Nature of Competition: Three Dimensions of Arbitrage

 

There are three types of arbitrage in association with  trade in the market. As arbitrage becomes prevalent, prices will be converging to a particular price level. There in economics as abstract science will be “one price” of each (independent) event which must be defined per period.

             In reality, what we have is not anything more than a rough trend to convergence, subject first of all to information deficiency disorder (IDD). When it comes to crossing over periods, the IDD gets even more problematic due to the maxim, “The only constant is change.” By definition of the would-be “doomsayer” (Heraclitus), the change is over the lapsing time (T^-1).

             By the way, “asymmetric information” is anything but news if in the real economy of unanimous and ubiquitous IDD. On the flipside, “being constant” would be news of GOST, or the greatest of all time. And, those’re the way it s.

 

Interspatial arbitrage. Getting down to the real business, suppose the two markets, the East-Gate and the South-Gate marts. The standardized apple of Golden Delicious (GD) sells @30 cents in the East while @40 cents in the South. Idealizing the noise called “transaction costs” away, we might think of arbitrage from three perspectives:

1)     Where to buy outright

2)     Where to sell out-left

3)     Buy, right or left, and sell, in reverse, at the same time

 

We could like a piece of cake conclude that there is a trend toward a certain price somewhere in between the two, say @33.375 cents, specific to the week of accounting (T^-1). 

               A caveat as per annum: “the only constant” is the cyclical price levels in the following 51 weeks (T^-1). This would be the polar opposite  to the “constant k” (T⁰) in the Cambridge Quantity equation, imagined for the annual income (P∙Y).  Shh, the prototypical Keynesian conjecture has run from the short run (merely 1 week) to the long run (so many as 52 weeks) all the way into the "dead" run (T⁰).  A good boy, exogenous to Cambridge, would not play with "runs." 

Inter-substitutive arbitrage. Additionally suppose the orange of Cara Cara (CC) sells @44 cents in the week, East and South. In the meantime, a syndicate of fruit specialists announces that a unit of CC contains twice as much nutrient in cal as a unit of GD.

             Consequentially, the prices in the following period would prefer to move toward 25 cent for GD versus 50 cents for CC, or the like.

Intertemporal arbitrage. For a starter, “saving” in practice is never for hiding money under the mattress or throwing money into the sea as in "so many theories." The Private Saving is always and everywhere in the asset Privately Invested for the sake of consumption sometime in the future.

             Marilyn the Rational usually sets the “value of time” @2% PA. Now, she plans a single occasion of trip to the moon over the two years of this and the next. Checking the fares all across Space A to Space Z, she gets the best offers: 1,000,000 dollars this year vs 1,030,000 dollars next year. She will logically choose this year over the next; in economics jargon she chooses consumption over saving cum investment

             As in the meantime her fans follow suit in droves, the price of the lunar trip tends to move 1,005,000 for this vs 1,025,000 for the next, or something similar. 

 

The trend toward one price. Ideally without transaction costs of all kinds, there would be one price in terms of utility per dollar (U^-1∙m^-1); all across the products (M^-1∙U^-1), all across the nation (L^-3) and all thru the time before we are all dead.

             To paraphrase: In ideally “abstractive,” a double imagination as it were, all products are inter-substitutive. Then, there will be one bang for the buck. All the utility values (M∙U) are always (T^-1) and everywhere (L^-3) comparable to a number of dollar bills (U^-1∙m^-1). For the sake of confirmation, the American rule of law bars the innocent citizens from discriminating the legal tender across products, places and times, subject to the “value of time” being also legal.

             Lo and behold, the one price all across and all through. Of course that’s a dream of theory. In practice, nothing is completely reliable and nobody is entirely trustworthy. Don’t even think about “Economics is real.”

             Beware that knowledge and “information” is always and everywhere “asymmetric.” A lining on the cloud: Sometimes you may take a complimentary trip to Stockholm for suggesting a triviality (M⁰∙U⁰) or some other infinitesimal costs (U⁰∙m⁰). That’s the way K-economics is.

             In the first place, there is no such thing as “Theory and Practice.” That’s either alchemy or a chimera; both are futile and infertile at the same time. 

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