Dynamic costs and moral hazard: A duality-based approach

The marginal cost of effort often increases as effort is exerted. In a dynamic moral hazard setting, dynamically increasing costs create information asymmetry. This paper characterizes the optimal contract and helps explain the popular yet thus far puzzling use of non-linear incentives, for example, in sales-force compensation. The result is obtained by complementing the standard dynamic program with a novel dynamic dual formulation. The dual program is monotonic and sub-modular, providing stronger results, including a proof for the sufficiency of one-shot deviations.