Competitive Scarcity with Cost Dependent on Production Rate and Resource Size

Abstract

In the preceding models we assumed a competititve firm extracting a finite resource that has a cost function that is dependent on the rate of extraction. In reality, however, cost of extraction increases not only with the rate of extraction but also with decreasing stock size. The smaller the remaining reserves, the deeper they may lie or the less the mineral is concentrated in the mine. The model of this chapter incorporates that stock effect into the cost function (Figure 18.1).¹ As a result of this stock effect, the scarcity rent rate can no longer rise at the rate of interest, and we surpass the intuitive model’s capacity to accurately follow the optimal production path.

Truth is the conformation of appearance to reality.

Alfred North Whitehead