A reflection on the theories of value

Theory of value is the foundation of economic theory. Today, the standard theory of value is the marginal utility theory of value. It was established one hundred fifty years ago, during the marginalist revolution around 1870s. Few people examine the foundation of a tall building after it is built. Similarly, few people examine the foundation of theory after the theory is firmly established. But a major shift in economic thinking often begins with the emergence of new understanding about value. For example, Mill (1871) asserted that he had left nothing in the laws of value for any future economist to clear up. This is shortly before Jevons and others, in the 1870’s, developed marginal utility theory of value that became the core of neoclassical economics.

During 1950s, Arrow and Debreu formalized the theory of value with the mathematical language of topology. The representative work of Arrow-Debreu theory is Debreu’s Theory of Value: An Axiomatic Analysis of Economic Equilibrium, in which Debreu stated: “In the area under discussion it has been essentially a change from calculus to convexity and topological properties, a transformation which has resulted notable gains in the generality and in the simplicity of the theory” (Debreu, 1959, p. x). The convexity and topological methods are detached from a quantitative measure of value. After Arrow-Debreu theory firmly established its dominance, research in the area of value theory became essentially dormant again in the next several decades.

In this note, we will discuss the problems with the marginal utility theory of value and explore alternative theories.

1.      A simple calculation

The most common utility function is logarithm utility function. Suppose the utility function of a commodity is

U = ln(x)

Where x is the amount of output of this commodity. The price of this commodity, as its marginal utility, is

dU/dx = 1/x

Total value of this commodity is the product of the output times price. This is

x*1/x = 1.

This is a constant number, no matter how much x is produced. With logarithm utility, the value of a commodity, as its marginal utility, drops rapidly with the quantity of output. Since total value of a commodity is constant and it is costly to produce a commodity, no one will produce such a commodity.

One might argue that this is just an issue of formality. The problem will be resolved with other types of utility functions. However, logarithm utility was the first utility function ever introduced (Bernoulli, 1738). Many sensory systems, such as sound, light and earthquake strength, are defined in logarithm scales. Logarithm utility is the most important utility function. If the marginal utility theory of value cannot be applied to logarithm utility, the rationale of this theory should be called into question.

2.      The rationale of marginal utility theory of value

Jevons (1871) discussed the rationale of the theory in great detail. When two parties exchange two commodities, marginal utility theory offers very convincing argument. However, in a market with many commodities and many people, the same argument may not apply as convincingly.

Imagine we go shopping in a supermarket. We will buy a lot of different products. The standard value theory suggests that we buy the amount of each product until the marginal value is equal to the cost. However, there can be other considerations when we shop. The fresh produces don’t last very long. We shop weekly. We often don’t buy more than a week’s supply. There could be many other constrains, the size of our car, the size of the storage in our homes, our habit or need to shop weekly. Other than marginal utility, many other factors influence how much we shop each item. Or we can put another way, the marginal utility of a product is influenced by many factors other than the price of the product.

From the above discussion, marginal utilities of different people influence the value of a commodity. It is not the sole determinant of the value. Are there other factors more important than marginal utility in determining value of a commodity?

3.      A scarcity theory of value

Economics is the study on the distribution of scarce resources. The distribution process is mediated by the price signals. Price, or exchange value, must be a function of scarcity. Walras (1873) stated that there are three types theory of value, utility, scarcity and labor. He thought utility theory is too broad, labor theory is too narrow. He proposed that value is a function of scarcity.

How well can a scarcity theory of value help us understand economic activities?

Entropy is a representation of scarcity in physics. An entropy theory of value is a scarcity theory of value. Arrow, of Arrow-Debreu theory, himself had explored the possibility of an entropy theory of value. Shannon developed the entropy theory of information. He measured information with the entropy function. After looking into Shannon’s theory, he concluded,

“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, 1983 (1973), p. 138).

The Shannon measure actually carries weight of information. For example, N symbols with identical Shannon measure carry N times more information than a single symbol (Shannon, 1948). That is why a sentence can carry more information than a single letter. 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.

Details of the entropy theory of value can be found at Chen (2018).

4.      Concluding remarks

Marginal utility theory of value is a subjective theory of value. The entropy theory of value, as a scarcity theory of value, is an objective theory of value. Both subjective utility and objective scarcity affect value. Which of them is more fundamental? Imagine you live in a desert, where water is very scarce. Drinking water is rationed. People are in a constant state of thirst. Would water have high utility? It must have. It is usually the scarcity that determines utility.

For more information, please read

Chen, J.   An Entropy Theory of Value, Structural Change and Economic Dynamics, (2018), December, Vol 47, 73-81