Allocation rules on networks

When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and an agent depicts the possibility of a transfer from the source to the agent. Given the supplies at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that for each pair of citizens in the network, the extension is robust with respect to the fairness principle. We call this condition pairwise robustness with respect to the fairness principle. We provide an algorithm and show that each fairness principle has a unique extension which is pairwise robust with respect to the fairness principle. We give applications of the algorithm for three fairness principles: egalitarianism, proportionality and equal sacrifice.

Gender differences in time allocation of poor children in Colombia

This paper studies the effect of credit constraints and constraints on transfers between parents and children, on differences in labor and schooling across children within the same household, with an application to gender. When families are unconstrained in these respects, differences in labor supply or education are driven by differences in wages or returns to education. If the family faces an imperfect capital market, the labor supply of each child is inefficient, but differences across children are still driven by comparative advantage. However, if interfamily transfers are constrained so that parents cannot offset inequality between their children, they will favor the human capital accumulation of the more disadvantaged child -generally the one who works more as a child. We use our theory to examine the gender gap in child labor. Using a sample of poor families in Colombia, we conform our predictions among rural households, although this is less clear for urban households. The gender gap is largely explained by the wage gap between girls and boys. Moreover, families with the potential to make capital transfers to adult children (e.g. those with large animals), can compensate adult sons for their greater child labor and reduced educational attainment. In such families, as predicted, the male/female labor gap is greater.