Marginal Utility

diminishing returns by ed stein

paradox of value

In economics, ‘utility’ is the amount of satisfaction received from consuming (using) goods and services, and ‘marginal’ refers to a small change, starting from some baseline level. Marginal utility describes the change in utility from consuming more or less of a product. Economists sometimes speak of a law of ‘diminishing marginal utility,’ meaning that consuming the first unit usually has a higher utility than every other unit. When the number of units that are consumed increases, their marginal utility decreases (and vice versa).

As 20th century English economist Philip Wicksteed explained the term, ‘Marginal considerations are considerations which concern a slight increase or diminution of the stock of anything which we possess or are considering.’ ‘Marginal cost’ is the cost of producing one more unit of a good. The ‘marginal decision rule’ states that a good or service should be consumed at a quantity at which the marginal utility is equal to the marginal cost (i.e. at a cost that justifies the satisfaction derived from the product).

Frequently the marginal change is assumed to start from the endowment (the natural state of something, before it is processed), meaning the total resources available for consumption. This endowment is determined by many things including physical laws (which constrain how forms of energy and matter may be transformed), accidents of nature (which determine the presence of natural resources), and the outcomes of past decisions made by the individual himself or herself and by others.

For reasons of tractability, it is often assumed in neoclassical analysis that goods and services are continuously divisible. Under this assumption, marginal concepts, including marginal utility, may be expressed in terms of differential calculus. Marginal utility can then be defined as the first derivative of the total satisfaction obtained from consumption of a good or service, with respect to the amount of consumption of that good or service. In practice the smallest relevant division may be quite large. Sometimes economic analysis concerns the marginal values associated with a change of one unit of a discrete good or service, such as a motor vehicle or a haircut. For a motor vehicle, the total number of motor vehicles produced is large enough for a continuous assumption to be reasonable: this may not be true for, say, an aircraft carrier.

Depending on which theory of utility is used, the interpretation of marginal utility can be meaningful or not. Economists have commonly described utility as if it were quantifiable, that is, as if different levels of utility could be compared along a numerical scale. This has affected the development and reception of theories of marginal utility. Contemporary mainstream economic theory frequently defers metaphysical questions, and merely notes or assumes that preference structures conforming to certain rules can be usefully proxied by associating goods, services, or their uses with quantities, and defines ‘utility’ as such a quantification.

Another conception is Benthamite philosophy (based on the founder of modern utilitarianism, Jeremy Bentham), which equated usefulness with the production of pleasure and avoidance of pain. British economists, under the influence of this philosophy (especially by way of 19th century political economist John Stuart Mill), viewed utility as ‘the feelings of pleasure and pain’ and further as a ‘quantity of feeling.’ Outside of the mainstream methods, there are conceptions of utility that do not rely on quantification. For example, the Austrian school generally attributes value to the satisfaction of needs, and sometimes rejects even the possibility of quantification. In any standard framework, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances.

The concept that marginal utilities diminish across the ranges relevant to decision-making is called the ‘law of diminishing marginal utility’ (and is also known as Gossen’s First Law, by Prussian economist Hermann Heinrich Gossen). This refers to the increase in utility an individual gains from increase in the consumption of a particular good. ‘The law of diminishing marginal utility is at the heart of the explanation of numerous economic phenomena, including time preference and the value of goods… The law says, first, that the marginal utility of each homogenous unit decreases as the supply of units increases (and vice versa); second, that the marginal utility of a larger-sized unit is greater than the marginal utility of a smaller-sized unit (and vice versa). The first law denotes the law of diminishing marginal utility, the second law denotes the law of increasing total utility.’

The law of diminishing marginal utility is similar to the ‘law of diminishing returns’ which states that if the amount of one factor of production increases as all other factors of production are held the same, the marginal return (extra output gained by adding an extra unit) decreases. As the rate of commodity acquisition increases, marginal utility decreases. If commodity consumption continues to rise, marginal utility at some point may fall to zero, reaching maximum total utility. Further increase in consumption of units of commodities causes marginal utility to become negative; this signifies dissatisfaction. For example, beyond some point, further doses of antibiotics would kill no pathogens at all, and might even become harmful to the body. Another example is that it takes a certain amount of food energy to sustain a population, yet beyond a point, more calories cannot be consumed and are simply discarded (or cause disease).

Diminishing marginal utility is traditionally a microeconomic concept and often holds for an individual. For an individual, the marginal utility of a good or service might actually be increasing. For example: bed sheets, which up to some number may only provide warmth, but after that point may be useful to allow one to effect an escape by being tied together into a rope; tickets, for travel or theatre, where a second ticket might allow one to take a date on an otherwise uninteresting outing; dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure.

Occasionally situations arise where marginal utility increases even at a macroeconomic level. For example the provision of a service may only be viable if it accessible to most or all of the population, and the marginal utility of a raw material required to provide such a service will increase at the ‘tipping point’ at which this occurs. This is similar to the position with very large items such as aircraft carriers: the numbers of these items involved are so small that marginal utility is no longer a helpful concept, as there is merely a simple ‘yes’ or ‘no’ decision.

Additionally, there are certain things on which the law of diminishing marginal utility does not apply: increasing usage and collection of rare items. For a collector of valuable artifacts, marginal utility increases with every purchase and thus the law of diminishing marginal utility does not apply under these circumstances. Similarly, some people purchase goods such as jewels and diamonds just to display them in order to uphold their social status. In this case, the law of diminishing marginal utility does not operate properly.

When people start using a commodity, the utility derived from it may start increasing. For example, the satisfaction of reading the first novel in a series may encourage consumers to read the rest in the series. Thus, assuming that each novel is more interesting/ captivating than the next, consumers’ have an increase in satisfaction after reading the first. In this case, the marginal utility does not decrease for each extra unit consumed, and thus the law of diminishing marginal utility does not apply to this situation.

The concept and logic of marginal utility are independent of the presumption that people pursue self-interest. Consider a water rationing situation; one can conceive of an individual who gives highest priority to his rose bush, next highest to his dog, and last to himself. In that case, if the individual has three rations of water, then the marginal utility of any one of those rations is that of watering the person. With just two rations, the person is left unwatered and the marginal utility of either ration is that of watering the dog. Likewise, a person could give highest priority to the needs of one of her neighbors, next to another, and so forth, placing her own welfare last; the concept of diminishing marginal utility would still apply.

‘Marginalism’ is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. The reason why the price of diamonds is higher than that of water, for example, owes to the greater additional satisfaction of the diamonds over the water. Thus, while the water has greater total utility, the diamond has greater marginal utility. The theory has been used in order to explain the difference in wages among essential and nonessential services, such as why the wages of an air-conditioner repairman exceed those of a childcare worker. The theory arose in the mid-to-late nineteenth century in response to the normative practice of classical economics and growing socialist debates about social and economic activity. Marginalism was an attempt to raise the discipline of economics to the level of objectivity and universalism so that it would not be beholden to normative critiques.

If an individual possesses a good or service whose marginal utility to him is less than that of some other good or service for which he could trade it, then it is in his interest to effect that trade. Of course, as one thing is sold and another is bought, the respective marginal gains or losses from further trades will change. If the marginal utility of one thing is diminishing, and the other is not increasing, all else being equal, an individual will demand an increasing ratio of that which is acquired to that which is sacrificed. In an economy with money, the marginal utility of a quantity is simply that of the best good or service that it could purchase. In this way it is useful for explaining supply and demand, as well as essential aspects of models of imperfect competition.

The ‘paradox of water and diamonds,’ usually most commonly associated with Adam Smith, though recognized by earlier thinkers, is the apparent contradiction that water possesses a value far lower than diamonds, even though water is far more vital to a human being. Price is determined by both marginal utility and marginal cost, and here the key to the paradox is that the marginal cost of water is far lower than that of diamonds. That is not to say that the price of any good or service is simply a function of the marginal utility that it has for any one individual nor for some ostensibly typical individual. Rather, individuals are willing to trade based upon the respective marginal utilities of the goods that they have or desire (with these marginal utilities being distinct for each potential trader), and prices thus develop constrained by these marginal utilities.

The concept of marginal utility grew out of attempts by economists to explain the determination of price. The term ‘marginal utility,’ credited to the Austrian economist Friedrich von Wieser by Alfred Marshall, was a translation of Wieser’s term ‘Grenznutzen’ (border-use). Perhaps the essence of a notion of diminishing marginal utility can be found in Aristotle’s ‘Politics,’ wherein he writes: ‘external goods have a limit, like any other instrument, and all things useful are of such a nature that where there is too much of them they must either do harm, or at any rate be of no use.’

Eighteenth-century Italian mercantilists, such as Antonio Genovesi, held that value was explained in terms of the general utility and of scarcity, though they did not typically work-out a theory of how these interacted. In ‘Della moneta’ (1751), Abbé Ferdinando Galiani, a pupil of Genovesi, attempted to explain value as a ratio of two ratios, utility and scarcity, with the latter component ratio being the ratio of quantity to use. French economist Anne Robert Jacques Turgot, in ‘Réflexions sur la formation et la distribution de richesse’ (1769), held that value derived from the general utility of the class to which a good belonged, from comparison of present and future wants, and from anticipated difficulties in procurement.

Like the Italian mercantists, the French economists of the 18th century saw value as determined by utility associated with the class to which the good belong, and by estimated scarcity. In ‘De commerce et le gouvernement’ (1776), Condillac emphasized that value is not based upon cost but that costs were paid because of value. This last point was famously restated by the Nineteenth Century proto-marginalist, Richard Whately, who in ‘Introductory Lectures on Political Economy’ wrote: ‘It is not that pearls fetch a high price because men have dived for them; but on the contrary, men dive for them because they fetch a high price.’

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