A New Paradigm for Economic Policy
New Directions in Modern Economics series
Edited by Claude Gnos and Sergio Rossi
Chapter 1: Relative prices are undermined by a mathematical error
The problem of the determination of relative prices pertains to explaining how numerical equilibrium prices can be established through direct exchange. A priori two possibilities may be envisaged. It may be assumed that numerical prices exist as a separate entity with respect to the physical goods to be exchanged in the market. It may be claimed that a numerical price can be arbitrarily tagged on to a commodity chosen as the standard. Let us consider the case of two commodities, razor-blades and pens, and their exchange in the commodity market. It is easy to show that, if supplies and demands are said to adjust through a variation in numerical prices, the determination of the equilibrium between razor-blades and pens requires the simultaneous solution of three equations. Suppose that the supply (demand) of razor-blades of a precisely defined kind varies as a mathematical function of the increase of a purely numerical price, from zero to infinity. When the stated price for one razor-blade increases, say from 3 to 4, the demand for razor-blades diminishes while the supply increases, the positive and negative variations being ascertainable through their physical quantities. One could equally assume inverse variations. The form of the mathematical functions, whether direct or inverse, is irrelevant given that the fundamental problem consists in determining the number of equations involved. One equation suffices for the determination of the numerical price at which the seller and the purchaser agree to trade precisely the same number of razor-blades: one commodity, one price.
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