Monopoly Scarcity with Variable Interest Rate

Abstract

Up to this point, we could solve the complex optimal depletion path problems with dynamic equations developed from our intuition of the behavior of a firm facing scarcity. We were able to generate the guiding differential equations by realizing that the firm would hold back on producing the resource, thus forcing up the value of the resource in the ground at the rate of interest. In this way extraction was chosen such that a balance is reached between the profits to be made from selling the remaining resource and putting the money in the bank at the going interest rate or leaving enough of it in the ground so that its value would rise at the rate of interest. In so doing, the resource-extracting firm would maximize the cumulative present value of the profits from sales of the resource. With those revenues, the firm would generate a fund whose present value will supply the firm the same net income as it would have if it were not dealing with a scarce resource.

Truth comes out of error more readily than out of confusion.

Sir Francis Bacon