A note on separability and intra-household resource allocation in a collective household model

This paper shows that it is possible to track the changes in the distribution of power within a couple by focusing on the changes in the pattern of private consumption when the consumption decisions are efficient and private consumption is separable from public consumption in individual preferences. We first show that the separability of private consumption from public consumption at the individual level carries over to the household level. Hence, changes in public consumption only matters through a change in the residual budget available for private consumption. When the consumption decisions within the household is efficient, private consumption decisions can be modeled as the solution of a problem consisting in maximizing a weighted sum of the private-consumption sub-utility functions of the spouses under the residual budget, the weights being unique and representing the distribution of power over the allocation of private consumption. The model presented in this paper can be used to analyze the changes in the household resource allocation due to, for example, childbirth.