The Mathematical Groundwork of Economics: An Introductory Treatise

Excerpt

Economics deals with the production, exchange, possession, consumption, andmoral use of material goods and immaterial services. The whole subject of wealth and welfare has two aspects, one subjective, or psychological, the other objective or material. From the one we may consider the attainment by economic action of an abstract good, or hedonistically the pleasure or satisfaction derived from the possession or use of things, or the desire to obtain goods; none of which terms are arithmetically measurable. From the other we may have in view material goods and actual services which can be measured by quantity or by money value. At first sight it might appear that mathematical reasoning was confined to the objective aspect, but this is not the case. If we cannot measure, it is true that we cannot apply the arithmetical processes of addition and multiplication and their converse; but we may be able to detect equality and inequality, relationship, continuity, variation, and other properties which lead to algebraic expressions.

It is proposed in the following treatment to have in mind two entities; the one incommensurable, the satisfaction derived from economic goods or in some cases the desire to obtain them, the other measurable, e.g. the physical quantity of goods. The second may be compared with a measurable shadow cast by an undefined object. The more exact relationship is as follows: write U (x, y . . .) for an algebraic function of measurable quantities x, y . . .; let it be so related to an entity we will call S (x, y . . .), where S is not a calculable function but the non-measurable satisfaction derived from quantities x, y . . ., that the following postulates are satisfied.

Postulates . (1) When x, y . . . vary without affecting the value of U (x, y . . .), more x balancing less y, &c., S (x, y . . .) remains unchanged.