Optimal Control of Investment, Level of Employment and Stockkeeping

Abstract

Numerical simulations of microeconomic processes usually suffer from poor models and therefore often can not exhibit real phenomenons. We present a new, very complex model of an enterprise — deduced from the model of Lesourne at al. (1978) and Feichtinger at al. (1986), see Koslik et al. (1993) — including own capital distributed among the enterprise (part X) and alternative capital assets (part X _m ), outside capital Y, level of employment L a stock S and a submodel with production and selling. The interest rate for outside capital ρ_k and the interest rate for alternative own capital assets ρ _m are taken from the real values of the last ten years (May 1983 to May 1993)². For the inflation i we take i := ρ _m −0.05. For the own capital X the management of the enterprise has to pay a risk premium ρ _{r, 1} X or ρ _{r, 2} X dependend on the risk of the business.

This research has been supported by the Deutsche Forschungsgemeinschaft within the project “Anwendungsbezogene Optimierung and Steuerung” and by the Bavarian Consortium on High Performance Scientific Computing (FORTWIHR)