Price Search, Consumption Inequality, and Expenditure Inequality over the Life Cycle

In this paper, we incorporate price search decision into an otherwise standard life-cycle model withincomplete markets and an endogenous labor supply, differentiating consumption from expenditure. In our model, consumers can allocate part of their time to searching for low prices, and this leads to an endogenous price dispersion. We have three contributions. First, we analytically study the determinants of price search and its relation to consumption and expenditure inequalities in a static model. Second, we study quantitatively the role of price search in a dynamic version of the model. A plausible calibration implies that the life-cycle increase in the cross-sectional variance of log consumption is about 40 percent lower than the increase in the cross-sectional variance of log expenditure. Third, we show that price search provides an additional quantitatively significant partial insurance mechanism against adverse income shocks.