Structure, applications and limits of dynamic production functions of the firm based on the input-output approach

Central to dynamic models is the concept of variables that refer to different instants and periods of time. Thus, formulating a dynamic model becomes necessary if the production environment changes in the course of time and if its current state affects the production with a delay. Such changes can mainly be traced back to fluctuations in demand as well as in the duration and connection of multistage production processes. This article shows different ways to formulate dynamic production functions. Primarily it is a contribution to production theory. In the second place it is an approach to production planning in order to forecast material requirements for different periods and intervals as well as the need for human and machine labor. A complete representation of the production process had to be extended into (at least) four dimension: the kinds of goods, their quantities as well as their arrangement in time and in space. Static production models generally represent only the relations between types and quantities of goods. Dynamic production models take the time dimension into account, but the following will neglect the space dimension. Production theory examines the inputoutput relations of goods constituting the manufacturing process. The time structure of input-output relations comes to the fore in formulating dynamic production functions, supplementing the type and quantity structure of goods. To access the time dimension of production, two basic approaches seem feasible. First, the manL~fa~turing process can be represented directly through parameters and variables that are defined as time-dependent such as production times. Such approaches are labeled as “production time models”. Secondly, quantity measurements like input, production and sales volumes may make up the central variables of the model. They all refer to a specific instant or period. While time is treated as a continuum in production time models, it may vary continuously or in discrete steps in production quantity models. Continuous variation leads to difference or differential equations for production quantity variables. This approach is appropriate for very precise modelling of partial processes and long-term global analysis as for growth processes. In contrast, discrete variation divides the planning period into a given number of intervals. No further attention is paid to the processes within an interval. Therefore, this approach seems to be suited for less detailed analysis of interwoven processes which feature discontinuous changes. As this