Price search, consumption inequality, and expenditure inequality over the life-cycle

In this paper, we differentiate consumption from expenditure by incorporating price search decision into an otherwise standard life-cycle model. With this extension, households can pay lower prices for the same consumption good if they allocate more time for price search. We first analytically show that under very general conditions, poorer (in both income and/or wealth) households search more and pay lower prices compared with wealthier ones. As a result, consumption inequality is smaller than expenditure inequality, and the gap between them increases over the life-cycle. Next, we quantify these mechanisms by calibrating our model to the US data. We find that the life-cycle increase in consumption inequality is about 30 percent lower than the increase in expenditure inequality. We also show that the availability of a price search option provides a large insurance mechanism against adverse income shocks and increases the welfare of a new born by 3.9 percent in consumption equivalent terms.