A simple General Constrained Dynamics (GCD) model for demand, supply and price shocks

In economics balance identities as e.g. C+K'-Y(L,K) = 0 must always apply. Therefore, they are called constraints. This means that variables C,K,L cannot change independently of each other. In General Equilibrium Theory (GE), the solution for equilibrium is obtained as optimisation under the above or similar constraints. The standard method for modelling dynamics in macroeconomics are Dynamic Stochastic General Equilibrium (DSGE) models. Dynamics in DSGE models result from the maximisation of an intertemporal utility function that results in the Euler-Lagrange equations. The Euler-Lagrange equations are differential equations that determine the dynamics of the system. In Glötzl, Glötzl, und Richters (2019) we have introduced an alternative method to model dynamics, which is constitutes a natural extension of GE theory. It is based on the standard method for modelling dynamics under constraints in physics. We therefore call models of this type "General Constrained Dynamic (GCD)" models. GCD models can be seen as an alternative to DSGE models to model the dynamics of economic processes. DSGE models are used in particular to analyse economic shocks. For this reason, the aim of this article is to show how GCD models are formulated and how they can be used to model economic shocks such as demand, supply, and price shocks. Since the goal of this paper is to lay out the fundamental principles to the formulation of such GCD models, very simple macroeconomic models are used for illustrative purposes. All calculations can easily be carried out with the open-source program GCDconfigurator, which also allows for the integration of shocks.