On the current state of economic theory

Jevons often gets the credit or blame of the current state of economic theory. However, Jevons made it clear that "I believe that dynamical branches of the Science of Economy may remain to be developed, on the consideration of which I have not at all entered." He also pointed out, by writing The Coal Question, that thermodynamics should be the future foundation of the dynamical branches of the Science of Economy. The theory of thermodynamics and statistical mechanics was at its infancy in Jevons’ time. It would be too much to ask Jevons to develop a fully grown dynamic theory of economics. However, more than one and half century later, the economic profession is still busy fortifying the citadel built by Jevons and others. Few venture out on the path directed by Jevons.  

The static theory of Jevons, or his theory of value, is indeed very captivating. Jevons presented a beautiful argument for the marginal utility theory in an economy of two persons. He observed, “the Laws of Exchange are found to resemble the Laws of Equilibrium of a lever as determined by the principle of virtual velocities”. From this resemblance, he derived the mathematical formulation of marginal utility theory of value.  

Jevons’ derivation is very impressive. It impressed many economists of later generations. Marginal utility theory of value has become the standard value theory over time. However, Jevons’ derivation cannot be satisfactorily extended to an economy with many people. The intuition for this is quite clear. In a two person economy, prices can be established by bargain. But in some larger economies, such as in a supermarket, customers don’t bargain individually. The prices are fixed by the stores. They are the same to every customer, independent of each customer’s individual utility function. A vast economic literature was developed to skirt this problem. But the problem remains. 

A look at the development in physics will help us understand the problem and its solution. To understand many particle problems, statistical mechanics was developed to replace statical mechanics, on which Jevons developed his economic theory. Economic theory tries to understand human society, which contains many people. A more realistic economic theory should be based on thermodynamics and statistical mechanics. Jevons had pointed out the future direction of economic theory long ago.  

Some people indeed made an attempt to develop economic theory from thermodynamics and statistical mechanics. The central concept in thermodynamics is entropy. Georgescu-Roegen observed that “there have been sporadic suggestions that all economic values can be reduced to a common denominator of low entropy” (Georgescu-Roegen, 1971, p. 283). However, he thought that linking economic value to low entropy would not be of much help to economists because “he would only be saddled with a new and wholly idle task --- to explain why these coefficients differ from the corresponding price ratios” (Georgescu-Roegen, 1971, p. 283). To this argument we may reflect on Shannon’s entropy theory of information. The entropy theory of information does not resolve all problems related to communication. But it does resolve the big problems in communication. Similarly, the entropy theory of value doesn’t resolve all problems in economic theory. But it does resolve the big problems in economic theory.  

The current standard theory of value remains the Arrow Debreu model, an offshoot of Jevons’ theory. Arrow defended the model on the ground that there is no “genuine alternative model”. Indeed, Arrow himself had been actively looking for a “genuine alternative model”. Naturally, he was attracted by the concept of entropy. This is what he observed, 

“the well-known Shannon measure which has been so useful in communications engineering is not in general appropriate for economic analysis because it gives no weight to the value of the information. If beforehand a large manufacturer regards it as equally likely whether the price of his product will go up or down, then learning which is true conveys no more information, in the Shannon sense, than observing the toss of a fair coin” (Arrow, 1973, p. 138). 

The Shannon measure actually measures the weight of information. For example, N symbols with identical Shannon measure carry N times more information than a single symbol. Similarly, the value of the information about the future price is higher to a large manufacturer than to a small manufacturer, other things being equal.   

If Arrow didn’t make such a simple mistake, he would have found a “genuine alternative model” of value long ago. 

Some think the Arrow Debreu model is not a particularly difficult language.  For this, we might discuss the theories of the earth centered world and the sun centered world. The theory of the earth centered world is not a particularly difficult language. It is a much simpler language than the sun centered world. However, if you want to describe the movement of planets accurately, the earth centered theory becomes much more complex than the sun centered theory. Similarly, the Arrow Debreu model, evolved from the statical mechanics, by itself, is a simpler language than statistical mechanics. But if we use the Arrow Debreu model to describe the real world, it becomes very complex. Indeed, the Arrow Debreu model is rarely being invoked in public discussion, although it is the very foundation of economic theory. It is in this sense that we suggest the Arrow Debreu model is difficult.