On borrowing limits and welfare

We study the effect of borrowing limits on welfare in several versions of exchange and production economies. There is a "quantity" effect of a larger borrowing limit which is beneficial for liquidity constrained agents, but essentially irrelevant otherwise. There is also a "price effect" which tends to increase the interest rate so that lenders are better off and borrowers are worse off. The combination of these effects produces that aggregate welfare in equilibrium (or ex ante welfare) displays an inverted U-shape as a function of the borrowing limit. In infinite horizon economies with incomplete markets we find a sizable "middle class" of not liquidity constrained but indebted agents that observes small gains, or even loses, after the borrowing limit is enlarged.