All the formulae thus far determine only relative prices and not the price level. To determine the level of prices, a normalizing condition is necessary. We shall introduce it in the following form:
= 1, (35)
where V is an arbitrary vector. We call it a group numeraire. Vector V can be chosen in various ways.
(1) Choose V as a unit vector with all components zero, but with unity for the rth element. Thus, we have chosen the price of the rth commodity to be one. In other words, we express the prices of all other commodities in units of the rth commodity. This is the case of a simple numeraire. If this rth commodity is gold we have the classical theory of gold as a measure of value.
(2) State that the money value of the gross social product is f monetary units. Then it follows that
P’X = f. This gives a group numeraire of
V = (l/f)X.
(3) Analogously, if we write V = (l/y)Y, the volume of national income will be y monetary units.
(4) Vector V can be chosen in various other ways — for instance, so as to maintain the given volume of personal consumption in money terms.