Model of the Manufacturer’s Behavior when Obtaining Loans and Making Investments at Random Moments in Time
This study considers the problem of a firm, which makes decisions regarding investments, production, and payment of dividends to the owners of the firm in conditions of uncertainty in the timing of the transactions. The task is set for the manufacturing agent on a finite planning horizon. The approach used to solve the optimal control problem arising in the economic model is based on the method of Lagrange multipliers. Sufficient optimality conditions are formulated and a system of partial differential equations with a shift that determines the solution of the problem is derived. The solution to this system is obtained in the case of constant prices and interest rates, and in the general case, approximate solutions are obtained at a high transaction frequency. It shows the specifics of the problem compared to the problem on an infinite horizon due to the presence of a boundary layer in which the analysis can significantly change compared to the analysis of the solution within the planning horizon. This model might be used as a block of a manufacturing agent in applied modeling of the computable intertemporal equilibrium of a country’s economy.