Pastures of Plenty: When is the Standard Analysis of Common Property Extraction Under Free Access Incorrect?

Abstract

There are two ways to calculate the dynamic path of aggregate extraction when there is free access to a common property resource: (1) calculate the rent-dissipating aggregate extraction in any period (as a function of the stock) and then derive the dynamic path using the transition equation and initial condition or (2) examine the path of aggregate extraction in a subgame perfect equilibrium as the number of players expands without bound. The latter approach is theoretically correct but often intractable. The former approach, which has been widely used for more than thirty years, is tractable and generally presumed to yield the identical aggregate extraction path. We show by example that this presumption is erroneous. We then provide conditions which suffice for the traditional approach to be correct.