Consumption with liquidity constraints: An analytical characterization

Abstract

How do liquidity constraints affect households? This is a well-researched subject with remarkably few theoretical results. This paper bridges this gap by providing a closed form expression for consumption with liquidity constraints for a wide class of utility functions (HARA). Using this expression, I prove that the consumption function is strictly concave in wealth if a relevant liquidity constraint exists. Moreover, households respond to a tightening of the liquidity constraint by reducing consumption, becoming more sensitive to wealth changes, and having a “more” concave consumption function in wealth. These results thus provide theoretical underpinnings for how contractions in credit supply affect households