Returns to scale and dynamics of multiple enterprises

This paper presents a dynamic theory of structural change in which functional changedriven by technological change and transactional change open opportunity for change inscale and scope of enterprises. Implementation of change in scale and scope ofenterprises is constrained by initial state conditions including resource endowments,access to credit, and regulation. In the presence of such constraints, the paper motivatesthe 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 firmthat encompasses discrete and continuous processes that are interdependent onintermediate goods as well as their production of environmental effects. Response toopportunity is governed as well by adjustment costs and incomplete markets. Thespecification is consistent with manufacturing, crop and animal agriculture, as well asservice-oriented enterprises. Potential for structural change is considered within thecontext of changes in prices, regulation, and technological change. We discussmanagement options that maximize uncertain profit over the planning horizon subject tochanging price regimes, regulations, and existing and new technology. We considerincentive as well as quota type policy to regulate environmental effects. While the modelis one of optimal control, the presence of constraints opens the opportunity for timing ofadjustment and constrains adjustment. We derive thresholds for change and show theirprincipal determinants. Based on this specification, we derive an indicator of flexibilityas 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 themodel based on numerical computation. The example illustrates both unbundling ofenterprises as conditions encourage reduction in scope as well as formation of relationallinks to recover what might be viewed as economies-of-scale by specialized enterprisesspawned by unbundling. The example also illustrates conditions necessary to induce ashift from traditional grazing animal operations integrated with crops to intensive feedlots. Within this context, shift in scale, specialization, and scope of enterprises isillustrated.To conclude, the utility of model is considered within general contexts to analyze thestructural 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.