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Let’s start with a quote of Keynes [The General Theory of Employment, Interest, and Money by John Maynard Keynes. Book II: Definitions and Ideas]

“The perplexities which most impeded my progress in writing this book, so that I could not express myself conveniently until I had found some solution for them, are:

firstly, the choice of the units of quantity appropriate to the problems of the economic system as a whole;..

“That the units, in terms of which economists commonly work, are unsatisfactory can be illustrated by the concepts of the national dividend, the stock of real capital and the general price-level:”

“The community’s output of goods and services is a non-homogeneous complex which cannot be measured, strictly speaking, except in certain special cases, as for example when all the items of one output are included in the same proportions in another output.”

In order to take the definition of the unit of goods we use the obvious statement.

We define the goods the market, as something that you want to sell or that you want to buy. Let’s try to express this in numbers

Do you love cakes? I will sell them to you. You will buy and will want again. Finally, you can eat 10 cakes a day. And I offer you still. You say, “Enough!” I suggest to you free of charge 12 cakes a day, and you ungrateful say me “No!”. Moreover, buying cakes, you have some time to consume them, and not buy a new one

What is it? It is the overproduction!

I repeat the question: How much can you eat on the day cakes – 10, 12, 15? It doesn’t matter for math, but in principle there is some maximum quantity which you can consume in a certain period (a day, a month, a year).

Let’s try to find the indicator and we will call its – the relative consumption-

P_relative. If the consumer is not in need of this product (saturation) P_relative.=1,

If the consumer is just starting to purchases a goods

P_relative. =0.

Therefore, the current state of the user can be reflected with help the value of the relative consumption

0 ≤ P_relative.≤1

We will continue the search for the mathematical determination of relative consumption.

More details of this figure can be determined from the following reasoning.

Let’s introduce a unit of measure (denoted it a) “specific relative consumption”. It will the ratio of real consumption ( P_relative) to the maximum possible (P_max.)

P_relative = P_real/ P_max=a

Then the maximum consumption in a given period will be equal to P_max. We assume that no material (money, prices) and external factors (season, fashion) don’t limit you.

Next, let’s see how much you are consuming a really – P_real.. By definition you can’t consume more than P_max. (P_real. < P_max.).

If you considered a group of n consumers, applied the name – RELATIVE CONSUMPTION.

It will be

A=an