Objective:

This paper is aimed at developing a stochastic microeconomic model useful to explain the behavior of a mother as the only participant in family spending.

Methodology:

In the proposed model, the mother has subsistence consumption subject to two constraints, the first one considers an uncertain income joint with savings deposits when there is a surplus, and the second one consists of her consumption habit (or routine).

Scope:

Through the proposed model, we determine the optimal proportion of income allocated to savings if the mother has a surplus, the hours devoted to labor, and the optimal strategy for future consumption.

Results:

Through a VAR model, it is shown empirical evidence, for the Mexican case, which confirms the results of the theoretical proposal by using data from consumption, wages, and the total number the single mothers, among other relevant variables, from 2005 to 2016. To do this, we examine Granger causality by means of the Toda-Yamamota procedure and analyse impulse-response functions. We also study the effect of the interest rate stability on the consumption of the head of the family during the period 2009-2017.

Conclusions:

The concept of habit formation plays a fundamental role in the decision making of the mother as head of the family since her past consumption does influence her future consumption.