ABSTRACT
In economies where human production is organized through the exchange of products as commodities, the statistical regularities of the exchange process (which may take a wide variety of forms from scattered barter through posted price outlets to highly organized auction markets) establish ratios at which different commodities trade. In well-established commodity systems some form of money typically evolves: the money prices of commodities, that is, the exchange ratios of commodities with money, are the familiar form these exchange ratios take. Under these circumstances it is possible to calculate the value of any collection, or bundle, of commodities by multiplying the quantity of each commodity in the bundle by its price. In mathematical terms, if the vector of commodities representing a bundle is https://www.w3.org/1998/Math/MathML"> x = { x 1 , … , x K } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315643755/af05e194-8719-4aab-8243-6ff44705a83c/content/inline-math_1106_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and the vector of money prices of the commodities is https://www.w3.org/1998/Math/MathML"> p = { p 1 , … , p K } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315643755/af05e194-8719-4aab-8243-6ff44705a83c/content/inline-math_1107_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> the value of the bundle x at price system p is: https://www.w3.org/1998/Math/MathML"> v [ p , x ] = p ⋅ x = p 1 x 1 + … + p K x K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315643755/af05e194-8719-4aab-8243-6ff44705a83c/content/math_448_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
