Returns to scale and dynamics of multiple enterprises

This paper presents a dynamic theory of structural change in which functional change driven by technological change and transactional change open opportunity for change in scale and scope of enterprises. Implementation of change in scale and scope of enterprises is constrained by initial state conditions including resource endowments, access to credit, and regulation. In the presence of such constraints, the paper motivates the existence of thresholds that introduce cusps in the optimal paths of control variables. The evolution of enterprises is considered within the context of a multiple enterprise firm that encompasses discrete and continuous processes that are interdependent on intermediate goods as well as their production of environmental effects. Response to opportunity is governed as well by adjustment costs and incomplete markets. The specification is consistent with manufacturing, crop and animal agriculture, as well as service-oriented enterprises. Potential for structural change is considered within the context of changes in prices, regulation, and technological change. We discuss management options that maximize uncertain profit over the planning horizon subject to changing price regimes, regulations, and existing and new technology. We consider incentive as well as quota type policy to regulate environmental effects. While the model is one of optimal control, the presence of constraints opens the opportunity for timing of adjustment and constrains adjustment. We derive thresholds for change and show their principal determinants. Based on this specification, we derive an indicator of flexibility as well as real options style valuation of the benefits of postponement of adjustment. The model’s specification is sufficiently complex as to preempt analytical consideration. Instead, we specify a numerical example and present illustration of the implications of the model based on numerical computation. The example illustrates both unbundling of enterprises as conditions encourage reduction in scope as well as formation of relational links to recover what might be viewed as economies-of-scale by specialized enterprises spawned by unbundling. The example also illustrates conditions necessary to induce a shift from traditional grazing animal operations integrated with crops to intensive feed lots. Within this context, shift in scale, specialization, and scope of enterprises is illustrated. To conclude, the utility of model is considered within general contexts to analyze the structural implications of change in economic conditions such as shifts in price regimes, change in process technology, change in IT technology, and changes in institutional rules.