An Analytic Solution to a Stochastic Consumption/Saving Problem with Liquidity Constraints

An analytic solution is obtained for a 3-period consumption-savings model with uncertain income and liquidity constraints. The results show that liquidity constraints induce precautionary saving and excess sensitivity by an optimizing individual. These 2 phenomena occur jointly, because both arise from the consumer's desire to avoid having liquidity constraints in the future. The analytic solution is also used to show how consumption-saving behavior changes with variations in model parameters and to characterize the threshold level of wealth at which the liquidity constraint becomes irrelevant. The results may also help in analyzing the effect of credit market imperfections on the economy and on the effectiveness of tax and debt policy in an overlapping-generation-type model.