Disequilibrium Analysis of Price Formation – Part 1

Courtesy of Professor Fekete @ NASOE:

DISORDER AND CO-ORDINATION IN ECONOMICS

 Jesús Huerta de Soto writes that economics, far from being a theory of choice or decision, is a theory of processes describing social interaction that bring about coordination displacing disorder; see [6]. It establishes the fact that, through the intervention of entrepreneurship, disorder (a state of coordination at a lower level) is promoted to a state of coordination at a higher level. Economics also establishes the fact that entrepreneurs generate and disseminate information through a system of various indicators such as prices, wages, rents, interest and discount rates.

But how do entrepreneurs diagnose disorder and, having done so, how do they bring about coordination at a higher level? How do they generate and disseminate information through the price system or other systems of economic indicators? And how does the market integrate fragmented bits of information and power residing in individual entrepreneurs, making it the driving force of coordination? These are some of the questions we wish to answer in this essay.

One important effect of entrepreneurship is the modification of the perception of means-ends nexus. New ends emerge and means for their attainment must be perfected. New means are discovered while old ones are abandoned. Coordination dispels disorder here, creating new disorder there. The parade of new opportunities for entrepreneurial action is unceasing. The never-ending sequence of disorder- coordination-disorder is the driving force of economic progress and civilization. Of particular importance is the co-ordinating activity of the shopkeeper. He is in constant touch with the consumer, learning at first hand the extent to which the latter is dissatisfied with the kinds and prices of consumer goods displayed on the shelves. How is information represented by the scattered knowledge residing in individual shopkeepers processed?

How is intelligence about the changing mood of the sovereign consumer transmitted? Only when the problem is presented in this way does it become clear that simplistic models such as the equilibrium theories, the equation of exchange and the quantity theory of money, are wholly inadequate and can never account for the complex processes involved in the formation of prices. The static supply/demand equilibrium analysis of price formation and its offspring, the quantity theory of money, are one- dimensional. They project a black-and-white image. They look at goods in total isolation. They admit no insight into the effect on the price of alternative products either at the input or at the output end of the production line. They make no allowance for deliberate variation of product quality on the part of 1 the producer. A disequilibrium theory of price formation would have to be three-dimensional. It must project an image in full color. It must take the inter-dependence of the price with those of the substitutes at both the input and output level into full account. In this essay we attempt to lay the foundations of such a disequilibrium theory. In the first part we establish arbitrage as the very driving force of the market process.

We shall use the language of traders engaging in arbitrage on a daily basis. Their guiding star is the spread, that is, the difference in price between two goods (baskets of goods or, better still, baskets of goods plus other resources). Their basic tool is the straddle, that is, the combination of a purchase and a sale. The arbitrageur is shuffling his straddles in pursuit of pure entrepreneurial profits. To the uninitiated it may look as though the arbitrageur is being guided by intuition of some sort. But theory can expose the basic facts governing arbitrage without appealing to intuition.

The disequilibrium analysis of price formation of consumer goods to be presented here isolates three basic types of arbitrage: (1) horizontal arbitrage of the consumer using one-legged straddles responsible for the formation of the asked price; (2) vertical arbitrage of the producer using two-legged straddles responsible for the formation of the bid price; and (3) bid/asked arbitrage of the market- maker using four-legged straddles which is responsible for closing the bid/asked spread.

In the second part of the paper we discuss the coordination problem of economics in terms of the landscape of spreads. Entrepreneurs are addressing themselves to selected spreads through arbitrage. Horizontal arbitrage, using one-legged straddles, has a role to play in retrospective (backward-looking) or defensive strategies designed to protect profitability, including deliberate variation of product quality to increase capacity utilization. Vertical arbitrage using four-legged straddles has a role to play in prospective (forward-looking) or aggressive strategies designed to uncover hitherto unexplored spreads. Pure entre-preneurial profits depend on the producer’s skill in meshing these strategies. The third part of this essay deals with the coordination problem as it confronts the retail trade, as well as international trade. Neither the law of supply and demand nor the quantity theory of money applies in these markets: we must appeal to a disequilibrium model. An increase in the volume of purchasing media due to higher spending or an influx of foreign exchange has no inevitable effect on prices but will, instead, lower the discount rate.

We must analyze short-term capital movements in terms of the widening spread between the discount rate and the marginal productivity of social circulating capital. We must take arbitrage between the bill market and the consumer goods market into account. The lowering of the discount rate is equivalent to an increase in the marginal productivity of social circulating capital. Increased demand brings out increased supply sufficient to accommodate it, with no increase in prices. Price changes, whenever they occur, reflect coordination involving other factors. In company with Jesús Huerta de Soto I maintain that it is possible to explain the market process: the formation of prices, rents, wages, interest and discount rates, without reference to equilibrium models, merely by focusing on dynamic processes. As a first step, here we develop the disequilibrium analysis of price formation.

PART ONE: ARBITRAGE

Whether recognized or not, arbitrage is the driving force of the market process. It is present in every market action, even though sometimes it may well be hidden. It is not generally recognized that barter — a sale and a purchase ‘telescoped’ into a single transaction — is an instance of arbitrage. By the same token so is every purchase, since an explicit choice always incorporates the implicit rejection of the nearest alternative. In this paper the word arbitrage is used in the broadest possible sense, in order to unify seemingly fragmented entrepreneurial activities and seemingly unrelated sources of pure entrepreneurial profit. Arbitrage is a market strategy, shifting the emphasis from sales to straddles and from prices to spreads.

Spreads and straddles

A straddle is a market position with a long and a short leg. The long leg could be an outright purchase but, more typically, it is a commitment to buy or, just as typically, the liquidation of a commitment to sell. The short leg could be an outright sale but, more typically, it is a commitment to sell, or the liquidation of a commitment to buy. These commitments, as well as their liquidation, are always made at the current price. Each straddle belongs to a spread, namely, the difference between the prices at which the commitments to buy and sell have been made (sale price less purchase price). The spread, like the price, is subject to change. But the information-content of a change in the spread, unlike that in the price, is highly significant. Indeed, the importance of arbitrage, and the reason why human action should be viewed from the vantage point of the spread rather than that of the price, is found in the fact that a single move in the price is mostly random. By contrast, in a well-traded market, a single move in the spread is not random. It is a signal carrying an important message. The knowledgeable arbitrageur can read it and make most of it. This ability of his is the true source of pure entrepreneurial profit. Our starting point is the fundamental observation of Carl Menger in Principles of Economics [1] that there is no such thing as a monolithic price. Markets do, in fact, quote not one but two prices: one higher and the other lower. In market parlance the higher one is called the asked price, while the lower is the bid price. The two are never equal, so that the bid/asked spread (asked minus bid price) is always positive. The fundamental question is this: how are the bid and asked prices formed? We shall see that, in fact, two entirely different processes are involved. The asked price is the outcome of competition on the part of the consumers (sic!), whereas the bid price is the outcome of competition on the part of the producers (sic!). Either process can be properly described as arbitrage, attacking a certain spread, using a certain type of straddle.

Four-legged straddles

When the arbitrageur sees a profitable spread, say, he finds the price of an item x too low while that of a related item y too high, he moves to set up his initial straddle consisting of the initial long leg (commitment to buy x) and the initial short leg (commitment to sell y) at the prevailing prices. In market parlance he has entered the market for x with his long and that for y with his short leg. The arbitrageur expects his spread to widen (to narrow in absolute value if the initial spread was negative). If the market moves in his favor, he takes profit by offsetting his straddle: he enters the same markets once more with long and short legs switched around. His opposite straddle consists of the terminal short leg (liquidating the commitment to buy x) and the terminal long leg (liquidating the commitment to sell y) at the new prices. His profit is the net change in the spread (terminal minus initial spread; if negative, he has made a loss). We refer to this as a four-legged straddle as profits from the arbitrage can be calculated only after all four legs are in place. Four-legged arbitrage is the basic strategy of warehousing. Suppose a grain-elevator operator normally fills one of his two bins with corn and the other with wheat. Further suppose that as a result of poor weather in the wheat-growing regions he expects the corn/wheat spread (wheat price minus corn price) to widen. Acting on this insight he sells his corn (initial short leg) and buys wheat, filling his corn bin with wheat (initial long leg). When his expectation is fulfilled and the corn/wheat spread has widened, he sells his wheat in the corn bin (terminal short leg) and buys corn refilling his corn bin (terminal long leg). Since the profitability of the arbitrage can be established only after all four legs are in place, this is a four-legged straddle. The bid/asked arbitrage of the market- maker also uses four-legged straddles. In this case all four legs are in the same market. The market-maker, as it were, is ‘warehousing’ long and short positions in the same commodity, closing them out as the price is moving in his favor. The foreign exchange trader’s basic tool is also the four-legged straddle. His business also has the characteristics of warehousing. To catch a glimpse of the true significance of the four-legged straddle, consider the fact that the volume of trade in the world’s foreign exchange markets is estimated at a mind-boggling one and one quarter trillion dollars per day — more than the annual budget of the U.S. government! Virtually all of this trading is hedged, that is, transacted through the vehicle of four-legged straddles. The importance of the four-legged straddle goes beyond these examples which are special in that the terminal legs liquidate the respective commitments of the initial legs. In the most general case this restriction is removed. In the second part of this paper we shall see examples of four-legged straddles with each leg in a different market.

Two-legged straddles

Consider the vertical arbitrage of the producer. The long leg x of his straddle is in the producer goods market and the short leg y is in the consumer goods market, where x is the input and y is the output of his production line. This is an example of a two- legged straddle, since profits from the arbitrage can be calculated already when the first two legs are in place. We reduce this to a four-legged straddle by adding two terminal legs at zero prices (so that entering the phantom legs won’t disturb the profitability of the arbitrage). The phantom legs are entered in order to satisfy the requirements of double-entry book-keeping. The four legs are: (1) placing an order for x (initial long leg) (2) taking an order for y (initial short leg) (3) taking delivery of x (terminal short leg) (4) making delivery of y (terminal long leg).

One-legged straddles

Consider the horizontal arbitrage of the producer. He buys the favored producer good x (his present input) while he refrains from buying the disfavored one y (his former input). Thus he creates a straddle with long leg x and short leg y, and the corresponding spread shows the profit (saving) that arises out of his switching from y to x. This is called a one-legged straddle, because the profit from the arbitrage can be calculated already when the single long leg x is in place. To satisfy the requirements of double-entry book-keeping, we reduce this to a four-legged straddle by entering three phantom legs. The four transactions are: (1) placing an order for x (2) cancelling the order for y (3) taking delivery of x (4) taking credit for cancelling the order for y. As in the previous case, these form a four-legged straddle. The terminal legs are entered at zero prices so as not to disturb profitability. We are now ready to present the disequilibrium analysis of the price formation of consumer goods in three steps: the formation of the asked price, the formation of the bid price, and the closing of the bid/asked spread.

Formation of the asked price

As noted already, the asked price is the outcome of the competition of the consumers. In more details, the asked price a of the consumer good x marks the point where the opportunity cost of buying an additional unit of x becomes critical to the marginal consumer. He is the first consumer to refuse to buy the uptick in the price of x — in view of his opportunity to buy a substitute, say, the consumer good x’. Consumers are doing horizontal arbitrage all the time: they constantly shift their custom. Their guiding star is the constellation of horizontal spreads. As a result of their competition, horizontal spreads will widen. But the spreads which belong to the one-legged horizontal straddles with the same long leg x cannot continue to widen indefinitely. Their widening will be checked by the marginal consumer of x. His refusal to buy x, and his buying x’ instead constitutes an opposite horizontal straddle and entering it will stabilize the spread. Of course, the person of the marginal consumer, and the item x’ he substitutes for x, are subject to change. Whenever another consumer takes over that role from the first the item x” he substitutes for x may well be different from x’. Indeed, over a period of time when the price of x is undergoing a change, hundreds of different people may, one after another, play the role of the marginal consumer of x, while x’ sweeps through the spectrum of all possible substitutes for x. This picture can be simplified if we personify the marginal consumer of x and think of him as a figure skater skating in the rink of consumer goods. His long leg is anchored to x while his short leg is skating through the possible substitutes of x. This, then, is the mechanism whereby the market integrates the fragmented knowledge of and power over the price of x that resides in individual consumers, crystallizing it in the form of a single indicator: the asked price for x.

Formation of the bid price

Recall that the asked price is the outcome of the competition of the consumers. Now we shall see that, by contrast, the bid price is the outcome of the competition of the producers. Here are the details. 5 The bid price b of the consumer good x marks the point where the opportunity cost of selling an additional unit of x becomes critical to the marginal producer. He is the first producer to refuse to sell the downtick in the price of x—in view of his opportunity to refuse to buy the producer good y, his input in the production of x. All producers of x are doing vertical arbitrage between consumer and producer goods all the time: they constantly shift their production lines from one vertical straddle to another. Their guiding star is the constellation of vertical spreads. As a result of the competition of producers the vertical spreads will shrink. But the spreads which belong to the two-legged vertical straddles with the same short leg x will not keep shrinking indefinitely. Their shrinking is checked by the marginal producer of x. His refusal to sell x and his refusal to buy y constitutes an opposite vertical straddle, and entering it will stabilize the spread. Of course, the person of the marginal producer of x, and his input y, are subject to change. When another producer takes over that role from the first, the item y’ he uses as his input for the production of x may not be the same as y. Indeed, over a period of time when the price of x undergoes a change, hundreds of different people may, one after another, play the role of the marginal producer of x, while y’ sweeps through the spectrum of alternative inputs suitable for the production of x. This picture can be simplified if we personify the marginal producer of x and imagine that his short leg is anchored to x on the bottom rung of a ladder, while his long leg is trying to get a firm foothold on the next rung, touching the alternative inputs suitable for the production of x. This, then, is the mechanism whereby the market integrates the scattered knowledge of and power over the appropriate level of the price of x that resides in the individual producers, crystallizing it in the form of a single indicator: the bid price of x. Our results can be summarized as follows. The asked price is determined by marginal utility. It can be characterized as the lowest price at which consumers can buy as much as they want without haggling — explaining how the asked price earns its name. The bid price is determined by the marginal profitability of production. It can be characterized as the highest price at which producers can sell all they have without haggling — explaining how the bid price earns its name. It follows that marginal utility must be higher than marginal profitability (otherwise no production will take place).

Closing the bid/asked spread

In the very nature of the case a>b,so there is a positive bid/asked spread a – b. The existence of a positive spread, as always, invites arbitrage. The arbitrageur attacking the bid/asked spread is called the market-maker (on the floor of the New York Stock Exchange, the specialist). The market- maker buys at the lower bid price and sells at the higher asked price (while everybody else must, unless prepared to haggle, buy at the asked and sell at the bid price). The guiding star of the market-maker is the bid/asked spread. Competition of market- makers causes the bid/asked spread to shrink. But the process of shrinking the bid/asked spread will not continue indefinitely. It will be checked by the marginal market-maker, whose withdrawal from arbitrage will stabilize the spread. Usually the spread is negligible (hence the impression of a single monolithic price). It clear that the spread is determined by the marginal profitability of the market-making business. Note the beneficial effect of the bid/asked arbitrage. Everybody benefits: the consumer enjoys a lower buying price, the producer is rewarded by a higher selling price. The analysis of the market process cannot be complete without the inclusion of the arbitrage of the market-maker. Of course, the three components of arbitrage (horizontal, vertical, and bid/asked arbitrage) are carried on simultaneously and continuously — not one after another as the theory might suggest. The decomposition of market agitation into three separate components has purely methodological significance. This completes the marginal analysis of the price formation of consumer goods. The corresponding analysis of the price formation of producer goods can be given mutatis mutandis (see below).

The sovereignty of the consumer

Competition of the producers may or may not have the effect of lowering the bid price of x. The marginal producer is confronted with the choice whether to compete or not to compete. If he decides to compete, he will adjust his selling price to that of his competition, and will try to restore profitability through horizontal arbitrage. If he decides not to compete, he will drop out of the ranks of producers and another man will take over as the marginal producer of x. In either case, the bid price will get lowered, with the asked price (driven by bid/asked arbitrage) to follow hard on its heels. This is what happens in the case competition is keen. If competition is dull, the marginal producer may prevail in his effort to hold the bid price. Analogously, competition of the consumers may or may not have the effect of raising the asked price. But the two cases are far from being symmetrical. The fact is that a rise in the asked price has an additional consequence. Unlike the lower bid price, a higher asked price tends to widen the vertical spread. This will bring out fresh competition for the producers. While a price rise induced by increased consumer demand are mostly temporary, lasting only as long as it takes for the producers to adjust, a decrease in price due to increased production, to the extent they reflect technological improvements and increased productivity, are mostly permanent. (Example: the dramatic fall in the price of personal computers). This is the feedback effect: increased competition on the part of the consumers brings about increased competition on the part of the producers. But note the absence of a feedback in the opposite direction. We conclude that consumers have a veto power over the marginal producer. The predominant role in the process of price formation belongs to the consumers. The role of the producers is subordinate. Because of this bias in favor of the consumer, marginal utility may be considered the primary factor in the formation of the price, while marginal profitability is secondary. This lack of symmetry between horizontal and vertical arbitrage is often referred to as the Principle of Sovereignty of the Consumer. *

Critique of equilibrium analysis

The superiority of our disequilibrium analysis over the conventional supply-and- demand equilibrium analysis of price formation is clear. The latter is a black-and- white, one-dimensional shadow of reality. It looks at the consumer good (together with its price and quantity) in total isolation. It doesn’t admit any insight into the effect on the price of alternative inputs or outputs, nor can it handle deliberate producer-induced changes in quality. By contrast, the disequilibrium analysis of price formation presents a three-dimensional image of reality in living color. It takes the interdependence of prices with those of alternative consumer goods at the level of output, as well as with those of alternative producer goods at the level of input, into full account. It can well handle the problem of deliberate producer- induced changes in quality. Disequilibrium analysis puts the market process, and the role of arbitrage in it, into high relief. F. A. Hayek in Prices and Production [2] and Ludwig von Mises in Human Action [3] clearly recognized the entrepreneurial activity of producers in setting up vertical straddles to attack selected vertical spreads. (Needless to say, they used a different terminology). The adjective “vertical” relates to the vertical structure of goods due to Menger, elaborated in Israel M.Kirzner’s Market Theory and the Price System [4]. This is a classification of goods according to their remoteness from the final consumer. Consumer goods are first order goods while those entering into the input of the production of consumer goods are of the second order. In general, goods that enter into the input of the production of nth order goods are of order n+1. Calling the straddle of the producer with commitments to buy an (n + l)st order good and to sell an nth order good “vertical” is just a plausible extension of Menger’s original terminology. Horizontal straddles and spreads are to be understood in exactly the same sense. The choice of the adjective here was inspired by Kirzner’s concept of “horizontally related goods and markets” mentioned in [4]. In his book Competition and Entrepreneurship [5] Kirzner also provides an important example of a horizontal straddle. It is the market position of the producer of a consumer good y who discovers that consumers are willing to pay more for y’, another consumer good that he can produce out of the same input basket x. Accordingly, the producer switches production from y to y’ to increase profitability. Notice that the producer has created a one-legged horizontal straddle at the level of first order goods, with the significant leg being the initial short leg y’. Of course, the producer of nth order goods can also avail himself of one-legged horizontal straddles in order to improve profitability. Complementary to this there is another type of horizontal arbitrage that will play a role in the marginal analysis of the formation of the asked price of an nth order good. The producer may want to increase profitability by replacing his input basket x by a cheaper one x’. In the latter case the producer’s horizontal straddle is at the level of (n + l)st order goods; in the former, it is at the level of nth order goods. By a simple extension of this terminology to the level of first order goods we may also call the market position of the consumer, who is shifting his custom from one product to another, a one-legged horizontal straddle at the level of consumer goods. None of the aforementioned authors referred to these entrepreneurial activities by the name arbitrage. But to do so is helpful in the present context as it brings out the important common element in the seemingly unrelated activities of the entrepreneurs, and it makes the classification of entrepreneurial activities possible. By the same token, consumer buying should also be recognized as an instance of horizontal arbitrage. After all, every purchase is an explicit choice involving the implicit rejection of the nearest substitute. It is true that the savings that arise out of the consumer’s horizontal arbitrage are not normally regarded as profits. There is no need to quibble over semantics. It would appear to be inconsistent to dismiss the consumer’s activity of comparing prices and quality before buying as non-entrepreneurial in character, having accepted as entrepreneurial the producer’s analogous activity of “shopping around” for alternative inputs — which certainly makes a direct contribution to profitability of the enterprise.

Price formation of producer goods

Marginal analysis is readily extended to the price formation of nth order goods. The asked price is the outcome of competition of the users of an nth order good doing horizontal arbitrage in terms of one-legged straddles. In more details, the asked price of an nth order good x marks the point where the opportunity cost of buying an additional unit of x becomes critical to the marginal user of x. He is the first among the producers of goods of order n – 1 i n refusing to buy the uptick in the price of x — in view of his opportunity to buy a substitute, another producer good x’ of order n instead. The bid price of an nth order good is the outcome of competition of producers doing vertical arbitrage between goods of order n and n+1 using two-legged straddles. In more details, the bid price of an nth order good marks the point where the opportunity cost of selling an additional unit of x becomes critical to the marginal producer of x. He is the first among the producers to refuse to sell the downtick in the price of x — in view of his opportunity in refusing to buy the producer good y’ of order n+1, the input of the production line for x. We have noted earlier the Principle of Sovereignty of the Consumer in the context of the production of consumer goods. The same principle extends to the production of higher order goods. The role of the producer whose product is less remote from the ultimate consumer is dominant, the role of the producer whose product is more remote is subordinate. (From this remark the Principle of Imputation can be easily derived.) It often happens that a higher order good serves as input for the production of several goods of different orders. For a long time coal was a consumer good as well as a producer good. Platinum is a second order good in artistic applications (e.g., in making jewelry), but it also serves as a higher order good in industrial applications (e.g., in making catalytic converters). Whenever a product serves both as an mth and an nth order good we may assume that the formation of the asked and bid price takes place at both levels. Should there be a substantial difference, multilateral arbitrage would close the spread between the gaping prices. (Exception: negotiated prices for industrial applications. For example, it is known that the platinum mining industry sells most of its production at negotiated prices which are normally set below the free market price. Not only does the industry lock in a price in this way, but it also carves out a market share in advance. Industrial consumers are, by contract, barred from reselling platinum in the free market, as this would defeat the purposes of the producer.)

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