The Economics of Altruism

One of the things humans value is the welfare of other humans, most obviously their children but often other people as well. How can we fit that fact into economic theory?

Gary Becker offered an answer,¹ an economic theory of altruism. His model does not fit all altruistic behavior, as we will see, but it incorporates altruism into economics with a single, simple, assumption that produces an evolutionary explanation for why altruism, including non-kin altruism, exists.

The Model

Economists represent the preferences of an individual by his utility function, a list of what he values and how. If bundle of goods A has a higher utility for him than bundle B that means that, given the choice, he would choose A over B. Becker’s assumption is that one of the items in the utility function of an altruist is the utility of another person.

That assumption narrowly constrains the form of altruism it describes, since it means that what the altruist wants for his beneficiary is whatever the beneficiary wants for himself. That does not describe all behavior that might be described as altruistic; we can imagine someone, perhaps a parent, wanting for his beneficiary not what the beneficiary wants but what he should want, what the altruist believes is good for him. But by constraining the effect of altruism on the altruist to a single extra variable instead of many it produces a theory with interesting implications.

One of them is that it is in the self-interest of the beneficiary to care about the welfare of the altruist.

To show why, I simplify the problem by limiting the altruist’s ability to help the beneficiary to transfers of money, a simplification I will later drop. The altruist has an income I_A, the beneficiary I_B. The altruist, who gets utility both directly from his own consumption and indirectly from the consumption of his beneficiary, divides the combined income, I_A+I_B, between them in the way that maximizes his own utility. As long as a dollar of additional consumption by the beneficiary is worth more to the altruist than a dollar more of his own consumption, it is in his interest to transfer another dollar.

If the altruist values additional consumption by the beneficiary more than his own additional consumption, he transfers income to the beneficiary. Because of declining marginal utility — of the altruists own consumption to him, of the beneficiary’s consumption to him, and of the beneficiary’s utility to the altruist — each dollar the altruist transfers increases the value to him of each dollar of his own consumption, decreases the value to the beneficiary of a dollar of the beneficiary’s consumption, decreases the value to the altruist of a utile of the beneficiary’s utility. The process stops when the value to the altruist of the increase in the beneficiary’s utility due to another dollar of consumption by the beneficiary gets down to the value to him of a dollar of his own consumption.

If at the initial incomes a dollar spent on himself is worth more to the altruist than a dollar spent on the beneficiary, there is no transfer.

Suppose the altruist’s income goes up. If he keeps the amount transferred to the beneficiary the same and spends the money on himself the value of the last dollar of his consumption goes down, making it lower than the value to him of the increased utility from another dollar of the beneficiary’s consumption, so he increases his utility by increasing the transfer.

Suppose the beneficiary has an opportunity to do something that increases the altruist’s income. It is in his selfish interest to do it, because after the altruist has adjusted the amount he is transferring the beneficiary will be better off. Suppose the beneficiary has an opportunity to do something that costs him a thousand dollars but increases the altruist’s income by two thousand. That will increase the summed income that the altruist, by his transfers, is dividing between the two of them, making beneficiary as well as altruist better off — provided only that the altruist is already making some transfer. As long as we only consider situations in which the altruist chooses to make some transfer, changes in the combined income of altruist and beneficiary have the same effect on the consumption of both whether they change the altruist's income or the beneficiary's income.

The beneficiary, if he understands this analysis, will find it in his interest to pay as much attention to maintaining the income of the altruist as to maintaining his own. In this respect, the beneficiary ends up acting rather as though he too were an altruist — even though he is actually indifferent to the altruist's welfare.

The generalization of the result, still subject to the condition that we only consider situations in which some transfer occurs, is that it is in the interest of the beneficiary to take any action that produces net gains to himself plus the altruist, in exactly the same sense in which we discussed net gains in the context of Marshall efficiency in an earlier post. Any change that is a Marshall improvement will also be an improvement for the beneficiary. A change that benefits the altruist by the equivalent of $5 and hurts the beneficiary by the equivalent of $3 will result in the altruist increasing his transfer to the beneficiary by at least $3 and less than $5; a change that injures the altruist by $5 and benefits the beneficiary by $3 will result in a reduction of the transfer by something between $3 and $5.

Your response to this result may be that it is not surprising; if the beneficiary hurts the altruist, the altruist punishes him by reducing the transfer, so the beneficiary finds it in his interest not to offend his patron. That is not what is happening. Nothing in the argument depends on the altruist knowing that the beneficiary is responsible for the change. Exactly the same thing will happen in the case of a change produced by some third party or by nature. If the change is a Marshall improvement, both beneficiary and altruist end up better off after the change and the resulting change in the amount the altruist chooses to transfer. If it is a worsening, both end up worse off.

The Rotten Kid Theorem

Consider a situation with one altruist ("parent") and two beneficiaries ("kids"). One of them is a rotten kid who would enjoy kicking his little sister. The analysis I have just described implies that if the dollar value to the rotten kid of kicking his sister (the number of dollars worth of consumption he would, if necessary, give up in order to do so) is less than the dollar cost to the sister of being kicked, the rotten kid is better off not kicking her. After the parent has adjusted his expenditure on the kids in response to the increased utility of the kid and the decreased utility of the kicked sister, the rotten kid will have lost more than he has gained. Here again, the argument does not depend on the parent observing the kick but only on his observing how happy the two kids are.

This result, that a rational rotten kid properly allowing for the effects of parental altruism will find it in his self-interest to kick his sister only if it is efficient to do so, is the Rotten Kid Theorem. Because of the altruist's peculiar utility function, which contains the beneficiaries' utilities among its arguments, both altruist and beneficiaries find it in their private interest to maximize Marshall efficiency, to make decisions according to whether the net effect on altruist and beneficiaries is or is not a Marshall improvement.

Altruism and Evolution

Gary Becker, whose ideas I have been describing, has proposed them as a solution to one of the puzzles of evolutionary psychology: the existence of altruism. If, as the theory of evolution implies, we have been selected by evolution for our ability to serve our own reproductive interest (roughly speaking, to act in such a way as to have as many descendants as possible), those who sacrifice their interest for the interest of others should have been selected out. Yet altruism seems to occur among a variety of species, including our own.

One explanation is that altruism toward kin, most obviously toward one’s children but the argument applies to other relatives as well, is not really altruism from the point of view of evolution; I am serving my reproductive interest by keeping my children alive so that they can have children. This still leaves altruism toward non-kin as a puzzle to be explained.² Becker's explanation is that altruism generates cooperative behavior via the mechanism described above, benefits the altruist as well as the recipient by giving each recipient an incentive to behave efficiently vis-à-vis the entire group. A group containing an altruist will be more successful than one that does not, will have more surviving descendants, so its genes, including the genes for altruism, will become increasingly common.

Although the altruist is promoting the reproductive success of his group vis-à-vis other groups, he is also sacrificing his own reproductive success vis-à-vis other members of his group since he is transferring resources from himself to them. If Becker's analysis is correct, genes for altruism should become less frequent over time within groups containing one or more altruists, but the genes of such groups should be becoming more frequent over time; only if the second process at least balances the first will altruism survive.

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1. In “A Theory of Social Interactions.”

2. An alternative explanation is that we evolved in environments where most people we interacted with were kin, making altruism towards non-kin an evolutionary error. Arguably our current behavior towards our outgroup is the survival of the pattern evolved for interacting with non-kin.