Reassessing the Labor Supply Curve
Prasch, Robert E., Journal of Economic Issues
It is no exaggeration to state that the supply and demand model of price determination is the most widely accepted theory in contemporary economics. In the professional and textbook literature, this model is used to determine the price of every kind of commodity from theater tickets to corn, oil, votes and wages. However, problems can arise when a model as abstract as the theory of supply and demand is too readily applied to situations in which it may be inappropriate. Indeed, Institutional economists have long maintained that the application of the supply and demand theory to the labor market is often an important instance of such an error [Galbraith 1997; Lester 1947, 1941; Power 1999; Prasch 2000, 1999, 1998b].
This paper will argue that labor is qualitatively different from other commodities in at least one crucial attribute. Specifically, when the price of a typical commodity falls, the conventional theory of supply maintains that suppliers will substitute out of the business of providing that particular item, and devote their productive capacity to the provision of some other item. In the standard models, this substitution is thought to occur with zero transactions costs. Now this idea is not necessarily wrong. For example, it is reasonable to suppose that a low price for minivans will induce automobile manufacturers to supply more trucks or sedans. But is it plausible to apply this line of reasoning to the aggregate labor market? Or the market for unskilled labor?
The problem is that most people depend upon the sale of their labor for the bulk of their income and, indeed, for their livelihood. In light of this fact, can we plausibly conclude that a low wage will induce more than a minority of people to substitute into leisure and forgo any effort to earn a living? After all, not many people live off the bounty of the land, depend upon their savings, or count on the beneficence of family and friends to meet their day-to-day needs. While this is the implication behind the conventional depiction of the labor supply curve, it is not a plausible representation of the situation faced by the overwhelming majority of people in the American labor market, to say nothing of conditions in Third World labor markets.
This paper will argue that with a more plausible specification of the relationship between income and the value of leisure, we can develop a more accurate model of the labor market without necessarily losing the primary merit of the received model--its analytic and pedagogical simplicity. Moreover, with an improved understanding of labor market dynamics we can see that progressive era labor market legislation, designed to mitigate the effects of bargaining power inequality in low wage labor markets, was in fact based upon sensible economic foundations [Prasch 2000, 1999, 1998b]. Rather than representing a "trade-off" between "equity and efficiency," minimum wage and maximum hours legislation may actually enhance, rather than diminish, the performance of the labor market.
The Neoclassical Labor Supply Schedule
The upward sloping factor supply curve holds a prominent place in textbook discussions of the labor market and the distribution of income. As one among several productive "factors" the conventional, or textbook, labor supply schedule shows that the quantity of labor supplied is a direct function of the inflation-adjusted, or real, wage. Moreover, this schedule is constructed from an aggregation of the labor-leisure choices made by all actual and potential workforce participants in the community [cf. Taylor 1998, 326-329; Katz and Rosen 1991, 133-150].
Despite this apparent consensus at the textbook level, there is some dissatisfaction with the conclusions that are typically drawn from the conventional model. An important problem is posed by our actual experience with labor markets. Over the years, numerous empirical studies have indicated that the labor supply schedule is either vertical or sloping downward to the right [Bluestone and Rose 1998, 28-30; Dessing, 1999; Gordon 1996, chap. 4; Kaufman 1994, 60-62; Lester 1941, 104-108; Mishel, Bernstein and Schmitt 1999, 307-314]. If this is the case, then the conventional representation of the labor market, specifically the shape of the labor supply curve, should be revised.
To partially address these concerns, the labor supply curve is often considered to be "backward-bending" at higher levels of wages. Conventional microeconomic theory is consistent with the idea that at high wages, and consequently high income levels, the representative worker will wish to purchase more of all "normal goods." Since leisure is a normal good, high wages can result in a lower quantity of labor being supplied to the market. This modified labor supply curve appears in Figure 1.
What drives this result is the belief that "leisure" is a commodity with properties like any other normal good. With increased levels of income, people will wish to purchase additional units of the good "leisure." Hence, the tendency to "substitute" out of leisure time into labor time, that would be the expected response to higher wages, is offset by the "income effect" that follows from these high wages. In technical language, economists say that at high wages the "income effect" comes to dominate the "substitution effect."
Despite this theoretical innovation, another problem remains. The labor supply schedule depicted in Figure 1 suggests that, at lower wages, the quantity of labor supplied will decrease as wages decline. Yet the empirical studies referenced above consistently fail to support this formulation. Recent American experience from the 1970s to the mid-1990s, which features the conjunction of falling or stagnating wages and increased work hours for the bulk of the population, fails to support the received view of the labor supply schedule [Gordon 1996, chap. 4; Mishel, Bernstein, and Schmitt 1999, 307-314; Schor 1992, chaps. 1-3]. Maryke Dessing surveys a broad range of empirical studies of Third World labor markets that also fail to support the upward sloping labor supply schedule [Dessing 1999].  These facts, considered in light of the implausible foundations of the conventional labor supply schedule, suggest that there is a need to reassess the shape of this schedule.
Intersubjective Comparisons of Utility
Textbooks typically, and uncritically, present Lionel Robbins's contention that utility is inherently subjective and that we can never know how much one person may enjoy any particular good, or set of goods, relative to any other person [Robbins 1984, chap. 6]. According to this argument, the intensity of any individual's relative preferences are beyond the economist's knowledge [Katz and Rosen 1991, 59; Taylor 1998, 116--117].
While this injunction is readily honored when consumer sovereignty or the distribution of income is under examination, it is quickly set aside when economists are constructing or applying favored theories. For example, every economist who engages in a cost-benefit analysis is de facto violating this rule [Lutz 1993, 7--11]. So long as the winners and losers of some new regulation or distribution are not identical, then some implicit comparison of the weight of their preferences has been built into the calculation (typically it is presumed that their preferences are of even weight). Another example occurs when economists conclude that there are substantial "gains" to be made from a policy of free trade even if some people will lose their jobs or otherwise incur costs. Again, implicit weights are given to the relative intensity of the preferences of those who win or lose from such policies. 
Economists make an additional intersubjective evaluation of preferences when they construct the labor supply schedule. There is an implicit assessment of the relative value of leisure to individuals, and to the aggregate of individuals, in the labor market. Specifically, it is presumed that the marginal utility of leisure to the person who consumes it is necessarily positive, even at the lowest levels of income. In other words, leisure is an end in itself, and additional hours of leisure will always retain a positive value.
Given this assumption concerning the value of leisure, an additional hour of leisure is always an addition to the consumer's utility, even if it is a very modest addition. But this assumption is not explicitly argued for. Rather, it is implicit in the structure of the assumptions underlying the model of the labor market. In addition, it represents another case of economists violating their own injunction against commenting on another person's preferences. This error is compounded when an aggregate labor supply schedule is constructed through the simple expedient of adding together the labor supply schedule of every individual in the market.
In light of the almost habitual violation of Robbins' injunction against intersubjective comparisons of preferences, it is reasonable to ask if any substantive advances can be made in economic theory without violating it. The fact is that much of economic theory, and virtually all economic policies, depend upon generalizations, comparisons, and aggregations of the preferences of various groups of people. In place of an often-violated rule against these practices, let us argue explicitly for the merits of the constructions and generalizations that we wish to employ.
Income and the Marginal Value of Leisure 
Given that comparisons between the preferences of individuals do, and must, take place in the course of discussions of economic analysis and policy, it is incumbent upon the researcher to make a case for the preferences that they specify in their models. In this paper, in the absence of a developed argument from within the current literature of labor economics, I will argue that the assumed position on the relationship between income and leisure is inaccurate.
The conventional economic model posits a positive relationship between income and the marginal utility of leisure. This seems very plausible. It is also plausible to argue that as incomes rise, people will place a higher value on an additional hour of leisure, and they often are willing to trade some of their income for more leisure time. However, while the received theory recognizes that a person with a lot of leisure on their hands may place a low marginal value on additional leisure time, additional leisure is always taken to be a good thing. Consistent with their attitude toward all other goods, the received theory presumes that more leisure is better. It is this latter assumption that I wish to challenge. Specifically, I would like to argue that under certain conditions, increased leisure is not a desirable thing and could even be perceived to be disagreeable.
This claim is based on several "stylized facts" that I take to be broadly acceptable once one reflects upon the relationship between leisure and income:
1. Leisure is a "joint product" of free time and purchasing power. For example, if I enjoy the perfect margarita on my spacious deck overlooking the ocean in front of my Laguna Beach home, my leisure is more fulfilling than if I spend the same quantity of time drinking a cheap beer in a dark and dingy apartment.
2. In the economics literature, "leisure" is an omnibus term for time not spent working for wages. Often it includes time spent on duties and chores that can more accurately be termed "personal work" [Prasch 1997; Mincer 1963]. Cleaning the house, paying taxes, and washing dishes all fall into this category. By contrast, the wealthy can afford to pay for someone else to attend to a substantial portion of their personal work, so they can devote a larger percentage of their non-work hours to the pleasures that are usually associated with the word "leisure." Indeed, as a partial response to this problem, and as a reflection of the changing distribution of income, we now see the emergence of firms that, for a fee, will attend to the personal work of others [Levine 1997, 114-118]. To the extent that the wealthy can substitute money for personal work, they can derive more utility from their non-work hours.
(3.) It is a misuse of language to assert that the destitute individuals living upon the sidewalks of our major cities are "enjoying leisure." For many poor people, additional free time is often a burden, not a boon.
If the three propositions presented above are accepted, and a linear function is assumed for convenience, then the relationship between income and the marginal utility of leisure is more accurately depicted as it is in Figure 2
In Figure 2, the marginal utility of leisure experienced by a representative individual increases with his or her income. What is different about the characterization presented here is the proposition that, at sufficiently low levels of income, the marginal utility of leisure actually becomes negative. In other words a destitute person, who spends his or her "leisure" looking for work, negotiating with the bureaucracy of an increasingly intrusive and judgmental welfare state, or listening to her children plead for food, may perceive additional "leisure" hours to be both long and painful.
I wish to reiterate at the outset that this generalization is constructed upon the three stylized facts discussed above. It is not based upon some concept of "refined taste" or any other aspect of snobbery. Rather, it acknowledges that the poor face a diminished quantity and quality of choices during the hours that they are not working for wages. It simply affirms that because the wealthy have more money, they also have more choices and are burdened with less personal work.
Revising the Labor Supply Curve
If it is the case that the marginal utility of additional "leisure" is a direct function of income, and low levels of income are incompatible with a decent standard of living, then it is possible that if wage levels decline far enough, economic agents (be it a person or a family) will be willing to work additional hours--even at very low wage levels. The argument is that this extra effort will enable that person or family to earn enough income to more fully appreciate the hours of leisure that remain. Graphically, the result is a second "bend" in the labor supply schedule as depicted in Figure 3. The level of wages at which this second "bend" takes place may be termed, in honor of the classical economists, the "subsistence wage."
Despite the above modification of the relation between income and the marginal utility of leisure it remains the case that, over an extensive range of values, lower wages will reduce the quantity of labor supplied. This range of the labor supply curve can be thought of as consistent with the behavior of middle- and upper-middle class Americans. However, Figure 3 also illustrates the proposition that once the real wage (W) falls below the subsistence wage (Ws), the quantity of labor supplied will begin to rise, even as the real wage continues to fall. This trend will continue until the total hours of work required to maintain a socially acceptable standard of living are too long to be sustainable. When the real wage falls far enough (to Wu), the hours worked will once again decline as the primary worker and his or her family abandon their attempt to maintain a standard of living consistent with effective membership in civil society and the labor force.
Multiple Equilibria in the Labor Market
If Figure 3 is an accurate reformulation of labor supply schedule, it follows that the labor market may be characterized by multiple equilibria. To illustrate this point, let us stay with the conventional representation of factor demand functions and assume that the labor demand schedule slopes downward to the right as depicted in Figure 4. 
The revised presentation of the labor supply schedule, taken in conjunction with a conventional labor demand schedule, indicates that there are now four points where the supply and demand schedules could cross each other. Two of these equilibrium points are stable and two are unstable. All four are of interest.
Suppose we accept the conventional presentations of labor market dynamics and agree that if the quantity supplied is greater than the quantity demanded, the real wage will fall, and when the quantity demanded is greater than the quantity supplied, the real wage will rise. Then Figure 4 demonstrates that when the market wage is higher than Wa, it will continue to rise. If the real wage is just below Wa, the wage will fall until a new equilibrium is achieved at point B. It follows that point A is an unstable equilibrium.
Between points B and C, the wage will tend to rise until it is consistent with the equilibrium at point B. It follows that B is a locally stable equilibrium. Given the stability of the equilibrium at point B, the range of wages between Ws and Wa is consistent with the self-regulating labor market of the textbooks--and the laissez-faire policy recommendations that typically follow from those presentations. For these reasons the range of wages between Ws and Wa is emphasized in conventional presentations of the labor supply schedule.
Wages below Ws are interesting since they capture some of the novel aspects of the revised labor supply curve. Here low wages induce a higher quantity of labor supplied. Below We, market dynamics will press wages ever lower as families supply additional labor hours in their attempt to sustain a minimally acceptable standard of living. Unfortunately, the willingness of the downwardly mobile to work additional hours further reduces the market wage--which continues to fall--thereby inducing additional work effort. Until the market achieves another locally stable equilibrium at point D, the quantity of labor supplied is continually greater than the quantity demanded.
Once the market wage falls to Wu the number of hours of labor required to maintain subsistence become unsustainable. At wages below Wu, the family is forced to abandon its goal of a subsistence standard of living, and cut back on its la bar supply. At this point they drop out of the regular work force and become indigent.
The lesson is that in a free market setting, inordinately low wages will continue to decline as a direct result of their already low level. In this market, poverty results in even greater poverty. With such a model of labor market dynamics we can affirm the insights of some of the earliest proponents of minimum wage legislation. An example is Henry Rogers Seager, a founder of the American Association of Labor Legislation, and an economics professor at Columbia University, "Under these circumstances, as our experience abundantly proves, the free play of economic forces results in starvation wages for thousands and hundreds of thousands of workers, and these starvation wages persist year after year, with little or no sign of improvement" [Seager 1913, 82-83].
These low-wage dynamics present an example of a positive feedback system, or "vicious circle," at work in the economy [Prasch 1998a]. With the revised labor supply schedule presented above, the market dynamics of the low wage sector push the wage away from the range that is consistent with a self-regulating market. Wages move ever further into a range that features "destructive competition" among those who supply labor and must earn their living exclusively from their labor. These dynamics are consistent with the findings of John Commons and John Andrews, "Another reason for the low wage scale . . . is the cutthroat competition of the workers for work" [Commons and Andrews 1916, 170].
Point D, which is consistent with a wage level below the subsistence wage, is another locally stable equilibrium point. Such a point might describe the labor market in a "labor surplus" economy such as that discussed in the work of W. Arthur Lewis . Indeed, Maryke Dessing surveys numerous empirical studies of low wage labor markets in developing countries that are consistent with the revised labor supply schedule depicted in Figure 4 [Dessing 1999].
implications for Economic Theory and Policy
Since the revised labor supply schedule in Figure 4 features two locally stable equilibrium points, reflecting high- and low- wage levels respectively, the proposed model is consistent with the literature on segmented labor markets [Edwards, Reich, and Gordon 1975; Gordon, Edwards, and Reich 1982; Harrison and Sum 1979]. In addition, the downward-sloping labor supply schedule at lower wage levels is consistent with the observation that, in the face of declining wages, many American families are now working longer hours in order to maintain their standard of living [Bluestone and Rose 1998, 28-30; Gordon 1996, chap. 4; Mishel, Bernstein, and Schmitt 1999, 307-314].
Given the existence of two stable equilibrium points, there is no a priori reason to believe that the equilibrium at point D has superior efficiency or welfare properties to the equilibrium at point B. Moreover, the wage level at point D can no longer be presumed to be uniquely equal to the marginal product of labor. These results are both true despite the fact that the low wage equilibrium at point D is determined in a completely free market setting. In addition, both equilibria are locally stable in the sense that once they are achieved, the market embodies no internal mechanism or force that exerts a tendency toward change.
If we accept the revised theory of the labor market presented above, a number of implications follow for the conduct of economic theory and policy. The first is that, at wage levels above Wa, the market is dynamically unstable in an upward direction. The quantity of labor demanded will continue to exceed the quantity supplied at every wage level. Since the quantity of labor supplied will continue to fall as the wage continues to rise, there is no reason to believe that any equilibrium will ever be achieved. The theory posits that these high wages will move continuously upward. This story is certainly consistent with the pay of American CEOs since 1980.  In such a state of affairs, there is a prima facie case for a progressive income tax on all wages over Wa. Moreover, and despite the touching concern of the "Supply-Side" school of economists, such a tax should not result in a decline in the quantity of labor supplied. Indeed the analysis presented above suggests that a progressive income tax would be more likely to increase the quantity of labor available to the market.
Second, and of more importance, a minimum wage set just above Wc would contribute to labor market stability and enhance general prosperity. While the above analysis affirms that a minimum wage is consistent with a decline in the level of employment, it does not contribute to involuntary unemployment. These results are broadly consistent with much of the recent theoretical and empirical research on the dynamics of the minimum wage [Brosnan and Wilkinson 1988; Card and Krueger 1995; Carter 1998; Prasch 1996; Prasch and Sheth 1999]. If the mandated wage is set slightly above Wc, the quantity of labor demanded will be greater than the quantity supplied, and the market process will ensure that wages will rise until the market achieves the locally stable equilibrium at point B.
Finally, this paper presents an implicit critique of the positivist tradition within contemporary economics, which has long eschewed cases of multiple equilibria. In opposition to that tradition, I would maintain that a theory of the labor market that features multiple equilibria affirms some interesting insights that have, over the past several decades, been unreasonably neglected by the mainstream of labor economists: namely the reality of segmented labor markets and the stabilizing properties of minimum wage legislation.
The above analysis, with its stress on the contingency of any given equilibrium wage, and the potential for multiple outcomes, captures some of the underlying complexity of "real world" labor markets, and points the way to a more enlightened approach to regulating low wage labor markets. A clearer understanding of the dynamics of low wage labor markets will enable economists to make a more constructive contribution to the ongoing public debate over minimum wage legislation and its role in a program of economic justice [Glickman 1997; Levin-Waldman 2000; Prasch and Sheth 1999; Waltman 2000].
The author is Visiting Assistant Professor of Economics at Middlebury College. He would like to thank Falguni A. Sheth, Maryke Dessing, Mathew Forstater, Jonathan Powers, Lonnie Golden, Anne Mayhew, Deborah Figart, and Ann Davis for their comments, assistance, and suggestions at various stages in the writing of this paper.
(1.) After the first drafts of this manuscript had been written and circulated, I was surprised to learn that another scholar, Maryke Dessing, was already circulating a paper, based on her dissertation, with an analysis of the labor supply curve remarkably similar to the one that I have presented in Figure 4. However, there is no question that our papers were developed independently of each other. Since they draw their inspiration from different sources, a full appreciation of the revised labor supply schedule is best gained by reading both papers. Specifically, Ms. Dessing developed her analysis in order to capture the dynamics of low wage markets in developing countries. My analysis developed out of my ongoing interest in the history of American economists on minimum wage legislation [Prasch 2000, 1999, 1998b].
(2.) Discussions of economic policy often include a dodge called "Hicks-Kaldor Compensation," which is a hypothetical restoration of the losses incurred by those who are harmed by a given policy change. However, so long as it is clear that such compensation will never be paid, an implicit intersubjective comparison of utility is being made whenever an economist proposes a policy change.
(3.) Falguni Sheth assisted in the development of this section.
(4.) The "Reswitching Controversy" of the 1950s and 1960s showed that there is no a priori reason to believe that the demand for labor schedule has this shape. Indeed, all of the participants in that debate finally concluded that neoclassical economic theory cannot determine the shape of factor demand curves [cf. Garegnani 1990; Harcourt 1972; Kurz 1990]. However, not all of the participants agreed on how best to interpret the result of this debate. Several, such as Paul Samuelson, indicated that they would prefer to maintain their belief in the conventional representation of factor demand schedules for normative reasons.
(5.) I note that it is merely consistent, since this market is institutionally complex. A partial development of the author's views on this subject have been presented elsewhere [Prasch 1998c] .
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Publication information: Article title: Reassessing the Labor Supply Curve. Contributors: Prasch, Robert E. - Author. Journal title: Journal of Economic Issues. Volume: 34. Issue: 3 Publication date: September 2000. Page number: 679. © 1999 Association for Evolutionary Economics. COPYRIGHT 2000 Gale Group.
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