Optimal wage payment strategy

Abstract

The article analyzes an economic model that describes the company development dynamics with management. The goal is to develop an optimal strategy for paying wages to the company’s employees maximizing the company’s capital over a certain period of time. The model is built on the basis of a first-order differential equation that connects the company development dynamics and the utility and wage functions. The function describing the costs associated with paying salaries to employees depends on time, the total capital of the company and the parameter of the control action, which takes values in the interval [0, 1]. It is an adapted modification of the Cobb-Douglas production function, in which the total capital of the company is used as capital, and the initial capital of the company is used as labor resources. The optimization model is presented as an optimal control problem with a free right end. This model formulation is new and has not been previously considered in the literature. Pontryagin’s maximum principle was applied to solve the case. Three cases of the optimal control specifying as a piecewise constant function over the entire time interval were studied: control equal to zero, control equal to one, and taking an arbitrary value from the interval [0, 1]. This made two paying wages strategies comparing possible: constant and proportional to the company wherewithal. The conducted studies have shown that the optimal control choice depends on the relationship between the inflation factor, the proportionality coefficient and the initial company’s capital. Conditions were obtained when the employees wages payment should occur at a constant level; otherwise, wages should be set in proportion to the capital of the company since if the conditions are not met, wages payment oat a constant level leads either to the complete ruin of the company or the level of capital drops to a lower level. The presented work obtained the conditions for the stationary solutions emergence, when, with any management, the company capital will remain at the initial one. Some of the research results were presented at conferences [1, 2].