This paper was published as a GPI working paper in October 2024.

Abstract

I study a static production economy in which consumers have not only preferences over their own consumption but also external, or “ethical”, preferences over the supply of each good. Though existing work on the implications of external preferences assumes price-taking, I show that ethical consumers generically prefer not to act even approximately as price-takers. I therefore introduce a near-Nash equilibrium concept that generalizes the near-Nash equilibria found in literature on strategic foundations of general equilibrium to accommodate ethical preferences. I find (narrow) sufficient criteria under which such equilibria exist, and characterize consumer behavior in all such equilibria. Finally I find that ethical preferences can have arbitrary impacts on consumer behavior in equilibrium, including motivating a consumer (1) to decrease her consumption of all goods which she would prefer in greater supply and vice-versa, or (2) not to exhaust her budget, even if her utility increases both in her consumption and in the supply of all goods.

1 Introduction

1.1 Motivation

A individual’s spending behavior affects not only the quantities of each good that she herself consumes, but also the total quantities of each good supplied. She may have preferences over all these quantities, and she may optimize her purchasing behavior accordingly. This paper explores a model of general equilibrium in which individuals do so.

Consider, for example, a consumer with concern for animal welfare. The consumer’s utility is increasing in his own meat consumption, holding supply fixed, but decreasing in total meat supply: in the supply of pigs and chickens in particular. The latter effect may, and often does, motivate consumers to purchase less meat than they would otherwise (or none at all).

It bears emphasizing that, despite the well-known result (Roberts and Postlewaite, 1976) that a consumer’s ability to impact equilibrium prices generically vanishes as the economy grows large, her ability to impact equilibrium supply does not. This is because, as the economy grows large and the price impacts of an individual consumer’s demand behavior shrink to zero, any such price impact influences the purchases of a number of other consumers that rises to infinity.

Consider a consumer’s decision to buy one more unit of some good at any given price. Compare (a) the impact of this decision on that good’s equilibrium prices and supply levels in a given economy with (b) the impact of the decision on equilibrium prices and supply levels in a “doubled” economy with twice as many agents but an identical distribution of endowments, preferences, profit shares, and production technologies. In the doubled economy, quantities supplied and demanded at any given price will double:

In the doubled economy, the units on the vertical axis do not change, but the units on the horizontal axis are doubled, as the rightward movement of the demand curve on the page resulting from a one-unit decrease in demand is halved. Thus, if buying one unit of some good causes its production to increase by 0.5 in an economy with, say, one billion participants, it also causes its production to increase by approximately 0.5 in the economy with two billion participants. The size of an “ethical externality” in this sense does not in general fall to zero as price impacts fall to zero and an economy approaches perfect competition.^[1][2]

In light of these ethical externalities, how should an animal-welfare-conscious consumer adjust his demands, relative to what they would be if he had no concern for animal welfare? If he believes that the production of a dollar’s worth of chicken creates more misery than the production of a dollar’s worth of pork, he may naively be inclined to prioritize reducing his purchases of chicken over reducing his purchases of pork. If the supply of pork is more price-elastic and demand for pork less price-elastic than that of chicken, however, this inclination may be misguided. Buying less chicken in this case simply causes the price to fall and the quantity demanded by other consumers to rise, with little net impact on the quantity of chicken consumed. Buying less pork, by contrast, generates a substantial decrease to the quantity of pork consumed. Cutting back on pork may thus be the higher priority.

Complicating matters further, our consumer must consider the impact of his purchases of a good not only on the quantity of that good, but on the quantities of all the goods he cares about. If buying less chicken causes other consumers to substitute to chicken from other meat products, whereas buying less pork causes other consumers to substitute to pork from vegetables, then cutting back on chicken may be the best policy after all.

Though this paper is intended primarily as a model of ethical consumerism, and the precise modeling assumptions made will be tailored to the ethical consumerist context, other agents with preferences over total supply levels also face the motivations and challenges described above. Suppose, for instance, that some goods impose more conventional (i.e. not “ethical”) externalities on a consumer, and that these externalities depend on the goods’ absolute supply levels rather than on supply per person. Then the utility-impacts of the consumer’s contributions to supply are not in general close to zero even when her proportional contributions are small. When she decides what to buy, she too must consider the impacts of her purchases on the equilibrium supply levels of all the goods that impose externalities on her.

This paper aims to characterize, in light of these complications, equilibrium market behavior by “ethical consumers”—and other consumers with preferences over own good-consumption levels and total supply levels—in a competitive production economy. That is, we will study strategic consumer behavior in general equilibrium with externalities.

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Results with relevance to actors in the EA community

Two results are especially relevant from the perspective of informing spending decisions by EAs. They are relevant regardless of whether the spender is an ethical consumer, deciding how to spend both on the basis of (a) how purchases impact total quantities supplied and (b) how much he enjoys consuming the goods he buys, or a pure philanthropist, deciding how to spend only the basis of (a). However, they apply only when the spender constitutes a small share of total spending on each good.

Impacts of expenditures on supply

Proposition 3 characterizes the impact that a given expenditure has on the supply of every good. (See Appendix A.2 for the expression in elasticity terms.) To summarize, suppose there are L goods in the world. Then,

1. Let ε denote the L × L matrix of cross-price elasticities of demand for the goods.
         To interpret this matrix, entry l,k (row l, column k) answers the question: if the price of good k rises by some small proportion (say 1%) and nothing else changes, how many times this proportion does aggregate demand for good l rise? (So if the answer is 2%, this entry of the matrix is 2.)
2. Let σ likewise denote the L × L matrix of cross-price elasticities of supply.
3. The matrix σ–ε will not be invertible, but it will have a certain generalized inverse, denoted (σ–ε)*, such that σ(σ–ε)* is the matrix that maps vectors of purchases to vectors of supply-changes. (Both vectors are of length L.)

The formula hopefully offers guidance about how to turn empirical estimates of price elasticities into best guesses about how spending on one good affects the supply of other goods one might care about. It might likewise form a first step toward guidance about what elasticities it would be most valuable to estimate, and how valuable it would be to estimate them, in order to improve these best guesses.

Anything goes

Proposition 9 says roughly that, subject to some technicalities, for any L × L matrix M you can write down, there is a well-behaved economy—one without any outlandish-seeming preferences or production tradeoffs—in which σ(σ–ε)* = M. For instance, M could flip the sign of every entry of some vector: buying less chicken could cause there to be more chicken produced, funding more of some kind of research could cause there to be less of that kind of research produced, and so on, all at once.

To illustrate how this can happen, suppose chicken is an inferior good for the chicken producers. They are currently eating chicken because it is cheap, but as they get richer, they tend to substitute to beef. Then if buying chicken makes chicken producers a bit richer, and if this wealth effect is strong enough, buying chicken reduces chicken supply on balance.

This result is rather unfortunate. It would have been encouraging to find that we had stronger reasons from first principles to believe that our altruistic efforts will not altogether backfire. Instead, we find that whether they backfire or not depends on the empirical questions about price elasticities outlined in the section just above.

One possible takeaway is that empirical work in this domain is more valuable than it might otherwise have seemed. Another is that, at least until the empirical questions have been answered, efforts to affect quantities by direct spending—i.e. via ethical consumerism and donations to charity—are somewhat less predictable than they might have seemed, and so perhaps it would make sense to shift philanthropic resources marginally from “direct spending” efforts to efforts to influence policy. At least in some domains, the effects of policy are less vulnerable to these sources of unpredictability: banning factory farmed chicken, for instance, seems very unlikely to raise its supply.

1. ^{^}

   Kaufmann et al. (2024) offer survey evidence that many consumers believe that their consumption decisions affect supply (either one-for-one or, as in Figure 1, partially but significantly), and summarize the literature that many consumers do in fact have ethical preferences over the aggregate supply of some goods strong enough to motivate non-negligible shifts in consumption.

2. ^{^}

   Note that this insight comes out only when we define competitive behavior in the usual way, as the limit of behavior across economies with finite but ever larger populations. Under the Aumann (1964) approach of modeling the population as a continuum, demand choices by individuals do not affect prices or supply.