant (in a statistical sense) determinant of the quantity demanded. Yet any such hierarchy of determinants is something to be discovered by analysis, rather than assumed at the outset.

In order to draw the two-dimensional representation of the demand curve illustrated in Figure C1-2, it was necessary to treat all of the non-own price demand determinants as if they were constant, even if they in fact were not constant (more about this below). A revision of equation (3) to represent this specification is given by

(5) Qx = f( Px / I, T, D, ... , Py, Pz, ... ),

where the slash (/) is used to separate the single demand determinant that is presumed to be variable (P) from all the rest, that are assumed not to change. Indeed, if any of the other determinants are variable, it is technically not even possible to draw a discrete locus for the demand curve in the two-dimensional space of the P-Q coordinate axes.

Economists employ the term "change of demand" to refer to the circumstance where some determinant of demand other than the item's "own price" has changed. The effect of such a change is to shift the own-price demand curve from its former locus to some position, as illustrated in Figure C1-3. Here, D1 is the original locus of the demand curve, and D2 is the new locus after something other than the price of the good has changed. For example, improving tastes and preferences for the good or service, or a decrease in consumer indebtedness, could possibly explain the illustrated right-ward shift of the demand curve.

Another perspective on the demand-shift phenomenon is provided by a three-dimensional graphic representation of the demand relationship. In this representation, the slash of equation (5) is moved one item to the right,

(6) Qx = f( Px, I / T, B, ... , Py, Pz, ... ).

In this relationship, two demand determinants, P and I, are presumed variable, while all other possible determinants are treated as if they were constant. A graphic representation of this relationship is given in Figure C1-4, where the third dimension (depth) is occupied by the income determinant. A number of "slices" (or vertical sections) have been made through the three-dimensional demand surface at different income levels. If the three-dimensional surface were viewed from a perspective opposite the price-quantity plane, in effect collapsing the surface into two dimensions, the viewer would see something like that represented in Figure C1-5. Here, the several vertical slices through the three-dimensional surface appear as a demand curve that shifts in two dimensions.

VRML 3-D View

The three-dimensional perspective enables another important observation. In Figure C1-4, the intersection of the demand surface with the floor (the income-quantity plane) traces out path RSTUV, which when viewed from above yields the two dimensional graph illustrated in Figure C1-6. In this figure, income is measured on the vertical axis, and is thus taken to be the demand determinant relative to quantity demanded on the horizontal axis. The path, RSTUV, thus traces out an income-demand curve (or Engel Curve, as it is referred to in the literature), for which the functional notation relationship would be given as

(7) Qx = f( I / Px, T, D, ... , Py, Pz, ... ).

In equation (7), the only variable determinant of demand is presumed to be income, while all other demand determinants, including price, are taken to be constant. As we noted above, price may not be the most significant demand determinant, and it is legitimate to move any of the demand determinants to the head of the list of determinants so that it may be analyzed, assuming all other determinants as givens.

The three-dimensional surface represented in Figure C1-4 is for two demand determinants, own-price and income, relative to quantity demanded. It is unfortunate that we can have access to no more than three graphic dimensions, because this necessarily limits our analysis to no more than two demand determinants at one time as long as we wish to stay with the graphic analysis. (We can treat more than two determinants at one time only by exiting the graphics and entering the realm of multivariate algebra.) However, within the realm of three-dimensional graphics, we can move any two determinants to the head of the determinant queue in order to construct a three-dimensional surface showing the relationship between quantity demanded and the two selected determinants. And by judiciously slicing the three-dimensional surface, we can extract two-dimensional demand curves showing the relationship between quantity demanded and any single demand determinant.

Normal and Inferior Goods. The income-demand curve illustrated in Figures C1-4 and C1-5 happens to slope upward from left to right (i.e., to exhibit a direct relationship between quantity demanded and income), and is therefore illustrative of the phenomenon of a "normal" good. A normal good is one for which quantity demanded increases when income rises, or decreases when income falls. An "inferior" good is one for which quantity demanded decreases when income rises, and increases when income falls. The two-dimensional income-demand curve for an inferior good would slope downward from left to right, with appearance similar to that of an own-price demand curve drawn on a set of price-quantity axes.

Most of the goods and services consumed by human beings are likely normal in the sense that people will consume more of them when their incomes rise. But there are also many examples of inferior goods to examine, although the items with respect to which they are inferior should be identified. For example, in the late twentieth century American culture, ground beef is probably inferior to most solid beef cuts; margarine is probably inferior to real butter, and Ford Escorts are probably inferior to Lincoln Town Cars. The word "probably" is included in the foregoing sentence because of the highly personal nature of preferences. Even if most of the members of American society would prefer a New York strip to a hamburger, there are some members of American society (teenagers come readily to mind) who might prefer a hamburger to the New York strip.

We should also stress that the characteristics of normalcy and inferiority are time and culture bound. For example, potatoes were probably regarded as inferior substitutes for mutton by eighteenth century Irish peasants, whereas twentieth century Americans tend to regard potatoes as complement to both steaks and hamburgers. The inferiority of potatoes relative to meat has ceased to be an issue for Americans, although the issue may be reopened in a choice between potatoes and rice.

The normalcy or inferiority of a good may be revealed in the income effect consequent upon a price change, as well as with an explicit change of income. We earlier identified the income and substitution effects of a price change as further (in addition to the principle of diminishing marginal utility) explanations of the law of demand. In the case of a normal good, the income effect may be expected to reinforce the substitution effect: when the price of a normal good falls, people will tend to increase their purchases of it, not only because it is now less expensive relative to substitutes, but also because they have realized an implicit increase of income due to the price change. In the case of an inferior good, however, the income effect will offset the substitution effect: when the price of the good falls, people will tend to consume more of it than more expensive substitutes, but the realization of its inferiority retards the increased consumption. Although economists have found little evidence of its existence, it is hypothesized that the income effect in the case of an inferior good may be so great as to more than offset the substitution effect. If such a phenomenon should occur, the own-price demand curve would appear to slope upward from left to right, and would thus be an apparent violation of the law of demand.

What are the managerial decision implications of inferiority and normalcy? In a growing economy, or during a period of cyclical expansion, the enterprise should attempt to produce normal goods or services since their demands will increase at the same or a faster rate than incomes are rising. The enterprise should avoid production of inferior goods since their demands will increase at a slower rate (or may even decrease) as incomes rise. However, during a period of cyclical decline, the enterprise would be better off in producing inferior goods because their demands will tend to decrease more slowly (or possibly even increase) as incomes fall. But, suppose that the main product lines of the enterprise are inferior goods that must continue in production through periods of expansion as well as contraction. In this case, the design strategy of the enterprise might be to alter the real nature of the product so that it becomes perceived to be a normal good relative to substitutes. Alternately, the enterprise's promotional strategy might be directed toward improving the clientele's tastes and preferences for the good, or altering the image of the good so that it is perceived to be normal rather than inferior.

Substitutes and Complements. Two other demand determinants that deserve the attention of the manager are the prices of substitutes (Py) and complements (Pz). Each of these determinants may of course be moved to the head of the determinant queue for analysis while assuming all other determinants (including the own-price of the item) constant. The functional notation equation of a substitute good demand relationship would appear as

Qx = f( Py / Px, I, T, D, ... , Pz, ... )

for which a so-called cross-price demand curve can be constructed. In the case of a substitute good, the cross-price demand curve slopes upward from left to right because when the price of the substitute Py is raised, although its quantity demanded Qy will decrease, the quantity demanded of the good Qx will increase. This increase can be illustrated as a movement upward along the cross-price demand curve, but would be a cause of a rightward shift of the own-price demand curve illustrated in Figure C1-3. We leave it to the reader to imagine the shape of the cross-price demand curve for a complement good, and the own-price demand shift implications of a change in the price of the complement.

The enterprise rarely has ability to directly influence the prices of goods that are substitutes or complements for those produced by the enterprise. But the management of the enterprise should be aware that competitors do produce substitutes for those produced by the enterprise, and that the pricing decisions of competitors can be expected to cause shifts of the own-price demand curves for the enterprise's products. Likewise, the management of the enterprise should be aware that its own pricing decisions will likely result in shifts of competitor's own-price demand curves, and may induce strategic responses from them. These possibilities will be considered again in Chapter 11.

Demand and Revenue. The price of the product can be understood to be its average revenue (AR), or the revenue per unit of the product sold by the enterprise. Thus, the total revenue (TR) that the enterprise will realize on the sale of Q units of its product can be computed by the formula

(8) TR = P x Q,

or if total revenue is known, the average revenue, or price, can be computed by solving equation (8) for P, or

AR = P = TR/Q.

Knowledge of these relationships enables us to derive an equation for a total revenue function from the equation for the demand function, or an equation for the demand function if that for the total revenue function is known. Either such equation can be specified employing the procedures discussed in the last section of this chapter. Suppose that demand equation (3) above has been specified with parameter values c=20 and d=-4, resulting in equation (10),

(10) Q = 20 + (-4)P.

We have omitted the subscript "d" in equation (3) for clarity of exposition. In order to derive the total revenue equation, we must first solve equation (10) for P,

(11) P = 5 - .25Q.

Since from equation (8) we know that TR = PxQ, we may derive the total revenue equation (12) by multiplying equation (11) through by Q,

P x Q = 5Q - .25Q2,

(12) TR = 5Q - .25Q2.

Alternately, had TR equation (12) been specified first, since AR = TR/Q, the AR equation could be derived by dividing the TR equation through by Q,

TR/Q = 5Q/Q - .25Q2/Q,

(13) AR = 5 - .25Q,

which is the same as equation (11) when it is recognized that P is the same as AR.

The derivation of these equations by simple algebraic manipulation enables us to illustrate in two dimensions the graphic relationship between AR and TR. The TR curve is shown in panel (a )of Figure C1-7; its associated demand curve (AR) is shown in panel (b). Corresponding average and total revenue curves for a linear demand relationship. Because the demand curve is linear with a negative slope, its associated total revenue curve is a second-order (or quadratic) equation that graphs as a parabola that opens downward and spans the positive-price range of the demand curve on the quantity axis. In Figure C1-7 we have also drawn a box in panel (a) below the demand curve formed by a horizontal at price P1 and a vertical at quantity Q1, the quantity that will be sold at price P1. We have also drawn a vertical in panel (b) below the TR curve a quantity Q1. By the formula for the area of a rectangle (area = length x width), we can assert that the area of the box in panel (a) measures the total revenue resulting from selling quantity Q1 at price P1. This same area is also represented by the altitude of the vertical at Q1 up to the TR curve in panel (b).

Figure C1-8 is a reproduction of Figure C1-7, but with several additional price-quantity boxes drawn below the AR curve, and corresponding verticals drawn below the TR curve. The reader should verify by inspection of the boxes that as price falls toward P3 and quantity increases accordingly, the boxed areas increase to a maximum corresponding to the tallest vertical below the vertex of the TR parabola. If the demand curve is indeed linear, the maximum total revenue will occur at a quantity that is half the horizontal axis intercept of the demand curve. In Figure C1-8, prices successively lower than P3 yield revenue rectangles of progressively smaller area The graphic approach illustrated in Figure C1-8 provides one means of identifying the price-quantity combination that yields the maximum total revenue, but it is not a means that yields an effective decision criterion. However, an alternate approach that employs concepts from the calculus can provide a useful revenue-maximization decision criterion.

The value of Q for which TR is at its maximum value can be found by differentiating the TR function with respect to Q, setting the differential equal to zero, and solving the resulting differential equation for Q. Thus, for TR equation (10),

TR = 5Q - .25Q2,

(14) dTR/dQ = 5 - .5Q.

Setting dTR/dQ = 0,

0 = 5 - .5Q,

and solving for Q,

Q = 10.

Thus, if the demand curve in panel (a) of Figure C1-8 is a graph of equation (3), the value of Q at Q3 is 10 units. Further, by substituting 10 for Q in the TR function, the maximized total revenue is found to be

TR - 5(10) - .25(10)2 = 25.

The revenue maximizing price can be found by substituting Q=10 into the average revenue equation,

AR = 5 - .25(10) = 2.5.

Thus, if the price denomination is the U.S. dollar and the unit denomination is 1000 each, a maximum total revenue of $25,000 can be realized by selling 10,000 of the item at a price of $2.50 each.

Economists refer to the differential of TR with respect to Q as the "marginal revenue" (MR). Conceptually, marginal revenue is the addition to total revenue consequent upon selling one more unit of the item, or

MR = DTR / DQ,

where DQ is 1 unit of the item. This is the approximate equivalent of the definition of the derivative,

dTR/dQ = DTR/DQ

as DQ approaches zero. MR can be reconciled to dTR/dQ if it is recognized that the closest that DQ can approach to zero is one unit of the item.

Equation (14), the differential of the TR function with respect to Q, can be rewritten as

(15) MR = 5 - .5Q.

A comparison of the MR equation (15) to the AR equation (13) leads to the inference that the two curves must share a common price-axis intercept (in this case 5), but that the slope of the MR function (.5) is twice that of the AR function (.25), and both are negative. This means that the MR curve must slope downward more steeply than does the AR curve. Figure C1-9 is a reproduction of Figure C1-7, but

with the MR curve drawn in. The most important observation to make in regard to Figure C1-9 is that the MR curve reaches zero at the quantity level for which the TR parabola attains its maximum value. This corresponds to the calculus procedure of setting the differential of TR equal to zero in order to find the Q for which TR is maximum.

The relationships described above provide a most useful managerial decision criterion. If the objective of the enterprise is to produce a quantity of an item and sell it at a price that yields the maximum possible revenue, it can do so by finding the quantity for which marginal revenue is zero. We qualify this conclusion immediately by noting that simple revenue maximization may not to be the behavioral objective of the management of the enterprise. Rather, the management may be oriented toward profit maximization (which, as we shall see in Chapters D1 through D4, is not likely to coincide with revenue maximization). Even so, we shall discover subsequently that marginal revenue is one of the two decision criteria that are relevant to profit maximization.


Looking Ahead

Chapter C2 extends the concepts developed in Chapter C1 into the realm of the statistical estimation of the demand function. A decision criterion, elasticity of demand, is first elaborated in Chapter C2, then the implications for elasticity of demand of various specification problems are considered.


CHAPTER C1 SUMMARY OF IMPORTANT POINTS

1. The theory of consumer behavior underlies the theory of demand.

2. Because consumers typically lack perfect ex ante information about their decision contexts, they must base their acquisition decisions upon a comparison of ex ante expected values with acquisition costs.

3. With notable exceptions, the realization of satisfaction in consumption obeys the principle of diminishing marginal utility.

4. Objects of compulsive consumption or addiction may violate the principle of diminishing marginal utility.

5. Managerial strategies may include efforts to manipulate the preferences of consumers or to change the non-quantity determinants of utility.

6. The law of demand is based upon the principle of diminishing marginal utility as well as substitution and income effects.

7. The own-price demand curve, a visual representation of the relationship between quantity demanded and the item's own price, all other determinants assumed constant, may be perceived as a two-dimensional slice through a three-dimensional surface.

8. A change in the price of the item will result in a change of quantity demanded, represented as a movement from one point to another along the own-price demand curve.

9. The locus of an own-price demand curve depends upon the non-price determinants of demand; the own-price demand curve shifts (or a different slice is taken through the surface) if any of the non-price determinants of demand change.

10. An income demand curve depicts the relationship between quantity demanded and income, all other determinants assumed constant; the income demand curve exhibits a direct relationship for a normal good, and an inverse relationship for an inferior good.

11. Managers will be expected to prefer to produce normal goods in a growing economy and during economic expansion; it would be rational to choose to produce inferior goods in a declining economy or during an economic contraction.

12. A cross-price demand curve depicts the relationship between the quantity demanded of an item and the price of a substitute or a complement; changes of cross prices cause shifts of the own-price demand curve.

13. The total revenue resulting from sale of an item is the product of its price and quantity sold; the average revenue, identical with price, is total revenue per unit sold.

14. If the demand curve for an item is linear, the total revenue from its sale is maximum at the price-quantity combination represented by the midpoint of the demand curve.

15. The output required for revenue maximization may be found by differentiating the revenue function, setting the differential equal to zero, and solving for the output level; the marginal revenue is zero when total revenue is maximum.


CHAPTER C1 SIGNIFICANT TERMS

behavior
conditioned response
capriciousness
deliberate decision
expected value
certain value
utility; total, marginal
diminishing marginal utility
addictive, compulsive behavior
demand, law of demand
income, substitution effects
demand curve
individual, market demand
inferior good
change of quantity demanded
determinants of demand
own price
change of demand
demand shift
demand surface
normal good
substitutes, complements
cross-price demand curve
revenue
average revenue


CHAPTER C1 QUESTIONS FOR DISCUSSION

1. Explain how conditioned response behavior can be modeled and forecasted.

2. How can a decision context be modeled if the decision maker has some information, but lacks knowledge of much that is relevant to the decision context.

3. What is the economic criterion for a consumer to use in deciding whether or not to acquire an item?

4. How can a consumer judge whether a choice to acquire an item was a good decision?

5. Critically evaluate a seller strategy to try to get consumers to over-estimate the expected value of the outcome of a consumer purchase.

6. Explain how an "all-or-nothing" acquisition decision differs from a "more-or-less" acquisition decision; how do the decision criteria differ?

7. Describe the phenomenon of "diminishing marginal utility" and discuss its decision significance.

8. Explore possible exceptions or violations to the principle of diminishing marginal utility, and discuss the decision implications.

9. Explain how a marginal utility function can be derived from a total utility function, and describe the shape of the latter in relation to the shape of the former.

10. Why would a rational consumer continue to consume more of a good even while realizing declining additional utility?

11. Identify an appropriate criterion that might be used by a consumer in deciding whether to continue to consume additional units of a good.

12. Critically evaluate utility-related strategies that the management of a firm might attempt to use in getting its customers to purchase more of its product.

13. How does the law of demand relate to utility theory?

14. Explain why demand curves normally slope downward from left to right.

15. Discuss possible exceptions to the law of demand and indicate the sources of the exceptions in utility theory.

16. Explain how variables other than the good's "own price" are treated in the construction of a two-dimensional demand curve.

17. Distinguish a "change of demand" from a "change of quantity demanded" and indicate possible causes of each; what is the managerial significance of the distinction?

18. Explain a "change of demand" with reference to a three-dimensional demand surface.

19. Describe the possible shapes of an income-demand curve and indicate the possible causes of the different slopes.

20. Distinguish inferior from normal goods and explain how these characteristics are revealed in own-price and income demand curves.

21. What are the managerial decision implications of inferiority and normalcy of goods in the firm's product line?

22. Distinguish substitutes and complements and explain the effects of changes in the prices of such goods upon the own-price demand curve.

23. Identify a so-called "cross price" demand curve and discuss the significance of it to managerial decision making.

24. Explain how, once the equation of a demand curve has been estimated, the analyst can generate the equations of the total and marginal revenue functions.

25. Describe the relationships among total, average, and marginal revenue graphs, and discuss the managerial significance of the relationships.

26. Show how the marginal revenue can be derived from a total revenue function via differential calculus.

27. Discuss the managerial decision significance of marginal revenue.


EXPENDITURE OPTIMIZATION PROBLEM

The data presented on the following page are for a hypothetical consumer who has $40 to spend on four categories of consumer goods: Food, Clothing, Housing, and Entertainment. The data contained in columns (2), (4), (6), and (8) are for the amounts of utility (or satisfaction, usefulness) that the consumer would gain from consuming each successive unit of each item, proceeding from the top of the page to the bottom. The data in column (10) are for the amounts of utility that would be lost by spending successive dollars from the consumer's bank account, proceeding from the top of the page toward the bottom. The problem is to allocate the limited budget so as to maximize utility. The consumer may acquire units of the consumable goods only by spending money and giving up utility according to the conditions specified in column (10).

1. Characterize the patterns of utility realization by the consumer in regard to each of the items purchased; ...in regard to the money spent.

2. What is the purpose of columns (3), (5), (7), (9), and (11)? Compute and fill in the numbers for these columns as needed.

3. What is the economic criterion for continuing to purchase each of the items? How many units of each should the consumer purchase? What total utility will the consumer realize if he/she purchases these quantities?

4. What criterion should the consumer use in deciding whether to spend successive additional dollars from the bank account? When the consumer stops spending money on the items, how many dollars will be left in the bank account? How much total utility will the remaining bank balance provide?

5. Is there any alternative collection of the four items and money, or any other purchase sequence by which the consumer could realize a greater mass of utility (total) than that achieved using those criteria specified in numbers (3) and (4) above?