Last week as part of this new series of posts on concepts in development economics I covered the idea that heterogeneity is part and parcel of developing-country markets, and that heterogeneity can drive outcomes to the point of causing economic underdevelopment and persistent poverty.
This week, I wanted to talk about nonseparability, which is probably one of my favorite things to teach when I teach development.
In most microeconomics classes, students learn about utility maximization–the theory of consumer behavior–and profit maximization–the theory of the firm–separately. That is true even in graduate courses; in the first doctoral-level microeconomic theory class I took in grad school, we studied the two separately, as presented in the first five chapters of Mas-Colell et al. (1995).
Yet, the economic actor that is perhaps the most important in developing countries is agricultural household, which is both a consumer as well as a producer of the same commodities. If you think about it, most rural households in developing countries grow one or more staple crops, which they consume some of.
When all the markets relevant to an agricultural household (e.g., labor, capital, and other input markets; the credit market; the market for the staple crop; etc.) exist, the household will first maximize profit on the production side of its activities, and then, conditional on the (full) income it derives from all its activities (including its production of staple crops), it will maximize its utility.
Note the sequence here: The household first maximizes its farm profit, then it maximizes its utility, which depends on farm profit. So while the household’s consumption decision depends on its production decision, its production decision does not depend on its consumption decision. (Yes, this implicitly assumes that there is only one utility function for the entire household–more on this in a second.)
The problem arises if too many* of the markets relevant to the household fail. For example, the household would like to send one of its members to go work for a wage on the local market, but high unemployment prevents them from doing so. Or the household would like to use chemical fertilizer on its plots, but it not sold on the local market. Or the nearest market where the household could sell its excess production of the staple crop is just too far and thus “failing” in the sense that it is just not worth going to. Or the household cannot borrow to finance its consumption during the hungry season. In that case, the households consumption and production decisions are no longer separable. That is, the household has to take its production decision in view of its consumption decision, and vice versa.
Beyond modeling considerations, does this matter? It does, because a household whose production and consumption decisions are nonseparable is almost sure to attain a level of welfare that is lower than that of an identical household whose production and consumption decisions are separable.** In other words, thin and fragmented or missing markets mean that entire households cannot attain their full potential when it comes to welfare.
In some sense, this is one of the reasons why some people outside of economics (and even some people within economics, such as heterodox economists) perceive (mainstream) development economists as “ideological” and as having too much faith in markets. In truth, I would venture to guess that for most of us who do development microeconomics in some form or other, that “faith in markets” is only a by-product of our faith in rational choice.
Ironically, it pretty much took a heterodox economist to call out mainstream economists on a fundamental logical inconsistency in the foregoing representation of the household. In a 1984 article in Economic Development and Cultural Change, Nancy Folbre pointed out that as much as mainstream economists like to focus on individual rationality, and that neoclassical results hold because individuals are capable of rational choice, it did not make much sense to take a collection of individuals (each of which with their own preferences and intrinsic motivations), roll them up into a single unit called a household, and slap a single utility function (i.e., a single set of preferences) on them. Since then, much ink has been spilled trying to model households as collections of individuals and on testing which properties of individual decision making (e.g., Pareto-efficiency) entire households satisfy empirically–or not.
Update: Asif ud Dowla found a link to a .pdf of what is perhaps the best reading on the topic, viz. Singh et al.’s (1986) book, which is the classic discussion on this topic. See chapters 1 for the basics, and chapter 2 for a discussion of nonseparability.
* Formally, separability (of the household’s consumption and production decisions) fails to hold once two markets relevant to the household’s activities fail. With only one market failing, the household can adjust its activities so as to compensate for that one market failure. See the chapter on household models in Bardhan and Udry (1999).
** I use almost surely in the statistical sense here, with the alternative having a measure virtually equal to zero. The two households would have identical welfare if and only if preferences and technology were such that the separable case led to an outcome identical to the nonseparable case, which is extremely unlikely.