Optimal self-financing microfinance contracts when borrowers have risk aversion and limited commitment

This paper examines optimal lending contracts between a single not-for-profit lender and a continuum of risk-averse borrowers, where the lending relationships are continually created and destroyed. The lender self-finances its costs via income from loans, while borrowers can walk away from the current relationship in any period and search for a new relationship. We characterize the optimal allocation by formulating the lender’s problem of maximizing social welfare and by resorting to a variational argument that takes into account the limited commitment problem and the endogenous outside option values of the borrowers. In the benchmark case of the Benthamite social welfare function, we find that the optimal stationary allocation exhibits novel consumption dynamics: Borrower consumption begins at a relatively low level, converges toward a particular level when the participation constraint is slack, and jumps up when the participation constraint binds. We then explore the role of limited commitment in generating such consumption dynamics and discuss the associated repayment profile.