Collateral caps and market equilibria under adverse selection

We study a competitive credit market with adverse selection, capacity-constrained banks, and an exogenous cap on pledgeable collateral. Our main contribution is to show how, in a capacity-constrained Bester – Rothschild – Stiglitz environment, an exogenous cap on pledgeable collateral changes the structure of the separating equilibrium set. When a binding collateral cap rules out the standard zero-profit separating allocation, the model admits a continuum of separating equilibria in which risky borrowers choose zero-collateral contracts, safe borrowers choose contracts with the maximum allowed collateral, and interest rates vary within a bounded interval. Banks earn strictly positive expected profits in most equilibria – even in a one-period game. We also show that an interest-rate ceiling truncates the equilibrium set by capping the risky-type interest rate, highlighting a rationale for considering maximum rate policies when collateral limits bind. Finally, we discuss how bank entry affects outcomes: as the number of banks grows, profits on risky types vanish, but rents on safe types persist because collateral caps continue to preclude profitable screening.