6.1 Formalizing Endogenous Preferences

We seek a formalism expressing the fact that activities not only fulfill existing needs or preferences but change or develop those preferences as well. The first step is to stipulate that while the fulfillment individuals derive from participating in a particular set of activities obviously depends on their preferences, those preferences in turn depend on the human characteristics individuals possess at the time. In other words, individuals' "instantaneous" preference orderings are parameterized by their "instantaneous" human characteristics. In this way individuals' "needs" change whenever any of their human characteristics change-which is what we mean by "derived needs."

6.1.1 Model 1: An Individual with Endogenous Preferences

M 1.1. Let U(t) represent an individual's instantaneous preference ordering at time t , and

M 1.2. Let C(t) represent the whole array of personality traits, skills, knowledge, and values a person has in period t. In other words C(t) = [ P(t), S(t), K(t), V(t) ] where each vector inside the brackets has many components as well, as discussed in chapter 5. For convenience we will assume C(t) is a vector with C components where each component is a postive real number, so that

M 1.3. The fulfillment, satisfaction, or utility achieved in period t becomes U(t) = U(P(t), S(t), K(t), V(t); (.)) or, U(t) = U(C(t); (.)) where (.) represents all the economic activities in period t that in any way affect the individual's wellbeing.

In general, an individual's instantaneous preference ordering should be defined on "activity space." That is, one's satisfaction is a function of all the activities carried out by groups in which one, in some sense, participates. In terms of the notation of chapter 5, (.) would be all the activities A_k(i,t) carried out by groups i in which the individual participates.¹

But for present purposes, we can adopt the traditional view that all welfare significant activities in which people participate can be interpreted as the consumption and laboring activities each carries out individually, which in turn are assumed to be fully described by the quantities of different "consumption goods" each consumes, and the number of hours each works in different kinds of job categories. While the more general conceptualization of individuals participating in various elements of group activity space is more appropriate to treatment of issues such as public goods and the labor process, for many issues that have been the primary focus of welfare theory, the traditional formulation is sufficient, and these are the issues we address first. So for now,

be a vector whose elements represent quantities of each commodity consumed by the individual at time t so that

be a vector whose elements represent hours of different kinds of labor the individual carries out at time t,

²
And instead of describing the welfare significant activity space for an individual at time t as (.) = A_k(i,t) where k ranges over all activities, and i ranges over all the groups the individual "participates in"--broadly definedwe describe it as the commodities consumed and labor done by the individual in period t or:

And for convenience we define U(t) as a continuous, differentiable function mapping elements from

The second step, which makes preferences "endogenous," is to stipulate that these various human characteristics are potentially functions of economic activities previously carried out. In this way participating in any economic activity has both what we call a "preference fulfillment effect"-- fulfills present preferences to a greater or lesser extent-and what we call a "preference development effect"--it influences future character structures, which in turn influence future preference orderings.

M 1.8. For each element i of an individual's personality characteristic vector P(t):

p_i(t) = p_i(Q(t-1), Q(t-2),.. . Q(0); L(t-1), L(t-2).... L(0))

And, similarly, for the other individual human state variables:

s_i(t) = s_i( Q(t-l), Q(t-2),. .. Q(0); L(t-1), L(t-2) .... L(0))
k_i(t) = k_i( Q(t-1), Q(t-2).... Q(0); L(t-1), L(t-2) .... L(0))
v_i(t) = v_i(Q(t-1), Q(t-2),. .. Q(0); L(t-1), L(t-2) .... L(0))

And for convenience we define each characteristic formation function at each point in time, as a continuous, differentiable function mapping elements from Â⁺_t(Q+L)to Â⁺.

M 1.9. Finally, the well-being an individual enjoys over his or her life would simply be some function of the well-being achieved in all time periods so that:

W = W(U(0),... U(T)).

M 1.10. But for our purposes nothing is lost by specifying an overall wellbeing function that is a linear function of fulfillment in each time period where t_t represents the individual's subjective rate of time discount for fulfillment in period t. So W is a linear function mapping elements in Â_(T+1) to  .

We complete our model of an individual with endogenous preferences with the budget constraint. We abstract from two complications irrelevant to our present purposes: income from initial stocks other than laboring capacities and borrowing and lending. For now there is no harm in specifying that expenditures in each period must be paid out of earnings in the same period. ³

M 1. 11. Let I(t) be income in period t, a continuous, differentiable function mapping elements in Â⁺_(C+L) to Â⁺, where

where p_i(t) is the price the individual must pay for a unit of good i in period t, and the nonsatiation axiom justifies the equality. Or, using vector multiplication

I(t) = p(t)•Q(t) is our budget constraint in each time period.

Although we agree with Gintis that a host of uncertainties is involved in any individual's estimation of these parameterized utility functions and human characteristic development functions, we choose to ignore these "uncertainty" issues. This is not because we think they are uninteresting, but because we have "other fish to fry." The theorems of this and subsequent chapters are our justification for the strategic decision to abstract from uncertainty by extending the assumption of "perfect knowledge" of traditional welfare theory to the new context of endogenous preferences. We will grant people "perfect knowledge" not only of the degree to which different "consumption-work bundles" fulfill their preferences of the moment and the relative prices and wages of different goods and jobs today, but "perfect knowledge" of how different consumption-work bundles chosen today will modify their future characteristics and how these new characteristics will change their preferences. Once again, the mere statement of the assumptions reinforces the reasonableness of Gintis' practical objections. But Debreu had already extended the perfect knowledge assumption to future prices and preference fulfillment effects in the spirit of the traditional welfare project-uncovering the implications of informed, individual, rational choice. In the same spirit we waive Gintis' objection.

6.2 Endogenous Preferences and Welfare Theorems

Traditional welfare theory teaches us how to estimate the welfare effects of economic choices. It interprets coincidence of relative supplies and desires as worthy of praise. And it establishes three "fundamental" theorems concerning the welfare characteristics of competitive, private enterprise market economies. Under appropriate assumptions:

1. At least one general equilibrium exists for any competitive, private enterprise market economy

2. Any general equilibrium of a competitive, private enterprise market economy is Pareto optimal

3. Any Pareto optimal outcome can be achieved as the general equilibrium of a perfectly competitive, private enterprise economy with the appropriate initial endowments

But traditional theorems assume exogenous preferences, so our first task is to reexamine traditional lessons under the assumption of endogenous rather than exogenous preferences as we model the phenomenon. In addition to being a matter of standard procedure in the development of what Kuhn termed "normal science," reexamination is necessary because Gintis claimed traditional welfare theory systematically misestimates and misinterprets welfare effects and that the second fundamental theorem of welfare economics is false under the assumption of endogenous preferences. Pollak, El Safty, and Hammond claim no fundamental conclusions are altered by treating preferences as endogenous unless welfare conclusions become impossible to draw altogether. Clarification is in order before we present our own view of how endogenous preferences are related to the fundamental issues of welfare economics. ⁴

6.2.1 Round One: Endogenous Preferences Do Matter

Treating preferences as endogenous certainly changes estimation of the welfare effects of specific actions and undermines the traditional interpretation of the welfare significance of coincidence between supplies and demands in partial equilibrium settings.

Misestimating Welfare Effects. Gintis was perfectly correct in pointing out that traditional theory misestimates the welfare effects of economic choices if consumption-work choices not only fulfill present preferences more or less satisfactorily, but also change future preferences by changing future human characteristics, thereby affecting the possibilities of obtaining satisfaction from future consumption-work possibilities. We formulate and demonstrate this proposition as Theorem 6.1.

The theorem is intuitively plausible since any theory that fails to consider a significant relationship would be expected to misestimate effects of related actions. However, to prove the proposition requires some effort and the results are illustrative.

First, if we adopt the conventional assumption that all functions are continuous and differentiable, and the convenient assumptions of an interior solution point and binding budget constraints, we can model the individual's welfare maximization choice as a "classical programming problem. " ⁶ We write the Lagrangian

Remembering that the choice variables are simply the quantities of each good to consume in each period and the number of hours to work at each different kind of labor activity in each period, we write the first order necessary conditions for a welfare maximum

For t = 0 ... t and q = 1 ... Q there would be (T+1) times Q equations of the above type. And

For t = 0 ... T and l = 1 ... L there would (T+1) times L equations of the above type. And finally

where for t = 0 ... t there would be (T+1) "budget constraint" equations of the above sort. The result we are seeking follows directly from observing that if preferences are endogenous we cannot assume that the first set of terms under the double summation in both (6.1) and (6.2) are zero. Quite the contrary, in the presence of "preference development effects" there is every reason to believe their sum can be either positive or negative.
Von Weizsacker, Hammond, and especially Pollak were not primarily concerned with the welfare effects of endogenous preferences - particularly conceived as fully informed rational self-molding. But it is difficult to imagine they would disagree with this conclusion. That few, if any, traditional theorists would disagree is even more apparent once one recognizes the similarity between this result and analogous results in human capital theory that have been long acknowledged.
Prior to the advent of human capital theory all the terms under the double summation signs were ignored in expressions (6.1) and (6.2). Human capital theory recognized the need for including the effects of the second set of terms under the summation signs. In (6.1) those effects are interpreted as "consumption" choices that are, at least in part, "investments" in "human capital." In (6.2) those effects are conceived as "on-the-job training" effects of work activities.
Human capital theory pointed out that a welfare theory that ignored the human capital and on-the-job training effects of consumption and work activity choices misestimates welfare effects by ignoring the effects on individuals' future budget constraints. A theory of endogenous preferences makes a completely analogous point; a welfare theory that ignores the effects of consumption and work activity on individuals' future preferences necessarily misestimates welfare effects by ignoring the effects on individuals' capacity to extract satisfaction from future options.
Presumably the only difference between Gintis, on the one hand, and von Weizsacker, Hammond, and Pollack, on the other, would be how much importance they attach to this new revelation-and whether to consider it reason to look for a new welfare paradigm. In any case, Gintis would no doubt agree that the necessary "correction" can easily be made as it was in the case of human capital theory, and as he, himself, has done.

Misinterpreting Coincidence of Supplies with Demands. Gintis' observation is correct. If people mold their desires to better coincide with the terms of availability that exist independently of those desires, the positive welfare implications of a coincidence between relative supplies and desires vanish. We demonstrate this claim as Theorem 6.2.

In traditional theory it was possible to "separate" supply and demand. As long as we treated preferences as exogenous, there was no possibility that demands could adjust to supplies. In this case, equality between ratios of marginal costs of supplying activities and ratios of marginal utilities for those activities was of great welfare significance because it occurred only if the "economy" supplied activities according to people's relative desires. ⁷ But Theorem 6.2 challenges the welfare significance traditionally imputed to "consumer sovereignty" as judged by people's "instantaneous preference orderings." Once demand is a function of supply, traditional partial equilibrium welfare theory goes by the wayside.

For convenience, our demonstration of Theorem 6.2 concerns a change in the relative prices of two goods in the last period, T. Then we explain why the result can be generalized to a change in relative prices in any period.
Suppose there is a change in the relative prices of the mth and nth commodities in period T, p_m(T) and p_n(T)^A. superscript A signifies prices after the change and a superscript O signifies original prices. We change the relative terms of supply by increasing the price of m relative to n in period T.

Since we are in the last time period, no terms are inside the double summation sign for T and commodity m and for T and commodity n in expression (6.1) under either the new or the old price system. So if the individual maximizes his or her welfare in each situation we are led directly to the conclusion:

The assumption of diminishing marginal utilities ⁸ yields

But a change in the relative proportions of commodities m and n consumed in period T will change the values of partial derivatives of utility in period T with respect to all the human characteristics found under the summation signs in all the necessary conditions for all the previous time periods since these partials are still functions of the quantities of commodities m and n in period T. Letting a(t) stand for any of our human characteristics, we can conclude that if a_i(t) increases enjoyment of commodity m relative to commodity n, then:

Alternatively, if a_i(t) increases enjoyment of n relative to m, then:

Although it is possible, there is no reason to suppose that the sum total effects of changes in the values of these partials in any one of the necessary conditions for q = 1 ... Q and t = 0 ... (T-1) would be such as to exactly cancel out at the old values of consumption and work activity choices for those periods. So, in general, we would expect that

q_i(t)^A would not equal q_i(t)^O and l_j(t)^A would not equal

l_j(t)^O for i = 1... Q, j= 1 ... L, and t = 0 ... T-1.

But our model implies different sets of human characteristics will develop under economic choice patterns

{ q_i(t)^A , I_j(t)^A} and { q_i(t)^O, l_j(t)^O } and,therefore, a different set of preference patterns for various comodity-work bundles will develop as well.

This concludes the demonstration of Theorem 6.2 provided the proof does not rest on choice of the final period, T, as the starting point. But the only convenience offered by this starting point is that a particular change in relative prices can be translated into a shift in the relative amounts of the two commodities consumed whose sign is determinant under the assumption of diminishing marginal utilities. Had we begun with a change of relative prices in any earlier time period, the direction of the shift in the consumption bundle for that time period would not have been determinant due to the many terms of indeterminate signs under the double summation signs. However, it should be clear that, in general, changes would be required in the values of any q_m(t) and q_n(t), for t = 0 ... (T- 1) to reestablish the necessary conditions after a change in the relative prices p_m(t) and p_n(t) Once the ratio of prices in period t for any two commodities has changed, no matter in what direction, changes will be required for all earlier consumption and work activity choices with consequent changes in human characteristics and preference structures exactly as argued above.
The phenomenon of rational adjustment of preferences, toward wanting what is presumed will be most readily available and away from wanting what is presumed will be difficult to obtain, should not be confused with another way that "utility" might be a function of "price"--namely "snob effects," "keeping up with the Joneses," or "conspicuous consumption. " ⁹ The clear difference between the phenomena can be appreciated by noticing that the direction of the individual's adjustment is exactly opposite in the two cases. Whereas the phenomenon we are discussing would lead rational individuals to diminish their desires for goods whose future price was expected to be high, the phenomenon of conspicuous consumption would lead individuals to value goods with high prices more. We might point out there is no reason both phenomena could not exist in the real world. But where it has been relatively easy for neoclassical welfare theory to dismiss "snob effects" as irrational, if not aberrant behavior, in which the individual at least "pays" for his snobbery, the phenomenon we refer to is characterized precisely by its rationality and, therefore, very much a "legitimate" focus of concern according to traditional welfare criteria.