Abstract
In this chapter, we analyze resource allocation within families, especially the transfer of resources between parents and children. What is the difference between a parent-children relationship and an ordinary relationship between humans? It can be explained by love or the “altruism” of parents towards their children. Parents’ altruism towards their children can be well understood from the biological and evolutionary viewpoints.
[T]ell me which one of you loves me most, so that I can give my largest gift to the one who deserves it most.
Shakespeare, W. King Lear. [I-1]
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Notes
- 1.
We can observe resource transfer between spouses and among siblings. Some analyses examine resource transfer between husbands and wives, as suggested by our discussion in Sect. 4.3. However, very few analyses investigate resource transfer among siblings, suggesting that their relationship does not have special characteristics, except for the general rivalry and battle for the love and wealth of their parents, as suggested by Shakespeare’s King Lear and the story of Cain and Abel in the Old Testament. See Sect. 5.2.3 for the discussion on strategic bequest motives and their effects on the relationships among siblings.
- 2.
See Cartwright (2000, Chap. 10) for considerations on the parent–children relationship from the perspective of the biology.
- 3.
The proposition is slightly different from the original one in Becker (1974), but let us show the essence of the Rotten-Kid Theorem by considering a simple sufficient condition in the proposition.
- 4.
Imagine a mountain whose contours can be drawn as the indifference curves labeled as \(P_1\), \(P_2\), and \(P_3\).
- 5.
Although it is assumed in Fig. 5.2 to be a simple line where \(c^*_k(a) = c^*_k\) for all a, it does not have to be such a line, in general.
- 6.
Note that the child is assumed to choose \(a^{**}\) because its utility is the same as that at B, that is, the minimum utility. If the parent wants to choose the action \(a^{**}\) for sure, the parent can increase the bequest slightly so that the utility of the child becomes strictly higher than the minimum.
- 7.
The credibility of the parent giving the bequest to the child may be in question. However, we assume here that it is credible because the legal system will allow the parent to commit to the statement. That is, the legal system works as the commitment device for the parent. See Remark 3.8 for the discussion on the credibility of the threat and the commitment.
- 8.
\(P^\prime (e)\) and \(P^{\prime \prime }(e)\) represent the first derivative and second derivative of the function P. We use the similar notations below.
- 9.
For simplicity, we assume that the child’s utility will not be discounted. Even if we consider the “inter-cohort discount factor,” as long as it is close to one, we can get the same results as those obtained here.
- 10.
We can derive the equation as follows. First, we rewrite the basic budget constraint as \(c^t_2 + d^t = y^t - c^{t+1}_1 n^t\), and using the definition \(\rho ^t \equiv {d^t \over c^t_1}\), we derive \(d^{t} = \rho ^t c^t_1\) and \(c^{t+1}_1 = {d^{t+1} \over \rho ^{t+1}}\). By substituting them, we have \(c^t_2 + \rho ^t c^t_1 = y^t - {d^{t+1}n^t \over \rho ^{t+1}}\). Now, as we have \(c^t_3 = d^{t+1}n^t\), dividing both sides by \(\rho ^{t+1}\) and adding them to both sides of the budget constraint above, we have \(\rho ^t c^t_1 + c^t_2 + {c^t_3 \over \rho ^{t+1}} = y^t\). Finally, by dividing both sides of the equation by \(\rho ^t\), we have Eq. (5.5).
- 11.
The problem will be especially serious when the traditional norm of children supporting their parents breaks down in the process of economic development.
- 12.
In a simple model with perfect capital markets, child allowance and the policy to reduce the pension payment when an individual has a smaller number of children are the same. However, there are many people who agree with the former policy and disagree with the latter. From the perspective of policy design, it is interesting to see that people indicate different attitudes towards policies that are essentially equivalent.
- 13.
In the model, it is assumed that the taxation to finance the child allowance does not have any distortionary effect.
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Yamashige, S. (2017). Resource Allocations within Families. In: Economic Analysis of Families and Society. Advances in Japanese Business and Economics, vol 16. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55909-2_5
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