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The ethic of care versus the ethic of justice: an economic analysis
The Ethic of Care versus the Ethic of Justice: An Economic Analysis
ROBERT
TAYLOR
University of California at Berkeley
ABSTRACT:
This paper offers the first economic analysis of the debate in moral and political philosophy over the relative virtues of the ethic of care and the ethic of justice. Specifically, the paper presents a formal model of the care-giving process whose parameters include many items of direct relevance to the care/justice debate, such as the average wage rates of men and women, the size of the population to be cared for, and the benefit attached to discovering and caring for the needy. The model developed herein provides useful insights regarding both perceived gender differences in commitment to care and the relevance of care to large-scale institutions.
Feminist theorists are increasingly fond of the term “care, ” but have yet to systematically explore its economic implications. -Nancy
Folbre
(1995,74)
Professor of Economics University of Massachusetts at Amherst
INTRODUCTION The publication of Carol Gilligan’s highly influential work In a DifSeerent Voice in 1982 sparked a spirited debate in moral and political philosophy that has continued unabated to the present day. In this book, Gilligan identified “two ways of speaking about moral problems”: the ethic of care and the ethic of justice. She distinguished between the two in the following way:
*Direct all correspondence to: Robert Taylor, Department kely, CA 94720; e-mail: [email protected].
of Political Science, University
Journal of Socio-Economics, Volume 27, No. 4, pp. 479-493 Copyright 0 1998 by JAI Press, Inc. All rights of reproduction in any form reserved. ISSN: 1053-5357
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In this conception [the ethic of care], the moral problem arises from conflicting responsibilities rather than from competing rights and requires for its resolution a mode of thinking that is contextual and narrative rather than formal and abstract. This conception of morality as concerned with the activity of care centers moral development around the understanding of responsibility and relationships, just as the conception of morality as fairness [the ethic ofjustice] ties moral development to the understanding of rights and rules (Gilligan, 1982, p. 19).
Perhaps more controversially, Gilligan maintained that the ethic of care was more closely associated with the female gender, the ethic of justice with the male. Gilligan’s magnum opus has engendered an impressive response: literally hundreds of articles (some of the best of which have been collected in Brabeck, 1989; Browning-Cole & Coultrap-McQuin, 1992; Larrabee, 1993) and a host of books (e.g., Okin, 1989; Tronto, 1993; Young, 1990) have been written dealing with the issues she raised. As this paper’s lead quotation indicates, however, none of this extensive literature has dealt with the economic implications of care. This paper will seek to fill this notable gap by providing an economic analysis of care and justice. In what sense is this controversy amenable to economic analysis? In order to answer this question, I must first define care and justice and then contrast these two approaches to morality. To provide care, one must identiJL the particular needs of concrete individuals-that is, one must engage in a search, both across individuals and within individual psyches-and then fulfill those needs. This active effort to collect and interpret information on individual needs and then satisfy them requires a great deal of time and attention. As Joan Tronto has aptly noted, “care requires that humans pay attention to one another, take responsibility for one another, engage in physical processes of care giving, and respond to those who have received care” (Tronto, 1995, p. 145). The mother who discovers and then treats a wound on her child, the person who questions and then listens sympathetically to a troubled friend, and the philanthropist who identifies and then provides time and money to favored charities are all actively engaged in care-giving. Justice, on the other hand, involves the application of formal rules that generally identify only a few key features of any situation as relevant so that a decision may be made with little delay. To quote from an essay by Owen Flanagan and Kathryn Jackson, justice’s advantage over care is one of “cognitive economy” (Flanagan & Jackson, 1987, p. 626). As an example of the justice approach, consider Robert Nozick’s Entitlement Theory, a tripartite set of rules defining a just system of ownership for all physical resources (Nozick, 1974, pp. 150-153). According to Nozick’s theory, a holding is just if it is obtained either through just acquisition from the state of nature (“just acquisition” being acquisition that does not worsen the condition of others, a requirement commonly referred to as the “Lockean Proviso”) or through voluntary transfer (e.g., trade, gift, or bequest). In theory, at least, this set of rules allows us to determine quickly which holdings are just and which
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are unjust by identifying only a few key features (nonworsening in acquisition, voluntariness in transfer) of the ownership system. ’ Clearly, one important difference between the ethic of care and the ethic of justice is that the former is much more time-intensive than the latter. Care-giving entails the time-consuming identification of individual needs; justice, on the other hand, requires the application of formal rules that often abstract away from the particularity of individual needs. A simple example may help clarify the distinction between care and justice and at the same time show why care is more time-intensive. Consider the task of dividing up a pie among a group of people. An application of the ethic of justice would probably lead to some rule, such as equal division, that the participants could quickly agree upon and implement, but that would probably fail to take into account the idiosyncratic needs of those involved. Applying the ethic of care here, on the other hand, would require more time-intensive communication among the participants in order to reveal individual needs and tailor the allocation to meet those needs.2 Time, however, is a scarce commodity, and decisions regarding its use are therefore economic in nature. Thus, the appropriateness of a care approach or a justice approach in any given setting hinges on the economic value of time. Specifically, the scarcer time is, the more attractive justice is relative to care. This simple insight forms the basis of the formal model of care-giving that is presented below. Its parameters will include many items of direct relevance to the care/justice debate, such as the average wage rates of men and women, the size of the population to be cared for, and the benefit attached to discovering and caring for the needy. This model will allow us to answer many of the puzzling questions that have been raised in the course of the care/justice debate, including the following three: 1.
What is the connection
between care and justice?
2.
Is care applicable
3.
Why might men and women have different approaches
to large-scale
institutions? to morality?
At first glance, using formal economic modeling to elucidate a problem in moral philosophy might seem perverse. However, economists such as John Roemer, Amartya Sen, and Robert Sugden have long used mainstream economic modeling techniques to shed light on issues traditionally associated with moral and political philosophy. (See, for example, Sen, 1984; Sugden, 1986; Roemer, 1994; 1996.) I heartily concur with John Roemer that the chief benefit of using economic analysis in political philosophy is to make its theories more precise so that their robustness, consistency, and feasibility may be tested (Roemer, 1996, p. 3). The formal model that I develop below allows us for the first time to carry out such tests on the ethic of care-with interesting and sometimes surprising results.
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A FORMAL MODEL OF CARE-GIVING The Intuition Behind the Model The model to be developed here has as its central feature a benevolent caregiver who searches within a population for the neediest individual. Because many people in the population will claim to be the most needy (care being a nice thing to receive), the care-giver must go through a screening process to collect information about the population and discern who the neediest person really is. The care-giver will have to settle upon an optimal amount of time to spend in search because time is scarce, i.e., has alternative valued uses. This optimal quantity of time will be determined in an economically rational way-namely, by an analysis of the costs and benefits of continued search. Several of the parameters to be included in this model will undoubtedly have a major impact upon the optimal search time. The wage rate of the care-giver, for example, will obviously influence how much time the care-giver will want to spend searching: time spent searching is time not being spent earning money. Two other important factors will be the size of the population being searched and the benefit to be gained from discovering the most needy member of the population. The larger the population, the more difficult it will be to find the neediest individual; the larger the benefit to finding him or her, the more motivated the care-giver will be to do so. Optimal search times that are very short will be associated with the ethic of justice, whereas those that are relatively long will be associated with the ethic of care. Short search times make it very unlikely that the neediest individual will be identified. The benevolent care-giver will therefore be forced into some second-best approach, such as the random selection of a person to care for or the provision of some very low but equal level of care to everyone. That is, the care-giver will be forced to apply some simple, abstract rule to make a decision instead of taking the idiosyncratic needs of the members of the population into account: this solution is, perhaps unfortunately, the essence of justice. Margaret Urban Walker makes much the same point when she notes the “moral incompleteness or inadequacy of these resorts” to justice (Walker, 1992, p. 171). One should note, however, that such expediencies may be unavoidable when time is particularly scarce. Only in a world where time were not scarce would care always be the preferred approach.3 Incidentally, treating the ethic of justice and the ethic of care as points (or perhaps ranges) on opposite ends of a time-intensiveness spectrum is one way to “connect” the two approaches to morality. One of the recurring questions in the literature concerns the relationship between care and justice: some authors, such as Rita Manning and Marilyn Friedman, claim that justice is a “side constraint” that limits the application of care (Manning, 1992, p. 50; Friedman, 1993, pp. 265267), while others, such as Jane Tronto, believe that care subsumes justice (Tronto,
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1987, p. 659). The model here is consistent with the views of those who hold that care and justice lie on a “continuum” (Dillon, 1992, p. 78). Setting Up the Model
In this model, a population of individuals is distributed continuously and uniformly along a line segment of length a. One of these individuals is the person in greatest need. The location of the neediest person on this line segment is random. A benevolent care-giver must search along this line segment to find the most needy person and provide care. The care-giver attaches value B to finding and caring for this person. The process of searching for the neediest person takes time, however, which has a constant opportunity cost of w, the care-giver’s wage rate. The care-giver has access to the search technology k = s(t), where the function s gives the length of line segment k that can be searched in time t. The search technology may be thought of as conversation: the care-giver must talk to individuals along the line segment to discern who the most needy person really is. We will assume that the difficulty of search increases with search time due to care-giver fatigue-the more individuals you have to talk to, the more tired you become and the less effective a conversationalist you will be. In other words, the marginalproductivity of search declines with the amount of time spent searching.4 Moreover, we will assume that the care-giver must commit to a search time in advance. This assumption is not particularly bizarre: after all, harried professionals commonly set aside time in advance for family, friends, and charity work, often in the form of vacation time. In the tradition of John McCall’s work on unemployment (e.g., John McCall, 1970), we could instead use a model of sequential search. Such a move would necessitate the introduction of some fairly sophisticated mathematics (specifically, optimal control theory) but would not lead to conclusions qualitatively different from those we will reach below. Optimization:
Choosing
an Optimal
Search Time5
The care-giver will determine the optimal length of time to search in an economically rational way-namely, by an analysis of the marginal costs and benefits of search. The marginal cost of search in this model is constant and equal to the opportunity cost of time w, which is simply the care-giver’s wage rate. Foregone wages are the only explicit costs of search here. The marginal cost curve for search (MC) is displayed graphically in Figure 1. The marginal benefit of search declines with the amount of time spent searching. Each additional hour spent searching increases the care-giver’s chances of finding the most needy person and therefore of receiving the psychic payoff B, but it does so at a decreasing rate due to the declining marginal productivity of search-care-giver fatigue makes each additional hour spent at search less and less beneficial. The marginal benefit curve for search (MB) is also displayed graphically in Figure 1.
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x MP of Search
MC = w = Wage Rate
Figure 1.
The care-giver will choose that search time where the marginal benefit of search just equals the marginal cost. Choosing a shorter search time would entail foregoing search whose marginal benefit exceeds the wage rate, whereas choosing a longer search time would require engaging in search less beneficial at the margin than the wage rate. The optimal search time t* is displayed graphically in Figure 1. It occurs where the marginal benefit and marginal cost curves intersect. The Relevance
of Care to Large-Scale
Institutions
I will now use the model of care-giving presented above to address a number of issues that have arisen in the care/justice debate. First among these issues is the applicability of care to large-scale institutions such as government and the marketplace. Several authors (such as Blum, 1982; Broughton, 1983) have questioned care’s relevance outside the confines of small groups such as families. Even those authors who are generally sympathetic to the care approach have expressed doubts about its wider applicability. Consider, for instance, the following quote from the introductory essay by Eve Browning Cole and Susan Coultrap-McQuin in their book An Ethic of Care: Finally, though it might work well in the context of private relationships, the ethic of care may not be easily applicable to a public arena of decision-making. In legislation and social policy, both the size of the population involved and the necessity for maintaining equity make it difficult to envision how an ethic of care might be fairly applied (Cole & Cot&rap-McQuin, 1992, p. 6; my emphasis).
Interestingly, the care-giving model provides strong support for these concerns. To see this, consider a change in a, the length of the line segment along which the population is arrayed. The length of the line segment may be viewed as a proxy for
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MB/MC
MC
Figure 2.
population size. What effect then will a change in population size have on optimal search time? Intuitively, we would expect population size and optimal search time to be inversely related: a larger population makes a care-giver’s search for the most needy individual more difficult and therefore less beneficial at the margin. Thus, one would expect the care approach to be less relevant to large populations than to small ones. This result is displayed graphically in Figure 2, where an increase in population size a causes MB to shift downward from MB to MB”, resulting in a fall in optimal search time from t’ to t”. As this comparative-statics exercise indicates, there may indeed be reason to question the applicability of care to large populations. As population size increases, optimal search time falls, making it less likely that the care-giver will be able to find and provide aid to the neediest individual and more likely that some formal rule will have to be applied. Care’s domain may be limited to groups such as families and circles of friends, where population size is small enough to make the identification of greatest need and the subsequent provision of care feasible. Differences in Commitment to Care Participants in the care/justice debate have frequently remarked that observed differences in commitment to the care approach appear to follow gender and ethnic lines. Carol Gilligan, among others, has made the “empirical observation” that care is more closely associated with the female gender than the male (Gilligan, 1982, p. 2) though this claim is not undisputed (see, for example, the section of Larrabee, 1993, entitled “Checking the Data”). Moreover, several authors (including Collins, 1990; Stack, 1986) have pointed out a similarly strong commitment to care and to contextual morality in the African-American community.
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t
Figure 3.
The care-giving model once again provides invaluable insights on this issue. To see why, consider a change in w, the opportunity cost of the care-giver’s time. Intuitively, we would expect the opportunity cost of time and optimal search time to be inversely related: as the care-giver’s time becomes more valuable (i.e., the wage rate increases), the marginal cost of search will rise and therefore he or she will want to devote less time to search and more time to work. Thus, ooze would expect that, ceteris paribus, groups with different average wage rates would have difSerent levels of commitment to care-specifically, those groups with relatively high average wages should be less committed to care and more committed to justice than those with low wages. This result is demonstrated graphically in Figure 3. Here, an increase in the opportunity cost of time w causes MC to shift upward from MC to MC’, resulting in a fall in optimal search time from t’ to t”. These comparative-statics results suggest that observed differences in commitment to care may be an artifact of differing wage rates.6 In 1990, white American males had an average wage rate of $12.35 per hour; African-American males, $10.87; white American females, $9.30; and African-American females, $7.79 (Panel Study of Income Dynamics, 1990). Because women and African-Americans have a lower opportunity cost of time, their greater commitment to the timeintensive care approach should not be surprising.7 Controversial theories ascribing observed differences in commitment to care to congenital differences or differences in socialization are, strictly speaking, inessential.’ Care and the Domestic-Public
Distinction
Political philosopher Will Kymlicka, a sympathetic critic of the care approach, has made the following important point in a discussion of the care/justice debate:
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I will argue that the emphasis
on objective unfairness (i.e., injustice), while initially plausible, is only legitimate in certain contexts-namely, interactions between competent adults. Indeed, it may be legitimate only when our interactions with competent adults are sharply separated from our interactions with dependents. If so, then the debate between care and justice reasoning becomes inextricably linked to the debate over the domestic-public distinction (Kymlicka, 1990, p. 277).
Kymlicka may be interpreted as saying that the ethic of care approach is quite relevant to children and incompetent adults (e.g., the mentally or physically handicapped), but not as relevant to competent adults, because the former group is in a greater state of dependency, or need, than the latter group. In other words, the care approach is more relevant in those situations where the needs of those in distress are particularly pressing. Again, the care-giving model provides support for Kymlicka’s assertion, although the connection is somewhat complex. To see it, first consider a change in B, which is the psychic payoff the care-giver receives for identifying and caring for the neediest individual. Intuitively, we would expect the psychic payoff and the optimal search time to be directly related: the greater the benefit of finding the neediest individual, the more beneficial the search will be at the margin and therefore the longer the care-giver will want to search. This result is displayed graphically in Figure 4. Here, an increase in payoff B causes MB to shift up from MB’ to MB”, leading to an increase in optimal search time from t’ to t”. In order to tie this comparative-statics result to Kymlicka’s comment, we must ask the following question: what is the most appropriate interpretation of B, the care-giver’s “psychic payoff’? Given that the care-giver is benevolent and undertakes caring labor “out of affection or a sense of responsibility for other people”
MB/MC
I
MC
Figure 4.
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(Folbre, 1995, p. 75) one might expect B to be highest in those situations where the needs of the individual being sought out are most pressing. That is, the caregiver, being motivated by sympathy for those in need, may be more highly motivated the greater the need is. Thus, one would expect the care approach to be more relevant in those situations where the needs of the distressed individual are greater.9 This result supports Kymlicka’s statement that care is more relevant than justice whenever one is dealing with children and incompetent adults. Interestingly, the comparative-statics results with regard to B and a reinforce a distinction alluded to by Kymlicka in the above quote: the distinction between the domestic sphere and the public sphere. Note that the domestic sphere is composed of households, which are small-number groups (low a), and that the domestic sphere is the primary locus of care for children (high B). The ethic of care would therefore seem to be particularly appropriate in the domestic sphere, whereas the ethic of justice would be largely out of place. The model constructed above thus provides a simple economic justification for the domestic-public distinction. CONCLUDING COMMENTS AND DIRECTIONS FOR FUTURE REASERCH The debate over the ethic of care and the ethic of justice has been long and contentious, and many (if not most) issues raised in the course of the debate have remained unresolved. The economic model of care-giving described above helped elucidate a number of these standing issues. First, the model presented a new way of looking at the connection between care and justice. Specifically, these two approaches to morality may be viewed as points (or ranges) on a time-intensiveness spectrum. Second, the model demonstrated that care is less relevant, and justice is more relevant, the larger the population under consideration. In other words, care is most appropriate in small groups such as the family and least appropriate in large institutions such as government and the marketplace. Finally, the model predicted that those groups with relatively low wages would have the highest level of commitment to the care approach due to their low opportunity cost of time. The validity of this prediction is borne out by the evidence pointing to a strong commitment to care on the part of women and minorities, who have relatively low average wage rates due to labor market discrimination and other factors. The basic model of care described above can be fruitfully extended in a variety of ways. For example, the possibility of improving the search technology (conversation) through investment might be introduced into the model. Many advocates of the care approach have expressed the hope that care might be applied to large-scale institutions (e.g., Ruddick, 1992; Stanfield & Stanfield, 1997). Although the modeling exercise just completed casts doubt on the feasibility of such an enterprise, I should point out that educational investments to improve the ability of citizens to identify and respond to needs would make the care approach more attractive in
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general. In terms of the model, such investments would increase the optimal search time by making search (conversation) more productive at the margin. Theoretically, then, increased educational efforts might make care more readily applicable to large-scale institutions, although the rates of return on these efforts would have to be compared with rates of return on other possible investments (including other types of investments in the cultural infrastructure) to determine their desirability. A second, more ambitious extension of the model would be to provide more active roles for the agents who inhabit it. Currently, the model contains one caregiver and a continuum of passive care-recipients. One might instead imagine a model where agents can be both care-givers and care-receivers and where individuals pursue either caring strategies or non-caring strategies in their interactions with others. The tools provided by evolutionary game theory might provide the means for examining the success rates of various strategies and the possibility of movement towards a steady-state population composition. In conclusion, the care-giving model examined above not only fills the literature gap alluded to by Nancy Folbre in this paper’s lead quotation, but also demonstrates the great promise of using standard economic modeling techniques to answer questions traditionally associated with other disciplines. A host of issues in moral and political philosophy in addition to the care/justice debate are surprisingly amenable to economic analysis and will hopefully serve as topics for future economic research.
Acknowledgments:
1 would like to thank Roger Frantz, Kathy Jones, Eric Brunner, Camilla Kazimi, Herb Emery, Yannis Venieris, Doug Stewart, and Jahn Hakes for their helpful comments on this paper.
APPENDIX As noted in the text, the marginal productivity of search declines with the amount of time spent searching due to care-giver fatigue. This assumption implies that the search technology s(t) is an increasing, strictly concave function oft, The care-giver’s task is to choose a search time t* that maximizes his or her expected utility. Assuming that the care-giver is risk-neutral, the optimization problem may be characterized as follows: s(t)
max j f(z)B
dz -
wt
=
F(S(t))B
- wt,
t 0
where f is the probability density function and F is the cumulative distribution function of the uniform distribution. F(s(t)) is the probability of finding the needi-
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est person in search time t, while B is the benefit attached to discovery. So, F(s(t))B is the expected benefit of searching for t units of time. Finally, wt is the opportunity cost of search time t. Given that we are dealing with a uniform distribution of length a, F has a fairly simple form-F(z) = z/a for all ZE [O,a]. We may therefore rewrite the optimization problem above and solve for t*: maxso t
a
B - wt
First Order Condition:
i s’(t*) - w = 0;
Second Order Condition:
z s”(t) < 0,
where the Second Order Condition follows from the strict concavity of s(t). Optimal search time t*, which is implicitly defined by the First Order Condition (hereafter FOC), therefore generates a global maximum. The first term in the FOC is the marginal benefit of search, whereas the second term is the marginal cost. The care-giver will choose the search time at which the marginal costs and benefits of search are equal. The care-giver’s decision is displayed graphically in Figure 1. How will optimal search time t* vary with changes in the model’s three parameters? By using the Implicit Function Theorem and the FOC, we may calculate these effects as follows:
B , dt” -= da
--=F, F,,
---a?’ B -s” a
dt” -= dw
-- F~ = -- -1
dt” -= dB
FB --=
1 F,,
--
iiS
I
>.
B -s” a
These equations demonstrate that optimal search time t* is inversely related to the population size a and the opportunity cost of time w but directly related to the care-
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giver’s incentive B. These relationships and 4.
are displayed graphically
in Figures 2, 3,
NOTES 1.
2.
3.
4.
5. 6.
7.
8.
Nozick’s Entitlement Theory is only one of many contemporary theories of justice. John Rawls (1971) and Ronald Dworkin (1981 a,b) offer liberal egalitarian theories of justice that contrast sharply with Nozick’s libertarianism. Even sharper contrasts are provided by James Buchanan (1975) and David Gauthier (1986) who present theories of justice in the Hobbesian contractarian tradition. (For an economic analysis of both Gauthier’s work and other contractarian theories, see Ken Binmore, 1994.) As some readers may note, the ethic of care resembles utilitarianism in certain ways. There are, however, two major differences. First, the ethic of care is completely informal. Unlike utilitarianism, it makes no attempt to quantify, much less aggregate, individual needs. In fact, utilitarianism’s tendency to “not take seriously the distinction between persons” (Rawls 1971, p. 27) is inconsistent with the ethic of care’s emphasis on the uniqueness of individuals and their needs. Second, the ethic of care deals more forthrightly with issues of implementation than utilitarianism, which is mostly silent on the question of how to obtain information on people’s preferences. In contrast, the ethic of care suggests particular methods (conversation and personal observation) to gather information on people’s needs. Some will find my characterization ofjustice as “second best” to be objectionable. Because I will subject care to some fairly searching criticism later in the paper, however, I thought it advisable to place it in the best possible light vis-a-vis its chief rival, justice. Just as Michael Sandel (I 982) pointed out the “limits of justice” in his communtitarian critique of Rawls, I will here point out the limits of care as a moral and political concept. The difficulty of search may increase with search time for reasons other than fatigue. Suppose, for example, that the care-giver knows in advance how difficult it will be to determine the neediness of each individual. A rational stategy would then be to interrogate the “easy” (i.e., transparent) individuals first and the “hard’ (i.e., opaque) individuals later (assuming, of course, that the difficulty of interrogation is uncorrelated with neediness). None of this implies, of course, that the marginal productivity of search always declines with search time (learning may lead to intial increases in productivity), but the law of diminishing marginal returns guarantees that at some point it will begin to decline. The following discussion of optimal search time and its determinants relies exclusively upon intuition and graphs. For a more formal treatment, see the accompanying Appendix. The causes of these wage differentials, including labor market discrimination, are unfortunately beyond the scope of this paper. An excellent source of references for recent articles on this important subject is Randall Filer, Daniel Hammermash, and Albert Rees (1996). The use of wage rates as a measure of the opportunity cost of time is not uncontroversial. For example, Kenneth Small, in a review of the urban transportation literature on the value of time, concludes that “a reasonable average value of time for journey to work is 50 percent of the gross wage rate” (Kenneth Small, 1992, p. 44). Note, however, that if the opportunity cost of time is merely a fraction of the wage rate, then the ordering of opportunity costs of time will be identical to the ordering of wage rates, leaving the conclusions reached above unaffected. On the other hand, some studies have suggested that the opportunity cost of time for women is higher than that for men. See, for instance, the study by Robert Deacon and Jon Sonstelie (1985) of the time spent waiting in gas lines during the oil crisis of the early 1970s. Ockham’s Razor, or the Law of Parsimony, suggests that one should avoid ascribing observed effects to unobserved (and perhaps unobservable) causes if at all possible. For this reason, using
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different wage rates between men and women to explain their differing levels of commitment to care is preferable to using differing preferences or values (e.g., variations in B resulting from differing levels of sympathy or altruism in men and women). B may also have an impact on the efficaciousness of search: the more needy the neediest individual is, the easier it may be to discover him or her in the population; needs may be more visible the larger they are. In terms of the model, this relationship would reinforce the positive effect of B on optimal search time.
REFERENCES Binmore, K. (1994). Game theory and the social contract. Cambridge: MIT Press. Blum, L. (1982). Kant and Hegel’s moral rationalism. Canadian Journal of Philosophy, 12,287-302. Brabeck, M. (Ed.). (1989). Who cares? Theory, research, and educational implications of the ethic of care. New York: Praeger. Broughton, J. (1983). Women’s rationality and men’s virtues: A critique of gender dualism in Gilligan’s theory of moral development. Social Research, 50, 597-642. Buchanan, J. (1975). The limits of liberty: Between anarchy and leviathan. Chicago: University of Chicago Press. Cole, E.B., & Coultrap-McQuin, S. (Eds.). (1992). Explorations in feminist ethics: Theory and practice. Bloomington: Indiana University Press. Collins, P.H. (1990). Black feminist thought: Knowledge, consciousness, and the politics of empowerment. Boston: Unwin Hyman. Deacon, R., & Sonstelie, J. (1985). Rationing by waiting and the value of time: Results from a natural experiment. Journal of Political Economy, 93(4), 627-647. Dillon, R. (1992). Care and respect. In E.B. Cole & S. Coultrap-McQuin (eds.), Explorations in feminist ethics (pp. 69-8 1). Dworkin, R. (1981a). What is equality? Part 1: Equality of welfare. Philosophy and Public &@irs, IO(3), 185-246. Dworkin, R. (198 I b). What is equality? Part 2: Equality of resources. Philosophy and Public Affairs, 10(4), 283-345. Filer, R., Hamermesh, D., & Rees, A. (1996). The economics of work and pay. New York: Harper Collins. Flanagan, O., & Jackson, K. (1987). Justice, care, and gender: The Kohlberg-Gilligan debate revisited. Ethics, 97, 622-637. Folbre, N. (1995). ‘Holding hands at midnight’: The paradox of caring labor. Feminist Economics, l(l), 73-92. Friedman, M. (1993). Beyond caring: The de-moralization of gender. In M.J. Larrabee (ed.), An ethic of care (pp. 258-273). Gauthier, D. (1986). Morals by agreement. Oxford: Oxford University Press. Gilligan, C. (1982). In a different voice: Psychological theory and women’s development. Cambridge: Harvard University Press. Kymlicka, W. (1990). Contemporary political philosophy: An introduction. Oxford: Clarendon Press. Larrabee, M.J. (Ed.). (1993). An ethic of care: Feminist and interdisciplinary perspectives. New York: Routledge. Manning, R. (1992). Just caring. In E.B. Cole & S. Cot&rap-McQuin (eds.), Explorations in feminist ethics (pp. 45-54). McCall, J. (1970). Economics of information and job search. Quarterly Journal of Economics, 84, 113-126.
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Nozick, R. (1974). Anarchy, state, and utopia. New York: Basic Books. Okin, S. (1989). Justice, gender, and thefamily. New York: Basic Books. Panel study of income dynamics. (1990). University of Michigan, Institute for Social Research. Rawls, J. (197 1). A theory of justice. Cambridge, MA: Harvard University Press. Roemer, J. ( 1994). Egalitarian perspectives: Essays in philosophical economics. New York: Cambridge University Press. Roemer, J. (1996). Theories of distributive justice. Cambridge, MA: Hdrvard University Press. Ruddick, S. (1992). From maternal thinking to peace politics. In J.B. Cole & S. Cot&rap-McQuin (eds.), Explorations in feminist ethics (pp. 141-l 55). Sandel, M. (1982). Liberalism and the limits ofjustice. Cambridge: Cambridge University Press. Sen, A. (1984). Collective choice and social welfare. Amsterdam: Elsevier Science. Small, K. (1992). Urban transportation economics. Chur, Switzerland: Harwood Academic Publishers. Stack, C. (1986). The culture of gender: Women and men of color. Signs: Journal of Women in Culture and Society, II, 321-324. Stanfield, J., & Stanfield, J. (1997). Where has love gone? Reciprocity, redistribution, and the nurturance gap. Journal ofSocio-Economics, 26(2), 1 I I-126. Sugden, R. (1986). The economics of rights, cooperation, and welfare. Oxford: Basil Blackwell. Tronto, J. (1987). Beyond gender difference to a theory of care. Signs: Journal of Women in Culture and Society, 12,644-663. Tronto, J. (1993). Moral boundaries: A political argument for an ethic of care. New York: Routledge. Tronto, J. (1995). Care as a basis for radical political judgments. Hypatia, /O(2), 141-149. Walker, M.U. (1992). Moral understandings: Alternative ‘epistemology’ for a feminist ethics. In J.B. Cole & S. Coultrap-McQuin (eds.), Explorations in feminist ethics (pp. 165-175). Young, I.M. (I 990). Justice and the politics of difference. Princeton: Princeton University Press.
ROBERT
TAYLOR
University of California at Berkeley
ABSTRACT:
This paper offers the first economic analysis of the debate in moral and political philosophy over the relative virtues of the ethic of care and the ethic of justice. Specifically, the paper presents a formal model of the care-giving process whose parameters include many items of direct relevance to the care/justice debate, such as the average wage rates of men and women, the size of the population to be cared for, and the benefit attached to discovering and caring for the needy. The model developed herein provides useful insights regarding both perceived gender differences in commitment to care and the relevance of care to large-scale institutions.
Feminist theorists are increasingly fond of the term “care, ” but have yet to systematically explore its economic implications. -Nancy
Folbre
(1995,74)
Professor of Economics University of Massachusetts at Amherst
INTRODUCTION The publication of Carol Gilligan’s highly influential work In a DifSeerent Voice in 1982 sparked a spirited debate in moral and political philosophy that has continued unabated to the present day. In this book, Gilligan identified “two ways of speaking about moral problems”: the ethic of care and the ethic of justice. She distinguished between the two in the following way:
*Direct all correspondence to: Robert Taylor, Department kely, CA 94720; e-mail: [email protected].
of Political Science, University
Journal of Socio-Economics, Volume 27, No. 4, pp. 479-493 Copyright 0 1998 by JAI Press, Inc. All rights of reproduction in any form reserved. ISSN: 1053-5357
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In this conception [the ethic of care], the moral problem arises from conflicting responsibilities rather than from competing rights and requires for its resolution a mode of thinking that is contextual and narrative rather than formal and abstract. This conception of morality as concerned with the activity of care centers moral development around the understanding of responsibility and relationships, just as the conception of morality as fairness [the ethic ofjustice] ties moral development to the understanding of rights and rules (Gilligan, 1982, p. 19).
Perhaps more controversially, Gilligan maintained that the ethic of care was more closely associated with the female gender, the ethic of justice with the male. Gilligan’s magnum opus has engendered an impressive response: literally hundreds of articles (some of the best of which have been collected in Brabeck, 1989; Browning-Cole & Coultrap-McQuin, 1992; Larrabee, 1993) and a host of books (e.g., Okin, 1989; Tronto, 1993; Young, 1990) have been written dealing with the issues she raised. As this paper’s lead quotation indicates, however, none of this extensive literature has dealt with the economic implications of care. This paper will seek to fill this notable gap by providing an economic analysis of care and justice. In what sense is this controversy amenable to economic analysis? In order to answer this question, I must first define care and justice and then contrast these two approaches to morality. To provide care, one must identiJL the particular needs of concrete individuals-that is, one must engage in a search, both across individuals and within individual psyches-and then fulfill those needs. This active effort to collect and interpret information on individual needs and then satisfy them requires a great deal of time and attention. As Joan Tronto has aptly noted, “care requires that humans pay attention to one another, take responsibility for one another, engage in physical processes of care giving, and respond to those who have received care” (Tronto, 1995, p. 145). The mother who discovers and then treats a wound on her child, the person who questions and then listens sympathetically to a troubled friend, and the philanthropist who identifies and then provides time and money to favored charities are all actively engaged in care-giving. Justice, on the other hand, involves the application of formal rules that generally identify only a few key features of any situation as relevant so that a decision may be made with little delay. To quote from an essay by Owen Flanagan and Kathryn Jackson, justice’s advantage over care is one of “cognitive economy” (Flanagan & Jackson, 1987, p. 626). As an example of the justice approach, consider Robert Nozick’s Entitlement Theory, a tripartite set of rules defining a just system of ownership for all physical resources (Nozick, 1974, pp. 150-153). According to Nozick’s theory, a holding is just if it is obtained either through just acquisition from the state of nature (“just acquisition” being acquisition that does not worsen the condition of others, a requirement commonly referred to as the “Lockean Proviso”) or through voluntary transfer (e.g., trade, gift, or bequest). In theory, at least, this set of rules allows us to determine quickly which holdings are just and which
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are unjust by identifying only a few key features (nonworsening in acquisition, voluntariness in transfer) of the ownership system. ’ Clearly, one important difference between the ethic of care and the ethic of justice is that the former is much more time-intensive than the latter. Care-giving entails the time-consuming identification of individual needs; justice, on the other hand, requires the application of formal rules that often abstract away from the particularity of individual needs. A simple example may help clarify the distinction between care and justice and at the same time show why care is more time-intensive. Consider the task of dividing up a pie among a group of people. An application of the ethic of justice would probably lead to some rule, such as equal division, that the participants could quickly agree upon and implement, but that would probably fail to take into account the idiosyncratic needs of those involved. Applying the ethic of care here, on the other hand, would require more time-intensive communication among the participants in order to reveal individual needs and tailor the allocation to meet those needs.2 Time, however, is a scarce commodity, and decisions regarding its use are therefore economic in nature. Thus, the appropriateness of a care approach or a justice approach in any given setting hinges on the economic value of time. Specifically, the scarcer time is, the more attractive justice is relative to care. This simple insight forms the basis of the formal model of care-giving that is presented below. Its parameters will include many items of direct relevance to the care/justice debate, such as the average wage rates of men and women, the size of the population to be cared for, and the benefit attached to discovering and caring for the needy. This model will allow us to answer many of the puzzling questions that have been raised in the course of the care/justice debate, including the following three: 1.
What is the connection
between care and justice?
2.
Is care applicable
3.
Why might men and women have different approaches
to large-scale
institutions? to morality?
At first glance, using formal economic modeling to elucidate a problem in moral philosophy might seem perverse. However, economists such as John Roemer, Amartya Sen, and Robert Sugden have long used mainstream economic modeling techniques to shed light on issues traditionally associated with moral and political philosophy. (See, for example, Sen, 1984; Sugden, 1986; Roemer, 1994; 1996.) I heartily concur with John Roemer that the chief benefit of using economic analysis in political philosophy is to make its theories more precise so that their robustness, consistency, and feasibility may be tested (Roemer, 1996, p. 3). The formal model that I develop below allows us for the first time to carry out such tests on the ethic of care-with interesting and sometimes surprising results.
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A FORMAL MODEL OF CARE-GIVING The Intuition Behind the Model The model to be developed here has as its central feature a benevolent caregiver who searches within a population for the neediest individual. Because many people in the population will claim to be the most needy (care being a nice thing to receive), the care-giver must go through a screening process to collect information about the population and discern who the neediest person really is. The care-giver will have to settle upon an optimal amount of time to spend in search because time is scarce, i.e., has alternative valued uses. This optimal quantity of time will be determined in an economically rational way-namely, by an analysis of the costs and benefits of continued search. Several of the parameters to be included in this model will undoubtedly have a major impact upon the optimal search time. The wage rate of the care-giver, for example, will obviously influence how much time the care-giver will want to spend searching: time spent searching is time not being spent earning money. Two other important factors will be the size of the population being searched and the benefit to be gained from discovering the most needy member of the population. The larger the population, the more difficult it will be to find the neediest individual; the larger the benefit to finding him or her, the more motivated the care-giver will be to do so. Optimal search times that are very short will be associated with the ethic of justice, whereas those that are relatively long will be associated with the ethic of care. Short search times make it very unlikely that the neediest individual will be identified. The benevolent care-giver will therefore be forced into some second-best approach, such as the random selection of a person to care for or the provision of some very low but equal level of care to everyone. That is, the care-giver will be forced to apply some simple, abstract rule to make a decision instead of taking the idiosyncratic needs of the members of the population into account: this solution is, perhaps unfortunately, the essence of justice. Margaret Urban Walker makes much the same point when she notes the “moral incompleteness or inadequacy of these resorts” to justice (Walker, 1992, p. 171). One should note, however, that such expediencies may be unavoidable when time is particularly scarce. Only in a world where time were not scarce would care always be the preferred approach.3 Incidentally, treating the ethic of justice and the ethic of care as points (or perhaps ranges) on opposite ends of a time-intensiveness spectrum is one way to “connect” the two approaches to morality. One of the recurring questions in the literature concerns the relationship between care and justice: some authors, such as Rita Manning and Marilyn Friedman, claim that justice is a “side constraint” that limits the application of care (Manning, 1992, p. 50; Friedman, 1993, pp. 265267), while others, such as Jane Tronto, believe that care subsumes justice (Tronto,
483
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1987, p. 659). The model here is consistent with the views of those who hold that care and justice lie on a “continuum” (Dillon, 1992, p. 78). Setting Up the Model
In this model, a population of individuals is distributed continuously and uniformly along a line segment of length a. One of these individuals is the person in greatest need. The location of the neediest person on this line segment is random. A benevolent care-giver must search along this line segment to find the most needy person and provide care. The care-giver attaches value B to finding and caring for this person. The process of searching for the neediest person takes time, however, which has a constant opportunity cost of w, the care-giver’s wage rate. The care-giver has access to the search technology k = s(t), where the function s gives the length of line segment k that can be searched in time t. The search technology may be thought of as conversation: the care-giver must talk to individuals along the line segment to discern who the most needy person really is. We will assume that the difficulty of search increases with search time due to care-giver fatigue-the more individuals you have to talk to, the more tired you become and the less effective a conversationalist you will be. In other words, the marginalproductivity of search declines with the amount of time spent searching.4 Moreover, we will assume that the care-giver must commit to a search time in advance. This assumption is not particularly bizarre: after all, harried professionals commonly set aside time in advance for family, friends, and charity work, often in the form of vacation time. In the tradition of John McCall’s work on unemployment (e.g., John McCall, 1970), we could instead use a model of sequential search. Such a move would necessitate the introduction of some fairly sophisticated mathematics (specifically, optimal control theory) but would not lead to conclusions qualitatively different from those we will reach below. Optimization:
Choosing
an Optimal
Search Time5
The care-giver will determine the optimal length of time to search in an economically rational way-namely, by an analysis of the marginal costs and benefits of search. The marginal cost of search in this model is constant and equal to the opportunity cost of time w, which is simply the care-giver’s wage rate. Foregone wages are the only explicit costs of search here. The marginal cost curve for search (MC) is displayed graphically in Figure 1. The marginal benefit of search declines with the amount of time spent searching. Each additional hour spent searching increases the care-giver’s chances of finding the most needy person and therefore of receiving the psychic payoff B, but it does so at a decreasing rate due to the declining marginal productivity of search-care-giver fatigue makes each additional hour spent at search less and less beneficial. The marginal benefit curve for search (MB) is also displayed graphically in Figure 1.
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x MP of Search
MC = w = Wage Rate
Figure 1.
The care-giver will choose that search time where the marginal benefit of search just equals the marginal cost. Choosing a shorter search time would entail foregoing search whose marginal benefit exceeds the wage rate, whereas choosing a longer search time would require engaging in search less beneficial at the margin than the wage rate. The optimal search time t* is displayed graphically in Figure 1. It occurs where the marginal benefit and marginal cost curves intersect. The Relevance
of Care to Large-Scale
Institutions
I will now use the model of care-giving presented above to address a number of issues that have arisen in the care/justice debate. First among these issues is the applicability of care to large-scale institutions such as government and the marketplace. Several authors (such as Blum, 1982; Broughton, 1983) have questioned care’s relevance outside the confines of small groups such as families. Even those authors who are generally sympathetic to the care approach have expressed doubts about its wider applicability. Consider, for instance, the following quote from the introductory essay by Eve Browning Cole and Susan Coultrap-McQuin in their book An Ethic of Care: Finally, though it might work well in the context of private relationships, the ethic of care may not be easily applicable to a public arena of decision-making. In legislation and social policy, both the size of the population involved and the necessity for maintaining equity make it difficult to envision how an ethic of care might be fairly applied (Cole & Cot&rap-McQuin, 1992, p. 6; my emphasis).
Interestingly, the care-giving model provides strong support for these concerns. To see this, consider a change in a, the length of the line segment along which the population is arrayed. The length of the line segment may be viewed as a proxy for
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MB/MC
MC
Figure 2.
population size. What effect then will a change in population size have on optimal search time? Intuitively, we would expect population size and optimal search time to be inversely related: a larger population makes a care-giver’s search for the most needy individual more difficult and therefore less beneficial at the margin. Thus, one would expect the care approach to be less relevant to large populations than to small ones. This result is displayed graphically in Figure 2, where an increase in population size a causes MB to shift downward from MB to MB”, resulting in a fall in optimal search time from t’ to t”. As this comparative-statics exercise indicates, there may indeed be reason to question the applicability of care to large populations. As population size increases, optimal search time falls, making it less likely that the care-giver will be able to find and provide aid to the neediest individual and more likely that some formal rule will have to be applied. Care’s domain may be limited to groups such as families and circles of friends, where population size is small enough to make the identification of greatest need and the subsequent provision of care feasible. Differences in Commitment to Care Participants in the care/justice debate have frequently remarked that observed differences in commitment to the care approach appear to follow gender and ethnic lines. Carol Gilligan, among others, has made the “empirical observation” that care is more closely associated with the female gender than the male (Gilligan, 1982, p. 2) though this claim is not undisputed (see, for example, the section of Larrabee, 1993, entitled “Checking the Data”). Moreover, several authors (including Collins, 1990; Stack, 1986) have pointed out a similarly strong commitment to care and to contextual morality in the African-American community.
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t
Figure 3.
The care-giving model once again provides invaluable insights on this issue. To see why, consider a change in w, the opportunity cost of the care-giver’s time. Intuitively, we would expect the opportunity cost of time and optimal search time to be inversely related: as the care-giver’s time becomes more valuable (i.e., the wage rate increases), the marginal cost of search will rise and therefore he or she will want to devote less time to search and more time to work. Thus, ooze would expect that, ceteris paribus, groups with different average wage rates would have difSerent levels of commitment to care-specifically, those groups with relatively high average wages should be less committed to care and more committed to justice than those with low wages. This result is demonstrated graphically in Figure 3. Here, an increase in the opportunity cost of time w causes MC to shift upward from MC to MC’, resulting in a fall in optimal search time from t’ to t”. These comparative-statics results suggest that observed differences in commitment to care may be an artifact of differing wage rates.6 In 1990, white American males had an average wage rate of $12.35 per hour; African-American males, $10.87; white American females, $9.30; and African-American females, $7.79 (Panel Study of Income Dynamics, 1990). Because women and African-Americans have a lower opportunity cost of time, their greater commitment to the timeintensive care approach should not be surprising.7 Controversial theories ascribing observed differences in commitment to care to congenital differences or differences in socialization are, strictly speaking, inessential.’ Care and the Domestic-Public
Distinction
Political philosopher Will Kymlicka, a sympathetic critic of the care approach, has made the following important point in a discussion of the care/justice debate:
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I will argue that the emphasis
on objective unfairness (i.e., injustice), while initially plausible, is only legitimate in certain contexts-namely, interactions between competent adults. Indeed, it may be legitimate only when our interactions with competent adults are sharply separated from our interactions with dependents. If so, then the debate between care and justice reasoning becomes inextricably linked to the debate over the domestic-public distinction (Kymlicka, 1990, p. 277).
Kymlicka may be interpreted as saying that the ethic of care approach is quite relevant to children and incompetent adults (e.g., the mentally or physically handicapped), but not as relevant to competent adults, because the former group is in a greater state of dependency, or need, than the latter group. In other words, the care approach is more relevant in those situations where the needs of those in distress are particularly pressing. Again, the care-giving model provides support for Kymlicka’s assertion, although the connection is somewhat complex. To see it, first consider a change in B, which is the psychic payoff the care-giver receives for identifying and caring for the neediest individual. Intuitively, we would expect the psychic payoff and the optimal search time to be directly related: the greater the benefit of finding the neediest individual, the more beneficial the search will be at the margin and therefore the longer the care-giver will want to search. This result is displayed graphically in Figure 4. Here, an increase in payoff B causes MB to shift up from MB’ to MB”, leading to an increase in optimal search time from t’ to t”. In order to tie this comparative-statics result to Kymlicka’s comment, we must ask the following question: what is the most appropriate interpretation of B, the care-giver’s “psychic payoff’? Given that the care-giver is benevolent and undertakes caring labor “out of affection or a sense of responsibility for other people”
MB/MC
I
MC
Figure 4.
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(Folbre, 1995, p. 75) one might expect B to be highest in those situations where the needs of the individual being sought out are most pressing. That is, the caregiver, being motivated by sympathy for those in need, may be more highly motivated the greater the need is. Thus, one would expect the care approach to be more relevant in those situations where the needs of the distressed individual are greater.9 This result supports Kymlicka’s statement that care is more relevant than justice whenever one is dealing with children and incompetent adults. Interestingly, the comparative-statics results with regard to B and a reinforce a distinction alluded to by Kymlicka in the above quote: the distinction between the domestic sphere and the public sphere. Note that the domestic sphere is composed of households, which are small-number groups (low a), and that the domestic sphere is the primary locus of care for children (high B). The ethic of care would therefore seem to be particularly appropriate in the domestic sphere, whereas the ethic of justice would be largely out of place. The model constructed above thus provides a simple economic justification for the domestic-public distinction. CONCLUDING COMMENTS AND DIRECTIONS FOR FUTURE REASERCH The debate over the ethic of care and the ethic of justice has been long and contentious, and many (if not most) issues raised in the course of the debate have remained unresolved. The economic model of care-giving described above helped elucidate a number of these standing issues. First, the model presented a new way of looking at the connection between care and justice. Specifically, these two approaches to morality may be viewed as points (or ranges) on a time-intensiveness spectrum. Second, the model demonstrated that care is less relevant, and justice is more relevant, the larger the population under consideration. In other words, care is most appropriate in small groups such as the family and least appropriate in large institutions such as government and the marketplace. Finally, the model predicted that those groups with relatively low wages would have the highest level of commitment to the care approach due to their low opportunity cost of time. The validity of this prediction is borne out by the evidence pointing to a strong commitment to care on the part of women and minorities, who have relatively low average wage rates due to labor market discrimination and other factors. The basic model of care described above can be fruitfully extended in a variety of ways. For example, the possibility of improving the search technology (conversation) through investment might be introduced into the model. Many advocates of the care approach have expressed the hope that care might be applied to large-scale institutions (e.g., Ruddick, 1992; Stanfield & Stanfield, 1997). Although the modeling exercise just completed casts doubt on the feasibility of such an enterprise, I should point out that educational investments to improve the ability of citizens to identify and respond to needs would make the care approach more attractive in
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general. In terms of the model, such investments would increase the optimal search time by making search (conversation) more productive at the margin. Theoretically, then, increased educational efforts might make care more readily applicable to large-scale institutions, although the rates of return on these efforts would have to be compared with rates of return on other possible investments (including other types of investments in the cultural infrastructure) to determine their desirability. A second, more ambitious extension of the model would be to provide more active roles for the agents who inhabit it. Currently, the model contains one caregiver and a continuum of passive care-recipients. One might instead imagine a model where agents can be both care-givers and care-receivers and where individuals pursue either caring strategies or non-caring strategies in their interactions with others. The tools provided by evolutionary game theory might provide the means for examining the success rates of various strategies and the possibility of movement towards a steady-state population composition. In conclusion, the care-giving model examined above not only fills the literature gap alluded to by Nancy Folbre in this paper’s lead quotation, but also demonstrates the great promise of using standard economic modeling techniques to answer questions traditionally associated with other disciplines. A host of issues in moral and political philosophy in addition to the care/justice debate are surprisingly amenable to economic analysis and will hopefully serve as topics for future economic research.
Acknowledgments:
1 would like to thank Roger Frantz, Kathy Jones, Eric Brunner, Camilla Kazimi, Herb Emery, Yannis Venieris, Doug Stewart, and Jahn Hakes for their helpful comments on this paper.
APPENDIX As noted in the text, the marginal productivity of search declines with the amount of time spent searching due to care-giver fatigue. This assumption implies that the search technology s(t) is an increasing, strictly concave function oft, The care-giver’s task is to choose a search time t* that maximizes his or her expected utility. Assuming that the care-giver is risk-neutral, the optimization problem may be characterized as follows: s(t)
max j f(z)B
dz -
wt
=
F(S(t))B
- wt,
t 0
where f is the probability density function and F is the cumulative distribution function of the uniform distribution. F(s(t)) is the probability of finding the needi-
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est person in search time t, while B is the benefit attached to discovery. So, F(s(t))B is the expected benefit of searching for t units of time. Finally, wt is the opportunity cost of search time t. Given that we are dealing with a uniform distribution of length a, F has a fairly simple form-F(z) = z/a for all ZE [O,a]. We may therefore rewrite the optimization problem above and solve for t*: maxso t
a
B - wt
First Order Condition:
i s’(t*) - w = 0;
Second Order Condition:
z s”(t) < 0,
where the Second Order Condition follows from the strict concavity of s(t). Optimal search time t*, which is implicitly defined by the First Order Condition (hereafter FOC), therefore generates a global maximum. The first term in the FOC is the marginal benefit of search, whereas the second term is the marginal cost. The care-giver will choose the search time at which the marginal costs and benefits of search are equal. The care-giver’s decision is displayed graphically in Figure 1. How will optimal search time t* vary with changes in the model’s three parameters? By using the Implicit Function Theorem and the FOC, we may calculate these effects as follows:
B , dt” -= da
--=F, F,,
---a?’ B -s” a
dt” -= dw
-- F~ = -- -1
dt” -= dB
FB --=
1 F,,
--
iiS
I
>.
B -s” a
These equations demonstrate that optimal search time t* is inversely related to the population size a and the opportunity cost of time w but directly related to the care-
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giver’s incentive B. These relationships and 4.
are displayed graphically
in Figures 2, 3,
NOTES 1.
2.
3.
4.
5. 6.
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Nozick’s Entitlement Theory is only one of many contemporary theories of justice. John Rawls (1971) and Ronald Dworkin (1981 a,b) offer liberal egalitarian theories of justice that contrast sharply with Nozick’s libertarianism. Even sharper contrasts are provided by James Buchanan (1975) and David Gauthier (1986) who present theories of justice in the Hobbesian contractarian tradition. (For an economic analysis of both Gauthier’s work and other contractarian theories, see Ken Binmore, 1994.) As some readers may note, the ethic of care resembles utilitarianism in certain ways. There are, however, two major differences. First, the ethic of care is completely informal. Unlike utilitarianism, it makes no attempt to quantify, much less aggregate, individual needs. In fact, utilitarianism’s tendency to “not take seriously the distinction between persons” (Rawls 1971, p. 27) is inconsistent with the ethic of care’s emphasis on the uniqueness of individuals and their needs. Second, the ethic of care deals more forthrightly with issues of implementation than utilitarianism, which is mostly silent on the question of how to obtain information on people’s preferences. In contrast, the ethic of care suggests particular methods (conversation and personal observation) to gather information on people’s needs. Some will find my characterization ofjustice as “second best” to be objectionable. Because I will subject care to some fairly searching criticism later in the paper, however, I thought it advisable to place it in the best possible light vis-a-vis its chief rival, justice. Just as Michael Sandel (I 982) pointed out the “limits of justice” in his communtitarian critique of Rawls, I will here point out the limits of care as a moral and political concept. The difficulty of search may increase with search time for reasons other than fatigue. Suppose, for example, that the care-giver knows in advance how difficult it will be to determine the neediness of each individual. A rational stategy would then be to interrogate the “easy” (i.e., transparent) individuals first and the “hard’ (i.e., opaque) individuals later (assuming, of course, that the difficulty of interrogation is uncorrelated with neediness). None of this implies, of course, that the marginal productivity of search always declines with search time (learning may lead to intial increases in productivity), but the law of diminishing marginal returns guarantees that at some point it will begin to decline. The following discussion of optimal search time and its determinants relies exclusively upon intuition and graphs. For a more formal treatment, see the accompanying Appendix. The causes of these wage differentials, including labor market discrimination, are unfortunately beyond the scope of this paper. An excellent source of references for recent articles on this important subject is Randall Filer, Daniel Hammermash, and Albert Rees (1996). The use of wage rates as a measure of the opportunity cost of time is not uncontroversial. For example, Kenneth Small, in a review of the urban transportation literature on the value of time, concludes that “a reasonable average value of time for journey to work is 50 percent of the gross wage rate” (Kenneth Small, 1992, p. 44). Note, however, that if the opportunity cost of time is merely a fraction of the wage rate, then the ordering of opportunity costs of time will be identical to the ordering of wage rates, leaving the conclusions reached above unaffected. On the other hand, some studies have suggested that the opportunity cost of time for women is higher than that for men. See, for instance, the study by Robert Deacon and Jon Sonstelie (1985) of the time spent waiting in gas lines during the oil crisis of the early 1970s. Ockham’s Razor, or the Law of Parsimony, suggests that one should avoid ascribing observed effects to unobserved (and perhaps unobservable) causes if at all possible. For this reason, using
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different wage rates between men and women to explain their differing levels of commitment to care is preferable to using differing preferences or values (e.g., variations in B resulting from differing levels of sympathy or altruism in men and women). B may also have an impact on the efficaciousness of search: the more needy the neediest individual is, the easier it may be to discover him or her in the population; needs may be more visible the larger they are. In terms of the model, this relationship would reinforce the positive effect of B on optimal search time.
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