A model for competition of technologies for limiting resources

A mathematical model for the development of technologies competing for common productive resources is proposed and analyzed. The model is based on the principles of evolutionary economics and is given by a "consumer-resource" system of equations. Consumers are homogeneous populations of firms employing the same technology. The output of firms is characterized by the production function with complementary factors. A technology can increase owing to the entry of new firms at a specific rate proportional to the output, and decrease due to ruin of a firm. Resources consumed enter the industry from the outside; unused resources leave the industry. The lower the minimum demand of a technology for a given resource, the higher its competitiveness with respect to this resource. We obtain the conditions for the coexistence of technologies, according to which each competitor should surpass the others in the efficiency of using one resource and be inferior to them in the efficiency of using other resources. We show the existence of two fundamentally different mechanisms of natural selection of the dominant technology, namely, by selection value and by the initial conditions. We investigate the potential possibility of regulating the technological diversity of the industry by managing the rates of resource supply.