Macro-economic equilibrium and price signal accuracy in non-scalar economy

The management of global commons is of vital importance for modern society. The current solutions attempt to internalize the cost of appropriation of commons by adding this to the cost of private resources. In this paper we will show that this approach has some fundamental weaknesses. To overcome these shortcomings, we have proposed to segregate the management of private and shared resources by using non-scalar numbers for the underlying economic signals of money and price. We prove that the resulting non-scalar economy always reaches a macro-economic equilibrium point where the level of appropriation of commons by the society remains steady. The second contribution of this paper is to show that the proposed design of the non-scalar economy would guarantee the accuracy of price signal with respect to the appropriation of commons. In other words, rational economic agents would ensure that the price neither underestimates nor overestimates the actual level of appropriation incurred. This will provide a powerful basis for an effective market system for the commons.