Optimal Capital and Labor Investment in Price Regulated Service Firms

Akan M., Geçici E.

Haliç Üniversitesi Sosyal Bilimler Dergisi, vol.4, no.1, pp.1-15, 2021 (National Refreed University Journal)

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1
  • Publication Date: 2021
  • Title of Journal : Haliç Üniversitesi Sosyal Bilimler Dergisi
  • Page Numbers: pp.1-15


Optimal investment behavior of a price-regulated service firm which faces a fluctuating demand curve, and whose price is determined by governments and municipalities, is studied through the use of the Optimal Control Theory. The aim of our study is to analyze the behavior of the firm when faced with the expected dynamic demand curve, and also to explain the inefficiencies of the firm in terms of machinery and labor. The firm is required to meet the demand at all times. Cobb-Douglas type of demand function is utilized in the analyses where both labor and capital are assumed to be quasi-fixed factors of production. Constant Elasticity of Substitution type of production function is also used in this analysis resulting in similar results. The rates of change of demand, the attrition rate of labor, and the depreciation rate of capital are the primary factors determining the optimal behavior. In other words, as long as the effect of the loss of capacity on capital and labor is greater than the decrease in demand, the investor will continue to invest in factors of production. The switching times between periods when investment in both factors is zero, when investment in capital is zero, and when investment in labor is zero are determined allowing better planning of maintenance periods of machinery and vacation planning.