In this paper an attempt is made to work out mathematically a pure theory of money. The method employed is to consider only those operations which are fundamental to all monetary economies. These fundamental operations are spending, saving, and investing and any relationships which can be shown to exist between them must, therefore, be valid for all economic systems employing money.
The quantities dealt with in this analysis are purely monetary ones: no considerations of value arise. The resulting equations, therefore, express relationships between different quantities of money or between different money flows.
We shall first investigate the operations of spending and investing and then consider the operation of saving.
In order to simplify the problem, we shall consider first an economic system of a restricted type and then later remove the restrictions in order to achieve generality. We postulate that this simplified system operates under the following two restrictions: (a) no investment is made except by an industrial unit; (b) there is no taxation.