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Equilibrium Between Supply and Demand in Absolute Monopolies

( Originally Published Early 1900's )

LET us briefly review our mode of reasoning in the cases heretofore considered. We have regarded price as the determining cause fixing the amount both of the supply and the demand, and so fixing them that they shall be equalized. The general rule is that an increase of price not only diminishes demand, but, as shown in the last chapter, stimulates supply, so that the equilibrium can always be established by properly adjusting the price. In showing how price stimulates supply, we have hitherto considered two cases :

1. That of free and unlimited competition on equal terms, in which the supply can always be increased to meet any demand that may arise, without any increase in the net cost of producing each unit of the commodity. In this case the price is fixed by the net cost of production.

2. That of a graduated monopoly, in which there is a large competition, but not on equal terms, the favored producers having a superior command of some form of skill or natural agents. This case has been considered in the last chapter.

We have now to consider as a third case that of an absolute monopoly, held by one or a limited number of persons.

Let us first suppose that a single individual or company has the exclusive command of some natural requisite of production, a mine of nickel or the right to make a patented machine. Then, having the sole command of the market, such a person can fix the price at his own pleasure. The law of averages will not be applicable, nor can we by scientific method lay down an absolute law as to what he will do. He may say he wants to keep the mine for his children, or to bequeath to them the patent-right. But although we cannot lay down a law of his action, we may assume that he will do what is most for his own interests ; that is, that he will fix such a price as will in the long-run yield him the largest profit. In determining what will be the largest profit various cases arise. If the quantity of the monopolized requisite is absolutely limited, the case will be different from that of a patented machine, in which there is no limit to the number of machines that the patentee may make. It is certain that the quantity of nickel contained in the earth is limited, so that by no efforts can more than a certain number of tons ever be produced. This fact must be kept in view by the owner, who may thus be led to confine his production to a certain definite quantity per annum, no matter how high the price may rise. On the other hand, the owner of the patented machine has a motive for making as many machines as be can, subject to the condition of not bringing the price so low as to lessen his profit.

Next imagine that instead of a single person there are two. These two persons may combine with each other by an agreement not to sell below a certain fixed price.. In this case the result will be the same as if they were a single person, because the two are acting in fact as a single economic agent. If they compete, that course will tend to lower the price. Whether it will reduce the price to such a point that the monopoly in itself shall become valueless depends upon the quantity demanded, the price which the consumers are willing to give, and the net cost of supplying it. Suppose, in the case of the nickel mine, that each miner is producing regularly at the rate of one thousand kilograms per annum, and making a regular profit of x dollars. If he reduces the price, the demand upon him will be increased in two ways. The total amount purchased will be increased according to the first law of demand and price, and he will also attract customers from his rival. Suppose then that his rival does the same thing, and that a competition is thus established as to who sells the cheapest. Will the result be to bring the price to the lowest paying limit ? Not at all. Every increase in the supply will require additional laborers and capital, and when the competing parties find that the in-crease of their facilities is neutralized by the lowering of the price, neither of them will depress the price any further. Thus the two, like the one, may be expected in the long-run to fix the price at the figure which yields the largest profit.

With only two competitors we may be sure that no competition will ever last long, and that they will, either tacitly or by common agreement, fix a scale of prices, and thus act as if they were a single person. The greater the number of competitors, the more difficult it will be to have any such understanding as to price. As a matter of fact, however, it is well understood that among the great metal manufacturers of the country, and indeed among nearly all those who produce commodities on a large scale, attempts are made from time to time to establish agreements either about price or quantities produced. It is, however, difficult to make any general and precise statement on this subject, because the state of the case is constantly changing. Agreements may be formal or informal, and each party sometimes adheres to them and sometimes breaks them. New competitors come in from time to time, and thus change the basis on which agreements were made. One thing can, how-ever, be said with certainty. The great staples of life which are really necessary to human advancement and welfare are not monopolized. For the monopolized articles the public can-not be compelled to give more than they are willing to give, and every rise of prices leads to less of the article being sold. Fortunately for the interests of mankind, absolute monopolies of insensitive products are quite exceptional.

The most common case of an absolute monopoly is that of patented machines. As a general rule these machines are things that people can readily go without, or find substitutes for. They are therefore to be regarded as sensitive commodities. To illustrate this, let us suppose that it is possible to sell in a certain city 100 sewing-machines of a certain patent at the price of $40 each, and that, for every dollar above $40 added to the price, there is a falling off of five machines per annum in the sales. Then at the price of $45 the sales would fall off to 75, and finally at the price of $60 nobody would buy the machines. The number salable at each price is shown in the first two columns of the following table

Price. Demand. Total Amount Cost. Profit.

$40 100 $4000 $3000 $1000
45 75 3375 2250 1125
50 50 2500 1500 1000
55 25 1375 750 625
60 0 0

The patentees can fix the price at pleasure. But, in accordance with the fundamental law of human nature on which economic science is founded, we suppose them so to fix it that they shall receive the largest income. To show how the income derived from different quantities of manufacture may be arrived at, let us suppose the cost of the machines, exclusive of interest upon the permanent original capital invested, to be $30 each. Then if the selling price is fixed at $40, the cost of the 100 machines which can be sold will be $3000, as shown in the fourth column of the table, and the profits will be $1000, as shown in the last column. If the price is raised to $45, they can sell only 75 machines ; the cost of these 75 machines being $2250, the profits will be $1125. If they put the selling price at $50, they can dispose of but 50 machines annually. The cost of these machines will be $1500, and the profits will be $1000. If they put the price at $55, they will sell but 25 machines annually, which will cost them $750, and their profits will be reduced to $625. At a price of $60 they will sell no machines at all, and therefore can do no business.

To correspond to the actual case in business we should of course make allowance for the cost of selling, which in such cases is considerable. If this cost is a constant premium on every machine sold, we have to add it to the price of the ma-chine. If it is a percentage of what the machine sells for, we may deduct this percentage from what the machine sells for in the first column. In any case it is a simple matter to make the necessary changes in the calculation, and we need not describe the process, because our object is to show the principle involved, which will best be seen by putting the case in the simplest form as shown in the table.

Since in each case the selling price must depend upon the will of the manufacturer, we cannot lay down an absolute and necessary law about it. But, for reasons already dwelt upon, the price concluded by the political economist will be that which secures to the manufacturer the largest profit; that is, in the case supposed, it would be $45.

Case in which, the Supply is absolutely limited. Not only may the whole supply of a commodity or facility be in the hands of one or a few persons or companies, but it may be incapable of increase beyond a certain definite limit. One ex-ample of this case is that of an ocean telegraph cable without other cables to compete with it. Only a certain number of words can be sent over the cable daily, and the cost will not be materially diminished by any diminution in the number sent. In this case we can establish a normal price which tends most to the public benefit, but which may not be the price most profitable to the owners of the cable. Since the lower the price the greater the number of messages, a price may be established at which messages enough will be demanded to keep the cable constantly employed. This may be called the normal price. Let us suppose first that the demand for sending mes-sages is comparatively insensitive, as shown in the table on the next page.

The first column shows the price per word taken at pleasure. Opposite each price is given the supposed number of words which senders will demand to be sent at that price per day; the last column shows the total receipts.

Price per Number of Words Total Daily
Word. demanded per Day. Receipts.

$2.40 5,000 $12,000
2.20 5,500 12,100
2.00 6,000 12,000
1.80 6,500 11,700
1.60 7,000 11,200
1.40 7,500 10,500
1.20 8,000 9,600
1.00 8,500 8,500

If the cable can send words without limit, the most profit-able price per word would be about $2.20, at which price about 5500 words would be demanded, and the daily receipts would be $12,100. But suppose that not more than 5000 words can possibly be sent. Then it would be most profitable to send this maximum number and keep the cable constantly employed. The price leading to this result would be $2.40. Suppose, however, that if the company pleased it could send 8000 words per day and no more. Then it would be most for the public benefit to fix the price at $1.20 per word, at which price the cable would be constantly employed. But the daily receipts would be only $9600.

The price actually charged might range anywhere between the extremes $1.20, the normal price, and $2.30, the price most remunerative to the company. If the company is chartered by the government and receives favors from it, the normal price is that which should be fixed, provided the company is willing to lay the cable on that condition.

The question may be asked : Suppose the company can make a profit by sending the messages at $1, or even 80 cents, per word ; would it not be better for the public to fix the rate at this lower price ? The answer of the economist is, No. By hypo thesis, the company can only send 8000 words per day. If the price is fixed at 80 cents, people will be coming in with 9000 words per day, so that there will be 1000 which cannot possibly be sent. In this case a selection must be made. On what principle shall we select the 8000 which are to be sent from the 9000 demanded ? Clearly the answer is that we should select the 8000 which are the most important. But how shall we determine which are the most important ? Sentimentality aside, there is but one possible way. The most important messages are those for which the senders are willing to pay the most. Hence the only course would be to find the senders of those 8000 words who are willing to pay the price of $1.20 per word. The only way of doing this is to charge $1.20 and to let the senders of the 1000 words who are not willing to pay this price give way to the others. No injustice is thus done, because no one need pay money unless the service is worth it, and it is perfectly right that those persons to whom the service is worth less than $1.20 per word should give way to those to whom it is worth more.

Another case of limited supply is that of the seats at theatres and other places of public amusement. There are, of course, only a certain definite number of seats at such places. The price of tickets may be so low that more people will demand them than can be supplied with seats, and they may be so high that many seats will be left empty. The normal price is that at which the demand will be just equal to the number of seats, and the general good is best subserved by this price. But this normal price will vary from time to time according to circumstances, rising higher when a celebrated actor is to appear, and falling when nothing of especial interest is presented. If the price be put much below the normal price, the tickets will be purchased by speculators with a reasonable probability of selling them again at a profitable advance.

The professional services of the lawyer or physician come under the same category. The physician can properly attend only a limited number of cases. If his fees are below a certain amount, which depends upon his reputation, the demand for his services will be greater than he can supply. If his charges are too high; he will remain a greater or less portion of the day idle. The normal price is that at which the demand will be equal to his power of attending patients.

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