Abstract
The paper considers a household family comprising of husband, wife and their child. Each parent consumes a private good and contributes voluntarily for a household public good which is child’s welfare. When divorce occurs, the court has an ex ante transfer mechanism for the parents such that truthful revelation of valuation of child’s welfare by each parent becomes strategyproof. Based on this, the sole custody of child is assigned to the parent having the highest value. We find that the transfer mechanism of the court fails to satisfy ex post individual rationality of some types of the parents. We also show that the court’s mechanism bundled with an appropriate child support order achieves higher child’s welfare and satisfies individual rationality only if the non-custodial parent is extremely altruistic in nature. Thus the paper successfully explains widespread prevalence of non-payment of child support from a perspective which was not discussed previously. More significantly, the paper ends with a policy prescription of replacing the conventional child support system by an equivalent amount of transfer from the government to the custodial parent, and shows that it has the potential to correct the intrinsic loopholes of child support.
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Notes
See OECD Family Database, OECD—Social Policy Division, Directorate of Employment, Labor and Social Affairs at http://www.oecd.org/els/family/database.html for details.
Le Bourdais et al. (2016) observed that in Canada on separation; previously married women suffered a larger decline in income as compared to cohabiting women. It was partly due to the non-inclusion of child support in women’s income tax returns. This particular policy made the divorced women having many children worse off even when they were more likely to receive child support payment from their ex-husbands. This is in contrast to the observation of Tach and Eads (2015) for the US. The economic consequences of divorce have declined due to the growth in married women’s earnings and their receipt of child support and income from personal network. On the other hand, economic consequences of cohabitation dissolution have worsened over time.
Ideally, parents contribute voluntarily both time and money which jointly determines the level of child’s welfare. But if we consider both the inputs in child’s welfare production function then the equilibrium contribution amount becomes indeterminate. We find a mention of such problem in Sanyal and Mukherjee (2019). Hence the paper considers only monetary contribution as an input to child’s welfare.
I thank the Reviewer for attracting my attention to this issue.
By valuation we mean the ‘willingness to pay’ for child’s welfare or the ‘marginal utility’ derived from its consumption. Naturally, a parent who is more caring will also have higher willingness to spend for child’s welfare.
In our model, the marginal utility derived from child’s welfare is unobserved by the third party. The conventional way of modeling such situation is to assume marginal utility as a parameter, which is possible only if the utility function is linear in child’s welfare. On the contrary, if we assume a general utility function of the form \(u^{i} = u^{i} (G,c_{i} )\) then we have \(\frac{{\partial u^{i} }}{\partial G} = u_{G}^{i} (G,c_{i} )\). Since \(G = g_{i} + g_{j}\), and \(g_{i}\) depends on \(i's\) valuation and \(g_{j}\) on \(j's\) valuation so we have a situation where \(i's\) marginal utility from child’s welfare depends on how \(j\) values it and vice versa. Now, this situation is inconsistent as the value of a good to an individual depends solely on his/her perception and is strictly independent of how other individual values it. Thus, following these arguments we find that single-peaked preference pattern represented by a quasi-linear utility function fits best in the model.
Apart from assignment of child custody, determination of optimal visitation time of the non-custodial parent is also another decision problem. For that we need to have time as another input into the child’s welfare production function. Since, we consider monetary contribution as the only input so the paper does not endogenously determine the optimal visitation time. Rather we develop the model for a given amount of visitation time.
In this paper we consider only the case of sole physical and legal custody.
Although efficient custody allocation decision is not contingent on the announcement of \(\alpha_{i}\) and \(\alpha_{j}\) by the respective parents, but an appropriate strategyproof mechanism eliciting true values of the parents for child’s welfare would require prior knowledge of \(\alpha_{i}\) and \(\alpha_{j}\).This will be evident later in Sect. 2.2.1.
In the theory of mechanism design, it is generally assumed that a mechanism designer is endowed with unlimited resources to incentivize individuals to implement the socially efficient outcome. In our paper, we take court as the mechanism designer. It immediately raises a vital question: since court is not a revenue raising authority so is it possible for it to finance such transfer mechanism? In this context we can argue that the government of every country has a concern, in particular, for the welfare of women and children. So it can allocate a fraction of its budget to finance this mechanism through the family court.
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Acknowledgements
I thank Prof. Vivekananda Mukherjee, Department of Economics, Jadavpur University, Kolkata, India for very helpful discussions. I am also grateful to two anonymous Reviewers of the journal whose insightful comments and suggestions have enriched the paper immensely. However, the usual disclaimer applies.
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Sanyal, T. A mechanism design approach to child custody allocation in divorce. Eur J Law Econ 47, 389–406 (2019). https://doi.org/10.1007/s10657-019-09618-5
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DOI: https://doi.org/10.1007/s10657-019-09618-5