Another motivation for gift-giving, perhaps a more natural one in the eyes of people from countries with well developed markets, is to consider the idea that persons have altruistic feelings towards each other. Within the economic
method-5There can still be inefficiency in that everybody could be made better off if all people would enter the market or all would stay in their gift exchange. This is due to the existence of externalities that are present in the model.
6This is partly due to the assumed tit-for-tat strategy of the players. But it seems that this or any such strategy where the cheater is ultimately punished is reasonable.
ology, this can be modeled as individuals having either preferences for the con-sumption level or the utility level of other individuals. The structure of a utility function that represents such preferences is given by Ui = Ui(xi, Uj(xj)), where xi
is the consumption level of person i. If person j has altruistic feelings for person ias well, there is an infinite regress: Ui = Ui(xi, Uj(xj, Ui(xi, Uj(...)). The regress easily becomes an unbounded process but Becker [1974] shows an example where it is not. For example, consider the utility function:
Ui = xαiUjβ. (2.1)
Then the reduced form of the utility function follows straightforwardly by sub-stitution and is given by:
Altruistic feelings will take care of a redistribution such that an optimal bal-ance results between personal consumption and consumption of the other. If the endowment of a particular individual is in his view relatively too high, he can gain by giving some of it to the others. Existence of gift giving can therefore be rationalized.
There are several aspects of this model with respect to efficiency that are note-worthy. First, the equilibrium allocation is generally not efficient because neither one of the players acts like a social planner despite their altruistic feelings. To see this, consider player i being altruistic towards j but not vice versa. Note that player i maximizes Ui by setting xi such that:
dUi
whereas a social planner would set xi such that:
dUi
In other words, the social planner counts player j twice: once because player j has his own utility, and one more time because player i derives utility from him.
In general, this means that the optimal choice of xi by player i differs from that by the social planner.
Within a family context, Becker [1974] has shown that an altruistic head of the family internalizes externalities within the other selfish family members by the
appropriate transfers (the ’rotten kid theorem’). However, this efficiency result is somewhat special (Bernheim and Stark [1988]). In particular, altruism can create inefficiencies, such as is the case in the ’Samaritan’s dilemma’. This dilemma concerns the problem that if a recipient knows that he will be helped out by an altruist, he has less incentives to, say, self-discipline himself by saving money for the future (Bernheim and Stark [1988] provide a more detailed discussion).
Another, related, efficiency result is obtained by Kranich [1994]. Suppose some players have preferences over the entire allocation of the economy, rather than just one’s own consumption level. This can be due to altruism, but also to a preference for fairness. In this case, Kranich proves that the set of Pareto-efficient equilibria is a subset of the set of all gift equilibria. In other words, the equilibrium that results when agents can freely redistribute endowments need not be Pareto-efficient. This can possibly be caused by the public good character that gifts can take. One can think of a case with three players. Would players 1 and 2 both give to a third player everybody may be better off, but if either one of the players gives then it is not profitable anymore for the other to give7.
Let us now consider the question whether altruism can account for reciprocity.
With only one good, the answer is negative.8 If we consider more goods, however, one can easily see that a recipient may indeed have an incentive to reciprocate.
If the endowments are sufficiently different between persons, they may all gain by redistributing, very much like the logic of international trade models. With altruistic feelings, this redistribution may be accomplished without further moti-vations, since each player gains indirectly by giving part of his or her endowment to another person who would be made better off.
Concerning adequacy, however, we see that altruism as a motivation to give is incongruent with giving in kind. Any cash gift would make the recipient bet-ter off9, without changing one’s own consumption, and it therefore necessarily increases one’s own utility. Hence we conclude that altruism alone is not a good
7Goldman [1978] puts less restrictions on preferences and finds that in that case the reverse also holds:
Pareto-efficient equilibria need not be gift-equilibria. It is for example possible that a gift from person 1 to person 2 may decrease the welfare of person 3 (because he cares, say, about the consumption level of person 1), hence moving away from a Pareto-efficient situation.
8This is true because in equilibrium it must be the case that if player 1 gives to player 2, player 2 has no incentive to give back. For suppose he has, then his utility from giving some of the good to player 1 must increase. But then player 1’s utility should also increase, since the utility of player 2 increases and his own consumption as well. This would contradict player 1 playing an equilibrium strategy.
9With the exceptions mentioned earlier.
candidate to explain most of the situations where gift-giving takes place, as it cannot explain the widely observed inadequacy of gifts. Still, there is at least one important situation where altruism cannot be excluded, namely that of charity.
Empirical studies are indeed supportive of the view that altruistic motives lie be-hind charity, although these studies at the same time demonstrate that altruism alone cannot be the unique motivation (see section 2.3.4 for more on this).