Analytical Solution of the Dynamic Incentive Problem with Consideration of the Learning Curve Effect

The article explores the dynamic incentive problem of workers of the industrial firm in continuous time with the learning curve effect. The initial dynamic problem of financial incentives was reduced to the optimal control problem. The problem of optimal control with continuous time was solved analytically using the Pontryagin maximum principle. As a result of the study, the choice condition for the optimal production volumes was found. The optimal production volumes for any model of the learning curve at each point in time should be chosen inversely to the labor intensity of the product and directly to the discount rate. In the absence of discounting: the optimal production volumes for any model of the learning curve at each point in time should be chosen inversely to the labor intensity of the products. The formulae were obtained for optimal production volumes, cumulative production volumes and agent labor costs for power and exponential learning curve models.