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In search of Giffen behavior.

IN SEARCH OF GIFFEN BEHAVIOR

I. INTRODUCTION

The existence of Giffen behavior has intrigued students of traditional consumer theory for many years. Stigler [1947 1948! and Hicks [1956! dealt with the Giffen good by dismissing it as a theoretical possibility but a practical impossibility. This solution was met with some discord, especially by Boland [1977!. According to Boland, if demand theory cannot be revised to dismiss the theoretical possibility of a Giffen good, it should at least be able to explain why Giffen goods do not exist empirically.

Dougan [1982! answered Boland's critique by demonstrating the impossibility of observing a Giffen good at the market level. Because the estimated demand curve is the locus of market equilibria derived from a shifting supply curve, it must slope downward in the long run if Walrasian stability conditions hold. This suggests empirical evidence of a Giffen good from market data is impossible to obtain. However, the possibility of Giffen behavior at the individual level is not ruled out.

More recently, Silberberg and Walker [1984! explored the consistency of Giffen behavior using Marshall's additive utility assumption. They conclude that the Giffen paradox is consistent with Marshall's assumptions, but deem its actual existence a "pathological case." Dwyer and Lindsay [1984! provide an interesting historical perspective of the often cited Irish potato example of Giffen behavior. They point out that no known reference by Robert Giffen to the Irish potato exists although the example abounds in principles and intermediate textbooks. (1) Furthermore, they argue that the classic Irish potato example of a Giffen good did not actually occur since a supply reduction due to the famine would have caused the price of potatoes to decline if potatoes were a Giffen good, but no such decline was observed.

Interestingly, recent experimental work by Battalio, Dwyer, and Kagel [1987!, Battalio, Kagel, and Kogut [1988!, and Silberberg, Warren-Boulton, and Asano [1987! provides some evidence for the existence of Giffen behavior. The Battalio, Kagel, and Kogut study found that "poor" rats (those whose incomes only allow below normal levels of fluid intake) decrease the quantity demanded for quinine water in response to a lower price. Rats used the increased purchasing power to buy larger quantities of root beer. In a controlled experiment involving monkeys, Silberberg, Warren-Boulton and Asano found an increase in the price of bitter food pellets caused consumption of these pellets to increase. Battalio, Dwyer, and Kagel found other evidence of Giffen behavior in the form of labor supply curves that were positively sloped at low wages, but backward-bending at higher rates.

Common textbook examples of Giffen behavior (meat and potatoes, beer and whiskey, or Alfred Marshall's transportation problem) employing typical indifference curve illustrations, take place in a two-commodity world with exogenous prices and a negative income effect strong enough to overcome the substitution effect. These classical examples rely on utility function implying unusually shaped indifference maps. By contrast, this paper shows how Giffen behavior can occur independent (to a large degree) of the form of the utility function. The model offers an alternative explanation of Giffen-like behavior that is consistent with commonly cited examples and recent experimental work. The results illustrate not only the possibility but the plausibility of Giffen behavior.

II. THE UTILITY MAXIMIZATION PROBLEM

Begin by considering the typical example of a Giffen good--that of potatoes and meat. The analysis is confined to peasants of very modest means. Assume the two goods meat (M) and potatoes (or spuds, S) have exogenously determined prices given by [P.sub.m! and [P.sub.s! respectively. The fixed income of consumers is denoted by R. Following the typical presentation of the Giffen problem, further assume peasant incomes are too small for subsistence on meat alone, but are sufficient for subsistence solely on potatoes.

Considering the notion of subsistence, let [C.sub.m! represent the calories per unit of meat consumed, [C.sub.s! the calories per unit of potatoes consumed, and N the minimum nutritional level (measured in calories) required for subsistence. For simplicity assume this constraint is linear. The problem facing the consumer is the maximization of utility subject to the usual budget constraint with the additional restriction that choices must allow subsistence. Formally,

U = U(M,S) for (M,S)

[epsilon!{(M,S) \ [C.sub.m.M! + [C.sub.s.S! [is greater than or equal to! N},

thus the utility maximization problem is

Maximize U = U(M,S)

subject to [P.sub.m.M! + [P.sub.s.S! [is less than or equal to! R

and [C.sub.m.M! + [C.sub.s.S! [is greater than or equal to! N.

The assumptions of the model and their implications are:

1. Peasant incomes are too small given the prevailing range of price for meat to allow subsistence on meat alone: [right arrow! R/[P.sub.m! N/[C.sub.m!.

2. Incomes are sufficient given the prevailing range of price for potatoes to allow subsistence on potatoes alone: [right arrow! R/[P.sub.s! N/[P.sub.s!.

3. Given linear constraints, the above two assumptions imply: [C.sub.s!/[C.sub.m! [P.sub.s!/[P.sub.m!.

Thus the nutritional constraint will be steeper than the budget constraint when quantity of potatoes is plotted along the horizontal axis.

The consumer's feasible choice set is illustrated in Figure 1 as area ABC. An increase in the price of potatoes moves both points C and A toward point B. Therefore, a potato price increase reduces the size of the feasible set and moves point A down and to the right to a point such as A' along the dashed budget line in Figure 1.

Any tangency between the consumer's indifference curve and the budget line along segment AC requires the usual conditions on the utility function for Giffen behavior. Notice, however, the probability of a tangency along AC declines as the price of potatoes rises because the size of the feasible set is reduced. The point of utility maximization when both constraints are binding will be at point A, assuming potatoes are not strongly preferred to meat.

Solving the two linear constraints simultaneously yields the demand functions:

[Mathematical Expression Omitted!

These demand functions produce positive levels of consumption and are homogenous of degree zero in prices and income. More importantly, the demand functions are independent of the specific form of the consumer's utility function.

Using these demand functions it is easy to show potatoes exhibit a Giffen effect while meat is an ordinary good. The own-price effects given by the slopes of the demand curves are

[Mathematical Expression Omitted!

The demand curve for potatoes is positively sloped and predicts Giffen-like behavior, while the demand curve for meat is negatively sloped as usual. It is also straightforward to show that potatoes are an inferior good while meat is a normal good.

The positive slope of the demand curve for potatoes is due entirely to an income-effect. (2) At the boundary of the constraint set where consumer equilibrium is achieved (point A in Figure 1), no possibility for substitution in consumption exists. Therefore, an increase in the price of potatoes reduces real income (and reduces the ability to consume meat). With no off-setting substitution effect, the inferiority of potatoes dictates the slope of this demand curve. Potatoes are inferior not because of the form of the utility function, but because they sustain the individual on the least income. In essence, the inferiority of potatoes is due to their superiority in subsistence efficiency vis-a-vis meat within the given budgetary restrictions. (3)

Under the assumed conditions, these characteristics do not change as the price of potatoes continues to increase. When the price of potatoes rises so high as to preclude the purchase of any meat (given the nutritional constraint), the consumer's feasible set becomes a single point: R/[P.sub.s! = N/[C.sub.s!, and only potatoes could and would be consumed. Further price increases

imply starvation or would require gifts of food from charitable organizations. (4)

III. A THREE-GOOD WORLD

Although the typical textbook examples of Giffen goods are generally limited to the two-good case, it is of interest to determine whether the Giffen effect vanishes when a wider variety of goods are available for consumption. To this end, denote a third generic good by x, which has an exogenously determined price, [P.sub.x! and a nutritional content of [C.sub.x! per unit consumed. The budget and nutritional constraints are of the same form as in the two-good case so that the consumer cannot afford to survive on meat alone, while there is sufficient income to survive solely on potatoes. Two possibilities exist for the third good: (1) the the consumer cannot afford to survive on good x alone, or (2) the consumer has sufficient income to survive on good x alone.

Assumption (1) implies x is a close substitute for meat, while (2) suggests a good with characteristics similar to potatoes. For ease of illustration, first employ assumption (1). The feasibility assumptions
imply [P.sub.s!/[P.sub.m! [C.sub.m!/[C.sub.m! and [P.sub.s!
/[P.sub.x! [C.sub.s!/[C.sub.x!. Therefore,


the isobudget line between meat and x lies everywhere inside the isonutrition line between meat and x. The feasible set appears as the shaded solid in Figure 2.

In this figure, point A corresponds to the case where no x is consumed (the two-good case from Figure 1). Point D corresponds to a case of no meat consumption and yeilds the same type of results as the two-good case. Point B corresponds to only potato consumption. If the price of any commodity increases, the feasible set collapses toward point B.

An equilibrium solution along the line segment AD such as at point Z implies positive consumption of all goods and yields the same type of Giffen behavior described in the two-good case. An increase in the price of potatoes moves line segment AD down and toward point B. Consumption of potatoes necessarily rises because the optimal consumption triple remains along the segment AD. Adding more goods with the same characteristics as meat would leave the general results of the two-good case unchanged. (5)

Assumption (2) implies [P.sub.s!/[P.sub.m! [C.sub.s!/[C.sub.m! and [P.sub.x![P.sub.x!/[C.sub.m!. The isobudget line between potatoes and x would now lie everywhere outside the isonutrition line between potatoes and x. This consumer's feasible set appears as Figure 3. Here point A corresponds once again to the two-good solution for meat and potatoes with no consumption of good x. At point E, no potatoes are consumed. Here, with positive consumption of all goods, a solution along line segment AE no longer leads to a Giffen effect for potatoes as their price increases. Instead, the consumer moves toward point E, increasing the consumption of x while reducing the consumption of both meat and potatoes. However, once the price of potatoes rises to preclude survival on potatoes alone, good x exhibits Giffen characteristics. Such a result is illustrated in Figure 4. Here the price of potatoes has risen so that N/[C.sub.s! = R/[P.'sub.s!. The analysis is now identical to that of the conditions for Figure 2.

For sufficiently low levels of income, the consumer may be forced to choose exclusively between potatoes and good x. Again, the good most efficient in providing subsistence exhibits Giffen characteristics. Thus a critical element in the Giffen controversy is the affordability of available consumption goods.

IV. A NUMERICAL ILLUSTRATION

Giffen behavior is most likely where a second rationing constraint is involved in consumption and income levels are very low. The model does not imply that we should expect to find actual aggregate data supporting an upward sloping market demand curve. Giffen behavior of the type implied exists at the individual level over a short-run time horizon.

How likely are such circumstances? Consider the consumption behavior of a male in the 23-50 age group. A reasonable daily caloric requirement for such a consumer is 2700 kcals per day. (6) Further assume this individual has limited short-run income of only $2.50 per day to budget on two food items: meat and potatoes. Assume the price of meat is $.25 per 100 grams ($1.15/lb.) of hamburger, while the price of potatoes is $.05 per 100 grams (.23/lb.). There are 264 kcals per 100 grams (approximately 3.5 oz.) of m edium-fat, cooked hamburger, while each 100 grams of boiled potatoes (with skin) contain 76 kcals. (7) Under these assumptions, the conditions for the existence of Giffen behavior implied by the model are met. The demand functions for meat and potatoes yield [M.sup.*! = 9.48 and [S.sup.*! = 2.59, or initially, the consumer chooses 948 grams of meat (approximately 2.09 pounds) and 259 grams of potatoes (approximately 0.57 pounds) per day.

Now suppose the price of potatoes rises to $.055 per 100 grams ($.25/lb), while all else remains constant. The solution becomes [M.sup.*' = 9.26 and [S.sup.*! = 3.35. The consumer now chooses 926 grams of meat (approximately 2.04 pounds) and 335 grams of potatoes (approximately 0.74 pounds) per day, with Giffen-like behavior resulting.

The example could be extended to include a third good such as rice, but the plausibility of Giffen behavior really depends upon potatoes being relatively more efficient per dollar at providing subsistence with incomes severely constrained. Annual income in the example is just over $900. While not likely to provide subsisitence in this country, it represents a reasonable income level in many less developed nations. Other plausible examples also exist. Stitzer et al. [1983!, for example, report results from a study of drug users with conditions similar to this model. They found drug addicts' choices between heroin and methadone follow a minimum intoxication level within a limited budget. Their empirical results are suggestive of Giffen-like behavior.

V. CONCLUSIONS

The preceding analysis presents a Giffen response from consumer preferences that typically generate non-inferior goods. This occurs when the nutrition constraint provides commodities with characteristics other than simple pleasure or satisfaction--the commodities must also provide subsistence. These findings are similar to the attribute or commodity characteristic utility analysis of Lipsey and Rosenbluth [1971!--Giffen goods can indeed arise with greater likelihood than is usually predicted by traditional consumer analysis, at least under certain circumstances.

The argument is virtually independent of consumer preference orderings. The model simply requires another binding constraint that imparts new characteristics to goods in the consumer's utility function. The most commonly used illustrations of the Giffen effect (potatoes and

meat, beer and whiskey, and Marshall's transportation problem) all appear to imply such a constraint. Thus these examples may have more validity as Giffen behavior than in ordinarily attributed to them.

The results of the three-good case suggest that adding "substitutes" for potatoes to the consumer's choice set reduces the likelihood of the Giffen effect. This is not surprising, but it is important to notice that simply adding a good to the consumer's choice set will not necessarily preclude the effect. The price of the additional good must be low enough to allow subsistence on this good alone. It is in this sense that the good is classified a "substitute" for potatoes. Even under this restriction, if the price of potatoes increases sufficiently the third good will exhibit Giffen characteristics.

So where should one look for Giffen behavior of the type described here? The analysis suggests the most likely place would be among the very poor, consuming a few staple items with limited substitution possibilities.

(*1) Associate Professor, Department of Economics and Finance, Louisiana Tech University and Associate Professor, Department of Finance, University of Nebraska at Lincoln respectively. The authors would like to thank George Stigler, Thomas Borcherding, and two anonymous referees for helpful suggestions. Dawn Mach, Bakti Luddin, and Jack Fulcher provided valuable assistance in obtaining the information for the examples. Any remaining errors are the responsibility of the authors.

(1.) As pointed out by referee, Marshall's original reference to Giffen goods concerned bread and meat. However, since the example of potatoes and meat is so widely cited, these goods will be used to make the central point of the paper below.

(2.) There is an implicit assumption of the absence of a credit market. The analysis is restricted to the short run so that alternative substitution possibilities are rulled out. We therefore rule out borrowing to achieve preferred commodity bundles. By assumption, we are dealing with individuals with extremely limited incomes hence, the assumption of no access to credit markets is not unreasonable.

(3.) The importance of the calorie constraint as a rationing device in generating a corner solution is apparent in this construction of the problem. Hirshleifer [1984, 145! also recognizes the critical element of subsistence in his presentation of Giffen goods. In his analysis, however, the Giffen effect is generated in the conventional fashion by relying on the shape of the indiference curves.

(4.) Dwyer and Lindsay note that relief agencies provided starving peasants with corn and corn meal during the worst of the Irish famine.

(5.) As with the two-good case, tangency on the surface defined by the points A, D, and C, corresponds to the traditional case with Giffen behavior possible through the form of preferences as reflected by the utility function.

(6.) The actual daily average caloric need for a U.S. male in this age group is in the range 2300 kcals to 3100 kcals per day. See the National Academy of Science's "Recommended Dietary Allowances," 9th rev. ed., Washington, D.C., 1980, in Food Values of Portions Commonly Used, by A. T. Pennington and Helen Church, 14th ed., Harper & Row, 1985, p. xix. Kcals is the scientific term for what is commonly referred to as calories. For an interesting discussion of income constrained calories intake for individuals in less developed countries, see Knudsen and Scandizzo (1982). Their information indicates that between 60 and 97 percent of individuals in six poorer countries receive less than 2400 kcals per day.

(7.) From Food Values of Portions Commonly Used.

REFERENCES

Boland, L. A. "Giffen Goods, Market Prices and Testability." Australian Economic Papers, June 1977, 72-85.

Battalio, Raymond C., Gerald P. Dwyer, Jr., and John H. Kagel. "Tests of Competing Theories of Consumer Choice and the Representative Consumer Hypothesis." Economic Journal, December 1987, 842-56.

Battalio, Raymond C., John H. Kagel, Jr., and Carl A. Kogut. "Experimental Confirmation of the Existence of A Giffen Good." Working Paper No. 88-41, Department of Economics, Texas A&M University, December 1988.

Dougan, William R. "Giffen Goods and the Law of Demand." Journal of Political Economy, August 1982, 809-15.

Dwyer, Gerald P., Jr. and Cotton M. Lindsay. "Robert Giffen and the Irish Potato." American Economic Review, March 1984, 188-92.

Hicks, J. R. A Revision of Demand Theory. Cambridge: Cambridge University Press, 1956.

Hirshleifer, Jack. Price Theory and Applications, 3rd ed. Englewood Cliffs: Prentice Hall, Inc., 1984.

Knudsen, Odin K. and Pasquale L. Scandizzo. "The Demand for Calories in Developing Countries." American Journal of Agricultural Economics, February 1982, 80-86.

Lipsey, Richard G. and Gideon Rosenbluth. "A contribution to the New Theory of Demand: A Rehabilitation of the Giffen Good." Canadian Journal of Economics, May 1971, 131-63.

Pennington, Jean A. T., and Helen Church. Food Values of Portions Commonly Used, 14th ed. New York: Harper & Row, 1985.

Silberberg, Eugene and Donald A. Walker. "A Modern Analysis of Giffen's Paradox." International Economic Review, October 1984, 687-94.

Silberberg, Alan, Fredirick R. Warren-Boulton, and Toshio Asano. "Inferior-Good and Giffen-Good Effects in Monkey Choice Behavior." Journal Of Experimental Psychology: Animal Behavior Processes 13(3), 1987, 292-301.

Stigler, George J. "Notes on the History of the Giffen Paradox." Journal of Political Economy, April 1947, 152-56.

_____. "A Reply." Journal of Political Economy, February 1948, 61-62.

Stitzer, M. L., M. E. McCaul, G. E. Bigelow, and I. A. Liebson. "Oral Methadone Self-Administeration: Effects of Dose and Alternative Reinforcers." 34(1), Clinical Pharmacology and Therapeutics, 1983, 29-35.
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Title Annotation:Giffen economic model
Author:Gilley, Otis W.; Karels, Gordon V.
Publication:Economic Inquiry
Date:Jan 1, 1991
Words:3340
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