The Law of Marginal Utility

This is the last of the major neoclassical economic laws we must cover. It completes the basic framework of neoclassic economics around which other economic statements can be derived. See reference [E1], chapter 7.

The law of marginal utility, sometimes called the law of diminishing marginal utility, is the fusion of two parts. The first is the idea that it is the utility or usefulness of something that gives it its value. The idea that value equals utility actually has a larger applicability, as developed by the founders of utilitarianism, Jeremy Bentham (1748-1832) and John Stuart Mill (1806-1873), than just in economics. These gentlemen applied ideas of utility to the determination of individual rights, the proper limitation of government powers, and to ethical standards. As the utility of anything varies with each individual, the value of anything is something that is strictly subjective, not objective. For this reason any of the conclusions that Bentham and Mill developed can be vigorously contested given a different set of personal values. 

In its application to the determination of economic value, the utility theory of value is greatly at variance to the ideas of the classical economists. Classical economists generally believed that the economic value of a good was due to the inputs needed to produce the good or service. Many classical economists such as Adam Smith and David Ricardo (not to mention Karl Marx) believed that the value of a good was entirely determined by the amount of labor needed to produce it, i.e. the labor theory of value.

An input theory of value has great troubles in explaining  the movements of prices. So long as the amount of inputs required to produce a good is constant, its value should be constant and its price should not change. This is directly contradictory to the law of supply and demand, especially as seen by Alfred Marshal’s supply and demand curves. The utility theory of value on the other hand can easily explain supply and demand. As the price of a good increases, the good’s producer would find the utility of producing more increases. This explains the law of supply. At the same time a consumer would find the utility of buying the good decreases as the increasing price takes away more of his limited resources. This explains the law of demand. Throughout the process of the price changes, whether up or down, the amount of labor and other inputs to produce the good can remain constant.

Another problem with an input theory of value can be seen with the following thought experiment. Suppose someone hires a worker to dig a hole  on another person’s land. (Ignore for the moment how the producer of the hole gets the permission to dig on another’s land.) Suppose the employer of the digger then tells his employee to fill the hole. Can the producer of the hole get the land’s owner to pay for the digging and refilling of the hole? From the labor theory of value, the producer of the hole has increased the land’s value by the amount of labor expended on it. Clearly, the land’s owner would never employ the producer of the hole to just to dig a hole and refill it because such an expenditure of labor has no utility for him. Now if the producer does something that has utility for the land owner, such as digging a hole for the basement of a house, the land owner would probably be willing to pay the producer for that service.

What can be concluded from this reasoning is that the advocate of an input theory of value has the relationship between inputs and economic value exactly backwards: We do not value a good because of the amount of inputs used to produce it; we use the inputs, even given their costs,  to produce the good because of the value (utility) of the good for us. If the value or utility of a good is less for us than the total value of the inputs required to produce it, we would be very masochistic indeed to put in an order for the good!

The second part of the law of marginal utility was supplied by the founders of the marginal utility revolution in 1870: Carl Menger, Leon Walras, and William Stanley Jevons. They independently noted that as the supply of a good  increases, the price of the last good sold (also known as the marginal utility) decreases. This is because the supply of a good becomes increasingly less useful as the consumer’s need is fulfilled. Once a consumer has no more need for the good, he will not pay anything for it. This view of marginal utility presupposes the utility theory of value.

How does the law of marginal utility relate to Marshal’s supply and demand curves? Suppose that the demand curve is initially given by D₁ as shown in the figure below. We then suppose that for some

reason  that the supply of the good increases to an extent that the market is partially saturated with the good. Then the consumers would buy a smaller number of the good at the same price as before the change. This means the demand curve would be shifted to the left to some new demand curve D₂ as shown in the figure. If for some reason the supply curve does not change, i.e. the suppliers have some inertia in changing their behavior, the new equilibrium price point where the two curves intersect will be at a point where both the price and the quantity sold will be smaller. After a while, however, the producers may decide they can maximize their profits at a lower price by producing the same number of goods as they were capable of before. If that happens the supply curve will also shift to the left until the intersection with D₂ is at a new equilibrium point where the quantity bought and sold is the original quantity with the equilibrium market price decreasing even further. This kind of behavior is often observed in markets when new technology and/or sources of supply are discovered that increases available supply at the same or lower cost.

The law of marginal utility also explains a famous conundrum concerning the relative prices of water and diamonds. The health of an economy depends a great deal more on a large supply of good water than it does on a supply of diamonds. Yet the price of diamonds is much, much greater than the price of an equivalent mass of water. The explanation for this given by marginal utility is that the relative scarcity of diamonds means that the demand for diamonds is not nearly as saturated as the demand for water. Then if more diamonds are produced, its price may not change much at all, whereas an increase in the supply of water by an equivalent mass or weight might be difficult to sell without dropping the price a great deal.

The law of marginal utility explains a great deal about changing amounts of goods produced with changing prices that the labor theory of value, or any other input theory, can not begin to address. Its designation as an economic law is well deserved.

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