Antal E . Fekete Towards a Dynaimic Microeconomics Introduction Alan Meltzer has once remarked that " we need a dynamic micro-theory " . The static supply / demand equihbrium analysis of pnce formation is one-dimensional . It looks at the product in total isolation . It admits no insight into the effect on the price of altemative products , either at the input or at the output end of the production line . It makes no allowance for delibérate variation in product quality on the part of the producer . A dynamic theory of price formation would have to be three-dimaisional . It would have to take the inter-dependence of the price with those of substitutes at both the input and the output level into full account . It would have to allow for delibérate variation in product quality . In the present paper we attempt to lay the foundations of such a dynamic theory , explicitly recognizing arbitrage as the driving forcé of the market process . We shall use the language of traders with daily experience with arbitrage . Their guiding star is the spread . the difference in price between two goods ( baskets of goods or , even more generally , baskets of goods and other resources ). Their basic tool is the straddle . the combination of a purchase and a sale . The arbitrageur is shuffling his straddles in pursuit of puré oitrepreneurial profit . To the uninitiated it looks as if he is guided by intuition . But theory can establish the basic facts goveming arbitrage without appealing to intuition . The marginal analysis of price formation of consumer goods to be presented here isolates three types of arbitrage : ( 1 ) the horizontal arbitrage of the consumer , responsible for the formation of the asked price , usmg one-legged straddles ; ( 2 ) the vertical arbitrage of the producer , responsible for the formation of the bid price , using two-l^ged straddles ; and ( 3 ) the bid / asked arbitrage of the market-maker , responsible for closing the bid / asked spread . In the second part of the paper we discuss problems of entreproieurship and profit in the light of arbitrage . Horizontal arbitrage has a role to play in retrospective strat^es to protect profítability , including variation of product quality and increasing capacity utilization . Vertical arbitrage using four-legged straddles has a role to play in Antal E . Fekete , Professor Emeñtus , Memorial University of Newfoundland , was Visiting Professor of Economics at Universidad Francisco Marroquín during 1996 . He is the author of several monographs and papers on monetary reform , and was recently the winner of the International Currency Prize for 1996 , awarded by Bank Lips , Ltd . ( Zürich ). His e-mail address is : fekete @nemann . math . mun . ca . Laissez - Faire 1

prospective , forward-looking strat^es of aggressively pursuing puré entrepreneurial profít . Entrqjraieurial success depaids on the skill to mesh these strategies . This paper is the fírst in a series . Much work remains to be done to deal with other types of arbitrage , such as inter-spatial and inter-temporal arbitrage having important implications in regard to tnter-regional and intemational trade and the formation of futures prices , and also arbitrage between the bond market and other markets , having important implications in r^ard to the formation of the interest rate structure . These and other related issues will be dealt with in subsequent papers . Arbitrage Arbitrage is the driving forcé of the market process . It is present in every market action , even though sometimes it may well be hidden . It is not often 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 altemative . The word 'arbitrage' is used in this paper in its broadest possible sense , in order to unify the seemingly fragmented activities of entrepreneurs and the seemingly unrelated sources of puré entrepreneurial profit . Arbitrage is a market strat^y that puts the emphasis not on sales per se but on straddles , and is motivated not by prices per se , but by spreads . 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 , again , more typically it is a commitmait to sell , or the liquidation of a commitmait to buy . The commitment to buy or sell ( or the liquidation thereof ) is always made at the current price . To every straddle there belongs a spread , that is , the difference between the prices at which the commitments to buy and sell have beai made ( sale price less purchase price ). The spread , like the price , is subject to change . But the information-contait of a change in the spread , unlike that in the price , is highly signifícant . In fact the importance of arbitrage , and the reason why human action should be viewed from the vantage point of the spread , rather than from that of the price , is found in the fact that a single move in the price is mostly random . By contrast , a single move of the spread ( in a well-traded market ) is a signal that is far from being random . The knowledgeable arbitrageur can read it make most of it . and This insight of his is the true source of puré entrepreneurial profit . Our starting point is the fundamaital observation of Cari Menger in Principies of Economics that markets do not quote one single monolithic price ; they in fact quote two prices : a higher and a lower one . In market parlance , the higher one is called the asked price , and the lower the bid price . The two are never equal , so that the bid / asked spread ( i . e ., asked minus bid price ) is always positive . The fundamental question to ask is how the bid and asked prices are formed by the market process . We shall see that the asked price is the outcome of the competition of the consumers , while the bid price is the outcome of the competition of the producers . Either process can be described as arbitrage , addressing a definite spread , using a deñnite type of straddle . Laissez - Paire 2

The four-legged straddle When the arbitrageur sees a profitable spread , say , he fínds the p rice of one item X too low while that of a related item y too high , he sets 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 prevaihng pnces . In market parlance , he has entered one market with the long 1^ and another with the short . The arbitrageur expects his spread to widen ( narrow in absolute valué , if n^ative ). If the market moves in his favor , he takes prqfit by ofFsetting his straddle : he enters the same markets once more but with the long and short legs switched around . Thus 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 pnces . 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 the profit from the arbitrage can be calculated only after all four l^s are in place . in place , this is a four-l^ged straddle . The foreign exchange trader's basic tool is also the four-l^ged straddle . This is not surprising if we contémplate that his business also has the characteristic of warehousing . To catch a glimpse of the true significance of the four-l^ged straddle consider the fact that the volume of the world's foreign exchange markets is estimated at a mind-boggling one and one quarter trillion doUars per doy , more than the annual budget of the U . S . govemment . Virtually all of this trading is hedged , that is , done through the vehicle of four-legged straddles . But the importance of the four-legged straddle goes beyond the range of these examples . Every type of arbitrage can be reduced to four-legged straddles . Note that the four-l^ged straddles above are special in that the terminal l^s liquidate the respective commitments made by the initial l^s . In the general case this restriction is removed . In the second part of this paper we shall see examples of a four-l^ged straddle in the general case , with each 1^ in a different market . The two-legged straddle Four-l^ged arbitrage is the basic strat^y of the wardiousing business . Suppose a grain- elevator operator normally filis one of his two bins with wheat , and the other with com . As a result of poor weather in the wheat-growing regions he expects the wheat / com spread to widai . Acting on his insight he sells his com ( initial short leg ) and filis his com bin with wheat ( initial long 1^ ). When his expectation is fulfílled and the wheat / com spread has widened , he sells his wheat in the com bin ( terminal short 1^ ) and replaces it with com ( terminal long 1^ ). Since the profitability of the arbitrage can be established only after all four legs are Consider the vertical arbitrage of the producer . The long 1^ x of his straddle is in the producer goods market and the short 1^ y is in the consumer goods market , where x is the input and y the output of his production line . This is called a two-legged straddle , because the profit 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 l^s at zero pnces ( so that the addition of the phantom legs does not afíect the profitability of the arbitrage ). The significance of the phantom l^s is to satisfy the requironents of double-entry book-keeping . The four transactions Laissez - Faire 3

involved are : placing an order for x , taking an order for y , taking delivery of x , makíng deliveiy of j^ . They correspond to the four l^s , respectively , of a straddle : ( 1 ) the initial long 1^ x , ( 2 ) the initial short 1^ > ' , ( 3 ) the terminal short leg x , ( 4 ) the terminal long 1^ > ^ . the opportunity cost of buying an additional unit of x becomes critical to the marginal consumer of x . He is the first consumer to refuse to buy the uptick in the price of x , and the reference is to his opportunity to buy a substitute instead , namely , the consumer good x \ The one-legged straddle 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 ). This creates a straddle with long leg x and short leg y , and the corresponding spread shows the profít ( saving ) that arises out of the switch from y to X . This is called a one-legged straddle because the profít 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 reduge this to a four-legged straddle by adding three phantom legs . The four transactions involved , corresponding to the four legs ( 1 ) - ( 4 ) named above , are : placing an order for x , cancelling the order for y , taking delivery of x , and getting credit for the cancelled order for^ , respectively . The terminal legs are entered at zero pnces , so that they will not affect the profitability of the arbitrage . We are now ready to present the marginal analysis of the pnce formation of consumer goods in three steps : the formation of the asked pnce , the formation of the bid pnce , and the closing of the bid / asked spread . Formation of the asked príce As noted above , the asked pnce is the outcome of competition by the consumers . Li more details , the asked price a of the consumer good x marks the point where All consumers of x 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 the competition of the consumers , the horizontal spreads will widen . But the spreads which belong to the one-l^ged horizontal straddles with long leg x will not continué to widen indefinitely . Their widening will be diecked 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 considers as his substitute for x , are subject to change without notice . Whenever another consumer takes over that role from the first , his substitute for x may not be the same x' ; it could be x ". 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 consumer of x , while x' sweeps through the spectrum of possible substitutos for x . This picture can be simplifíed 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 1^ is anchored to X , while his short 1^ is skating through the possible substitutos of x . This , then , is the mechanism whereby the market integrates the fragmented power over the price of X that resides in individual Laissez - Faire 4