We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion...

This paper endogenizes the borrowing constraints on capital in a production economy with incomplete markets. We find that these limits get looser with income, a property that is consistent with US data on credit limits. The framework with endogenous limits is then used to study the effects of a...