Quantum theory of economics

Pretty neat title huh? :-)

I had in mind that naming this theory as a "quantum theory" would reflect a quest for a new micro- or even microscopic economic theory based on discrete individual events. Referring to the previous writing, “what’s the right value” (see the blog below), I just think a new economic theory is needed...

Without further ado let’s start:
I would first propose to empty your minds from all of the previous economic theories, all postulates about intrinsic values, laws of demand and supply or concepts for market value, since when an individual transaction occurs I think none of those really matter…except only as mental reference points in the minds of the buyer and the seller.

Let’s just look at what happens in the real world when a “thing” T = goods, service, user right, option or whatever a person or an organization can legally own, changes ownership that is a transaction occurs. Let’s also assume that the ownership is defined legally unambiguously and both the buyer and the seller have enough credibility in each other's minds so that they trust each other to keep their end of the contract and that they in fact are worth the trust.

A transaction takes place if
1) Buyer B and Seller S agree on the price P of T.
2) B will pay the agreed price P as cash equivalents and S gets T or whatever documentation assigns the ownership of T to her possession
I suppose that’s enough, don’t you think?

In order to study when does the first condition 1) get satisfied, we should investigate what are the things that actually affect S’s and B’s opinions about the right value for P when they negotiate the deal? In the order of importance imo, For S there should be at least
- The need or wish to sell. What is S’s negotiation target price M and what is it based on? Would S be ready to give T away for free in some cases, or would she be very unwilling to sell even double the expectation for whatever is quoted as market price?
- B's ability to negotiate the cheapest possible price that makes S to sell T to B
- External valuation factors that affect S's opinion about the value of M, such as
o Reference prices from previous similar type of deals
o The projected market price based on expected future availability and valuation of T
o In case it would be possible to earn money with T, the expected future income enabled with T
o Any goodwill (such as strategic value) S thinks B should assign to T
o Aesthetic or emotional values that S has assigned to T
o …what else?

Similarly for B it should hold
- The need or want to buy. What is B’s negotiation target price N and what is it based on? How much would B be ready to pay (Nothing or all of his money or perhaps even borrow some more?)
- S's ability to negotiate the highest possible price that B is willing to pay for T
- External valuation factors that affect N, such as
o Reference prices from previous similar type of deals
o The projected market price based on expected future valuation and availability of T
o In case it would be possible to earn money with T, the expected future income enabled with T
o Any goodwill (such as strategic value) B holds for T
o Aesthetic or emotional values that B holds for T
o …what else?

By now it seems to get rather complicated doesn’t it? But the bottom line is that unless the price is strictly regulated by some authority - which it never can be, since as you know, even in the most regulated economies there is always black market valuation – the actualized prices are always a subjective agreement between the seller and the buyer.

But in order for the transaction to get completed by the satisfying the condition 2) there is also an upper limit on how much the buyer can afford. The transaction does not occur if T costs more than what B is able to pay. Let’s denote that value as A. But defining A is not simple either. One could think that B has only as much money that he has liquid assets, but of course he could also borrow more. And since the amount that B can get in debt is again based on the subjective valuation of her credit and other assets or even future looking commitments there is in principle no upper limit for A. But since, of course, the higher the price (P), the more improbable it becomes that B is able to raise all the money and in practice A should be finite. At least it can’t be more than all the resources in the world that can be assigned an ownership legally.

Now here is my quantum theory based on the individual deals Q as discrete quantums of economy:

I claim that a Market value V(T) for a thing T is the expected value calculated over the sum of all the prices, P, of all the possible individual deals, Q, between Buyers, B, and Sellers, S, that could commence and consequently produce a sets of individual deals Qi with prices Pi. it would be a “quantum theory” since individual deals are discrete, and the term the deals Qi would be the “quantum” incidents of economy that you could correspond to the quantums in physics terminology.

So in order to calculate V(T), I should be able to write a sum/integral over the probability distribution for individual deals, Qi, so that the V(T) is an integral over all possible transactions over pricse P(Qi) = Pi. Individual Pi's in turn are defined as P(Qi) = P(MN), where M and N are the probability distributions or “wave functions” representing buyer’s and seller’s negotiation prices. If M = N then the Price P = M =N, but if they differ, price P(MN) will be an integral from 0 to A over the convolution (I guess :-)) of the probability functions M and N, where A is the maximum sum of money a buyer can get.

Or something of the sort =)

Unfortunately I have no integral sign or a summing sigma available for this blog so I have a good excuse not to write down the equations! But I would think that the people skilled in the art of dealing with probability spaces or better yet the quantum mechanical formalism should be able to get the idea. Thus I would leave it as homework to write down the equations (…and then solve them for a case of European car industry! Lol)

But hand waving theorizing does not end here!…to further continue the analogy to physical quantum mechanics, the equation for Price as P(Qi) = Pi(MN) could perhaps be understood as a Hamilton function or something like that. Wouldn’t it then be possible to use also statistical mechanics to calculate macroeconomic values based on the market values for V(T) ?

Well...if given something close to an infinite amount of time, I might perhaps be able to device some credible looking equations with a standard mathematical notation used in probability theory. Mathematicians are interested usually only about the theoretical description of things and proving them. Once I had written down the statements and equations and checked that they are formally right…I would be done. But physicists have the apparatus to actually calculate something with actual concrete numbers (which unfortunately I don’t). So in order to use the quantum mechanical tools, I would need to ask help from physicists…as bitter as it might be =) And with physicists helping I might get easier acceptance for the cool title “quantum theory of economics”.

One more addition: Wouldn’t it be cool if it were possible to use Feynman graphs to describe the interaction between Buyer and Seller. One could use the solid lines for things and wavy lines for money maybe. Think about it!

I don’t think I am even close to being the first to take the microscopic approach and propose a theory based on integrating over individual deals, yet I might be the first who is arrogant enough to call it a quantum theory and draw parallels to the physical theories as carelessly, even in a tongue-on-cheek blog… but it’s intriguing isn’t it? Unfortunately making a proper theory is way beyond me. Both in terms of my time and capacity as a mathematician….so I would plead for help: If there are people who are interested in this, let me know. I spend an unbelievable amount of time in SL and PH so finding me or someone who knows me shouldn’t be that hard. In fact I have thought of proposing a collaborative effort around this. It would be a very interdisciplinary study, since our M and N “wave functions” would be based on individual people’s wants, needs, valuations, credit limits and every human aspect that makes them buy or sell things.

That’s all for now
*winks*
Q

PS This whole thing is not very thoroughly proofread yet, so I might correct small obvious errors and make the writing more readable afterwards. But the idea should be there already.

PPS first corrective edition done on March 17th

PPS Second revision, March 27th (thanks Strider!!!)