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2. Determination of Money Prices
Let us first take a typical good and analyze the determinants of its money price on the market. (Here the reader is referred back to the more detailed analysis of price in chapter 2.) Let us take a homogeneous good, Grade A butter, in exchange against money.
The money price is determined by actions decided according to individual value scales. For example, a typical buyer's value scale may be ranked as follows:
The quantities in parentheses are those which the person does not possess but is considering adding to his ownership; the others are those which he has in his possession. In this case, the buyer's maximum buying money price for his first pound of butter is six grains of gold. At any market price of six grains or under, he will exchange these grains for the butter; at a market price of seven grains or over, he will not make the purchase. His maximum buying price for a second pound of butter will be considerably lower. This result is always true, and stems from the law of utility; as he adds pounds of butter to his ownership, the marginal utility of each pound declines. On the other hand, as he dispenses with grains of gold, the marginal utility to him of each remaining grain increases. Both these forces impel the maximum buying price of an additional unit to decline with an increase in the quantity purchased.3 From this value scale, we can compile this buyer's demand schedule, the amount of each good that he will consume at each hypothetical money price on the market. We may also draw his demand curve, if we wish to see the schedule in graphic form. The individual demand schedule of the buyer considered above is as shown in Table 6.
We note that, because of the law of utility, an individual demand curve must be either “vertical” as the hypothetical price declines, or else rightward-sloping (i.e., the quantity demanded, as the money price falls, must be either the same or greater), not leftward-sloping (not a lower quantity demanded).
If this is the necessary configuration of every buyer's demand schedule, it is clear that the existence of more than one buyer will tend greatly to reinforce this behavior. There are two and only two possible classifications of different people's value scales: either they are all identical, or else they differ. In the extremely unlikely case that everyone's relevant value scales are identical with everyone else's (extremely unlikely because of the immense variety of valuations by human beings), then, for example, buyers B, C, D, etc. will have the same value scale and therefore the same individual demand schedules as buyer A who has just been described. In that case, the shape of the aggregate market-demand curve (the sum of the demand curves of the individual buyers) will be identical with the curve of buyer A, although the aggregate quantities will, of course, be much greater. To be sure, the value scales of the buyers will almost always differ, which means that their maximum buying prices for any given pound of butter will differ. The result is that, as the market price is lowered, more and more buyers of different units are brought into the market. This effect greatly reinforces the rightward-sloping feature of the market-demand curve.
As an example of the formation of a market-demand schedule from individual value scales, let us take the buyer described above as buyer A and assume two other buyers on the market, B and C, with the following value scales:
From these value scales, we can construct their individual demand schedules (Table 7). We notice that, in each of the varied patterns of individual demand schedules, none can ever be leftward-sloping as the hypothetical price declines.
Now we may summate the individual demand schedules, A, B, and C, into the market-demand schedule. The market-demand schedule yields the total quantity of the good that will be bought by all the buyers on the market at any given money price for the good. The market-demand schedule for buyers A, B, and C is as shown in Table 8.
Figure 33 is a graphical representation of these schedules and of their addition to form the market-demand schedule.
The principles of the formation of the market-supply schedule are similar, although the causal forces behind the value scales will differ.4 Each supplier ranks each unit to be sold and the amount of money to be obtained in exchange on his value scale. Thus, one seller's value scale might be as follows:
If the market price were two grains of gold, this seller would sell no butter, since even the first pound in his stock ranks above the acquisition of two grains on his value scale. At a price of three grains, he would sell two pounds, each of which ranks below three grains on his value scale. At a price of four grains, he would sell three pounds, etc. It is evident that, as the hypothetical price is lowered, the individual supply curve must be either vertical or leftward-sloping, i.e., a lower price must lead either to a lesser or to the same supply, never to more. This is, of course, equivalent to the statement that as the hypothetical price increases, the supply curve is either vertical or rightward-sloping. Again, the reason is the law of utility; as the seller disposes of his stock, its marginal utility to him tends to rise, while the marginal utility of the money acquired tends to fall. Of course, if the marginal utility of the stock to the supplier is nil, and if the marginal utility of money to him falls only slowly as he acquires it, the law may not change his quantity supplied during the range of action on the market, so that the supply curve may be vertical throughout almost all of its range. Thus, a supplier Y might have the following value scale:
This seller will be willing to sell, above the minimum price of one grain, every unit in his stock. His supply curve will be shaped as in Figure 34.
In seller X's case, his minimum selling price was three grains for the first and second pounds of butter, four grains for the third pound, five grains for the fourth and fifth pounds, and six grains for the sixth pound. Seller Y 's minimum selling price for the first pound and for every subsequent pound was one grain. In no case, however, can the supply curve be rightward-sloping as the price declines; i.e., in no case can a lower price lead to more units supplied.
Let us assume, for purposes of exposition, that the suppliers of butter on the market consist of just these two, X and Y, with the foregoing value scales. Then their individual and aggregate market-supply schedules will be as shown in Table 9.
This market-supply curve is diagramed above in Figure 33.
We notice that the intersection of the market-supply and market-demand curves, i.e., the price at which the quantity supplied and the quantity demanded are equal, here is located at a point in between two prices. This is necessarily due to the lack of divisibility of the units; if a unit grain, for example, is indivisible, there is no way of introducing an intermediate price, and the market-equilibrium price will be at either 2 or 3 grains. This will be the best approximation that can be made to a price at which the market will be precisely cleared, i.e., one at which the would-be suppliers and the demanders at that price are satisfied. Let us, however, assume that the monetary unit can be further divided, and therefore that the equilibrium price is, say, two and a half grains. Not only will this simplify the exposition of price formation; it is also a realistic assumption, since one of the important characteristics of the money commodity is precisely its divisibility into minute units, which can be exchanged on the market. It is this divisibility of the monetary unit that permits us to draw continuous lines between the points on the supply and demand schedules.
The money price on the market will tend to be set at the equilibrium price—in this case, at two and a half grains. At a higher price, the quantity offered in supply will be greater than the quantity demanded; as a result, part of the supply could not be sold, and the sellers will underbid the price in order to sell their stock. Since only one price can persist on the market, and the buyers always seek their best advantage, the result will be a general lowering of the price toward the equilibrium point. On the other hand, if the price is below two and a half grains, there are would-be buyers at this price whose demands remain unsatisfied. These demanders bid up the price, and with sellers looking for the highest attainable price, the market price is raised toward the equilibrium point. Thus, the fact that men seek their greatest utility sets forces into motion that establish the money price at a certain equilibrium point, at which further exchanges tend to be made. The money price will remain at the equilibrium point for further exchanges of the good, until demand or supply schedules change. Changes in demand or supply conditions establish a new equilibrium price, toward which the market price again tends to move.
What the equilibrium price will be depends upon the configuration of the supply and demand schedules, and the causes of these schedules will be subjected to further examination below.
The stock of any good is the total quantity of that good in existence. Some will be supplied in exchange, and the remainder will be reserved. At any hypothetical price, it will be recalled, adding the demand to buy and the reserved demand of the supplier gives the total demand to hold on the part of both groups.5 The total demand to hold includes the demand in exchange by present nonowners and the reservation demand to hold by the present owners. Since the supply curve is either vertical or increasing with a rise in price, the sellers’ reservation demand will fall with a rise in price or will be nonexistent. In either case, the total demand to hold rises as the price falls.
Where there is a rise in reservation demand, the increase in the total demand to hold is greater—the curve far more elastic—than the regular demand curve, because of the addition of the reservation-demand component.6 Thus, the higher the market price of a stock, the less the willingness on the market to hold and own it and the greater the eagerness to sell it. Conversely, the lower the price of a good on the market, the greater the willingness to own it and the less the willingness to sell it.
It is characteristic of the total demand curve that it always intersects the physical stock available at the same equilibrium price as the one at which the demand and supply schedules intersect. The Total Demand and Stock lines will therefore yield the same market equilibrium price as the other, although the quantity exchanged is not revealed by these curves. They do disclose, however, that, since all units of an existing stock must be possessed by someone, the market price of any good tends to be such that the aggregate demand to keep the stock will equal the stock itself. Then the stock will be in the hands of the most eager, or most capable, possessors. These are the ones who are willing to demand the most for the stock. That owner who would just sell his stock if the price rose slightly is the marginal possessor: that nonowner who would buy if the price fell slightly is the marginal nonpossessor.7
Figure 35 is a diagram of the supply, demand, total demand, and stock curves of a good.
The total demand curve is composed of demand plus reserved supply; both slope rightward as prices fall. The equilibrium price is the same both for the intersection of the S and D curves, and for TD and Stock.
If there is no reservation demand, then the supply curve will be vertical, and equal to the stock. In that case, the diagram becomes as in Figure 36.
- 3. The tabulations in the text are simplified for convenience and are not strictly correct. For suppose that the man had already paid six gold grains for one ounce of butter. When he decides on a purchase of another pound of butter, his ranking for all the units of money rise, since he now has a lower stock of money than he had before. Our tabulations, therefore, do not fully portray the rise in the marginal utility of money as money is spent. However, the correction reinforces, rather than modifies, our conclusion that the maximum demand-price falls as quantity increases, for we see that it will fall still further than we have depicted.
- 4. On market-supply schedules, cf. Friedrich von Wieser, Social Economics (London: George Allen & Unwin, 1927), pp. 179–84.
- 5. The reader is referred to the section on “Stock and the Total Demand to Hold” in chapter 2, pp. 137–42.
- 6. If there is no reservation-demand schedule on the part of the sellers, then the total demand to hold is identical with the regular demand schedule.
- 7. The proof that the two sets of curves always yield the same equilibrium price is as follows:
Let, at any price, the quantity demanded = D, the quantity supplied = S, the quantity of existing stock = K, the quantity of reserved demand = R, and the total demand to hold = T. The following are always true, by definition:
S = K - R
T = D + RNow, at the equalibrium price, where S and D intersect, S is obviously equal to D. But if S = D, then T = K - R + R, or T = K.