The Measure of Value by an Absolute Standard
( Originally Published Early 1900's )
WE have to introduce certain mathematical conceptions into this subject. One of the most common of these is that of one quantity varying directly or inversely as another quantity. A simple example is that of total cost varying directly as price per unit. If I have to buy a box of tea, then the higher the price per pound the more I must pay for the box. This relation is expressed algebraically by saying that the money I must pay for the tea is equal to the product of the price into some fixed quantity.
Let M = the total amount of money I must pay; P = the price per pound.
Then the law of relation is expressed by the equation M = P X C. (a)
C being the constant quantity. When we say that C is a constant quantity, we mean only this, that it does not necessarily vary when P varies, or that we suppose it constant in order to get a relation between P and M. In the present example we can readily see what C is. It is the number of pounds of tea in the box. If this is 120, then we have for the cost of the tea M=PX120.
To take another example, let us inquire what sum total of values can be exchanged by a piece of money in a year. Let us put E, the total amount of exchanges required ; D, the number of dollars in the coin; N, the number of times that the coin changes hands in the course of the year.
It is evident that the higher the value of the coin—that is, the greater the value of D—the greater the value of the exchanges it will effect, other conditions being equal. Hence we may write E=DXC.
A very little consideration will show that the constant C is equal to N, the number of times the coin changes hands in a year. The relation between the three quantities is therefore expressed by the equation E=DXI. (b)
We may therefore also say that the quantity of business which a coin will transact in the course of a year is proportional to the number of times it changes hands.
Inverse variation comes into play when one quantity increases as another diminishes. If I have a fixed sum of money, it is evident that the higher the price per pound of an article the less of that article my money can buy. This relation is expressed by saying that the amount I can buy is equal to some quantity divided by the price per pound. Using the same notation as in the first example (a), and putting Q for the quantity I can buy, we shall have in this case.
Here it is evident that C represents the fixed sum of money which I have to buy with, the same as M in the first example. -From equation (6) we derive, by an algebraic operation,
This equathon expresses the fact that if a certain definite amount of business is to be transacted by a coin, then the smaller the value D of the coin the greater the number of times it must change hands.
In all the above cases it is obvious what the constant quantities mean. But sometimes, although we may form a definite idea of these quantities as constants, their meaning depends upon a great many conceptions. One of these conceptions, which we must have at command, is that of a scale of prices. Suppose that the price of everything next year should be double its price this year. Then, other conditions being equal, double the amount of money would be required to buy and sell the same goods, since the amount of money required for each purchase necessarily varies as the price. By a scale of prices is meant a general average of prices of all goods bought and sold. If this average of prices increases, we say that the scale of prices increases, and vice versa. Let us call the scale S, and let us put M for the amount of money required to make all the exchanges. Then, since the higher the scale the greater the amount of money required, we may write the equation M=SXC, (c).
C being some constant.
What this constant is depends upon a great many causes ; one of which is the total amount of commodities to be bought and sold. It also depends upon what standard of comparison we take for S; that is, for what scale of prices we regard S as equal to unity. But in this case all that is necessary is to ad-here to a scale when once adopted. For example, the scale of prices was about twice as high in 1864 as it was in 1861. Hence it required twice as much money to transact a given amount of business in 1864 that it did in 1861. If we call the scale of 1861 unity, that of 1864 will be 2. If we call that of 1864 unity, we had in 1861 S = 1/2.
It is evident that the constant quantity in equation (c) depends upon and varies with the total amount of business to be transacted. Therefore if we put B = the total amount of business, we may write C=BxK,
K being some other constant quantity.
If we substitute in equation (e), the latter will become M=SXBxK, which means that the quantity of money required will vary both as the scale of prices and the amount of business to be transacted.
In all cases of this sort we may consider the algebraic symbols as the measures of certain economic causes. The effects of these causes will then be studied by supposing some one cause to vary while all the others remain constant. Thus we shall get the effect of the variation in that particular case. By considering each of the causes in succession to vary, we get the effects due to the variation of all the causes. The last equation is an example of introducing two varying causes, scale of prices and quantity of business.
Suppose the price of everything to be twice as high this year as last, while the quantity produced remains the same. In ordinary language, it would be said that all values had doubled. But it is clear that really nothing would have been any more valuable or useful than before. The measure-ment of values by prices is therefore not entirely satisfactory. To illustrate the exact nature of the defect, let us suppose an analogous case in measuring length. On getting up some morning, a father measures the heights of his children with what purports to be a foot-rule. He finds that the boy who yesterday only measured four feet now measures eight. Marking his own height, he finds it to be eleven feet. He might claim that his entire family was twice as tall as yesterday, and that he was himself a giant. But the more reasonable explanation would be that his supposed foot-rule was only one half its proper length, and that the actual size of everything else remained unchanged.
Now the measure of values by money is, in principle, similar to the measure of lengths with a rule. When we say a man is six feet high, we mean that his height is equal to six of a certain length which we call a foot. So when we say that a barrel of flour is worth $5, we mean that its value is equal to five pieces of money each of which we call a dollar. In order therefore that we may never be deceived in actual values, both the foot and the dollar with which our comparisons are made must remain unchanged. There is no difficulty about the foot, because it is a material substance, and we can readily find matter which does not vary in its magnitude from year to year. But since value is only a mental conception, and dependent upon human desire, there can be no absolute dollar to compare with. The current dollar may be variable in value, as well as a barrel of flour, and we must always remember that calling a thing, whether metal or paper, one dollar, or one pound, or one franc, no more gives it a fixed value than calling a stick one foot makes it a foot long.
Is there then any way by which we can approximate to a real standard of value ? To show how we may reach such an approximation, let us again return to the case of the foot-rule. It is very evident that in the case we have supposed, that of a man finding himself twice as tall as lie was before, common-sense would tell him that the rule with which he measured was only half as long as before. In other words, the logical process would be to measure the rule by the heights of himself and children instead of measuring them by the rule. If he found that yesterday the combined measures of himself and of his children were 16 feet, while to-day they all together measured 20 feet, he would conclude that the rule to-day was shorter than it was yesterday in the ratio 20 : 16, or that it had shrunk 20 per cent. This result would indeed rest on the assumption that there was no actual change in the heights of the family, and whatever error this assumption might be subject to, the same error would his result be subject to. It is evident that in the case supposed the errors arising from this assumption would be much less than that arising from the supposition that the length of the measure was invariable.
In the same way, in devising an absolute standard of value the most logical process is to suppose that the general or average values of commodities remain unchanged from year to year, and that a general rise or fall in prices is caused by a diminution or increase in the value of the dollars in which the price is expressed. Now, if the changes thus indicated were the same with all commodities, that is, if all prices rose or fell exactly in the same proportion, there would be no difficulty. But as a matter of fact we never find this to be the case. We must therefore seek for some general average which shall be as near as possible to what we want. One possible hypothesis would be this: We might assume that the absolute value of everything produced by the population of the country remains unchanged except that as population increases the total value produced increases in the same ratio. In other words, we may suppose the average productiveness of each individual to remain the same from year to year.
If then we could determine the total money value of all that is produced by all the inhabitants of the country, and divide the result by 60,000,000, or such other number as might ex-press the total population, we should have for the quotient a certain number of dollars which would be the average productiveness of each individual, measured in current money. If we found this average to fluctuate from year to year, we should conclude that it was due to changes in the value of the dollar with which the value produced was measured.
The Tabular Standard of Value. As a matter of fact it is impossible to determine the total productiveness as just defined with any approach to accuracy. We cannot learn what every man is doing or making by any system of inquiry. The next best course is to take as our standard of comparison the value of a certain number of the great staples of life.
Flour is one of these. In the city of New York a barrel of flour which sold for $5 in the year 1883 would only bring $4 in 1885. If we regard the value of the dollar as in-variable, we should say that the value of the flour was 20 per cent less in the latter year than in the former. But if we regard the value of the flour as invariable, then we should say that the value of the dollar was 25 per cent greater in 1885 than in 1883.
Instead of depending on flour alone for a comparison, we should take all commodities which are consumed in appreciable quantities. The table below will show the method bet-ter than any amount of description. We have here a list of twenty articles of nearly universal consumption. Of each article we take what we may suppose to be a rude approximation to the quantity which a person may consume in a year. To discover the actual average amount consumed by each person would be a difficult problem, and the quantities in the table must be considered as only rude guesses, the object being to illustrate the principle and not to give a fact with the utmost exactness. With each article is given the cost of the assumed quantity from the wholesale price in the city of New York at certain periods separated by four years. The numbers given are the averages during the years ending June 30th, of 1876, 1880, and 1884. The prices are taken from the reports of the Bureau of Statistics of the Treasury Department.
Adding up the several columns, we find that the collection of commodities described in the table cost $111.66 in 1876; $98.27 in 1880 ; and $101.33 in 1884.
We now proceed on the supposition that the real value of this collection of articles remains unchanged. But when measured in dollars the value was less by 12 per cent at the second epoch than at the first. From this it would follow that each dollar was worth about 13 per cent more in 1880 than in 1876. From 1880 to 1884 there was a slight increase in the amount of money necessary to purchase the collection. We therefore conclude that during that period there was a slight depreciation in the value of the dollar. It is probable that since 1884 the value of the dollar has again been slightly increasing, so that less money would purchase the collection now than was required during that year.
To perfect this table many additions and modifications are necessary. We should include the rate of wages paid to various classes of laborers whenever it can be exactly determined. But in estimating the rate of wages it would be necessary to take into account the unemployed as well as the employed. Suppose, for example, that out of ten carpenters eight were getting $2 per day, while two were unemployed. Then the average wages of the carpenters would be $1.60 and not $2. The wages of domestic servants, washerwomen, and other classes who render personal services would also have to be taken into account. Manufactured articles, clothing for ex-ample, should be more fully represented.
One source of error in drawing conclusions from such a table can be more easily seen than avoided. The improvements constantly being made in manufactures lead to their being really cheaper when measured in terms of human labor, which is our proper ultimate standard. This improvement should be allowed for, if possible, by increasing the quantities in our standard collection.
As a general rule the changes of value to which our current dollar is subject are very little noticed or considered by the public at large. Yet, as we shall hereafter see, nothing is more essential to enable us to understand the condition of the social organism than this knowledge. The value of the dollar ought to be determined from month to month by some central authority and made known to the public.
It will be remarked that the changes in the amounts of money necessary to purchase the tabular collection of commodities correspond to the changes in the general scale of prices defined in § 8. The relation between this scale and the absolute value of the dollar may be stated as follows :
The absolute value of the dollar varies inversely as the scale of prices.
It should also be remarked that the conception which we have called " absolute value of the dollar" is frequently called " purchasing power." This popular form of expression is well adapted to give a clear notion of the subject, since any one understands how a dollar may purchase more at one time than at another.
It has been proposed to adopt a tabular standard of value as that for the payment of debts which are due only at the end of long periods of time. The public debts of the principal nations of the world have gone on for several generations; ground-rents in our great cities have sometimes been continued for a hundred years or more. In these cases the essential condition of the contract is that, in consideration of a service rendered at one time, the party receiving it agrees to pay a sum of money at some distant future time. The objection to this system is that no one knows what the absolute value of the money will be when the time of payment comes. We know as a mat-ter of history that great changes in the value of the monetary unit have occurred, and can sometimes trace their causes. The great additions to the gold supply of the world made by the discovery of gold in California and Australia in 1848 and 1850 resulted in a diminution of the value of the dollar. Hence when old debts were paid during the few years preceding 1860, the creditor received a less value than he supposed he would get. During our civil war paper dollars were issued in such quantities that their value fell to one half that of the gold dollar or less. One half of all old debts payable during 1864 may be said to have been forfeited. During the years 1865 to 1880 there appears to have been a pretty steady appreciation in the dollar. The result was that everybody who during the years 1863 to 1865 contracted debts payable now has to pay double the value on which he based his agreement.
Now, one object of the tabular standard of value is to arrange an equitable system for the payment of such debts. This system is in brief that of providing that the payments shall be made, not in so much gold, silver, or other current money, but shall consist of such a quantity of the current money as shall purchase a stipulated collection of commodities.