A model of incentive wages as an optimal control problem

This articles considers a «shirking» model under the theory of efficiency contracts, which determines the profile of a worker's individual wages depending on his experience. The profile is a stimulating condition to increase productivity and the period of employment. Certain additional assumtions reduce the model to a nonclassical variational problem or a linear optimal control problem. We prove nonemptiness criteria and the existence of solutions, find necessary and sufficient conditions for optimality, give an algorithm to solve the problem, and present the results of simulations.