A Theory of Kinked Marginal Utilities

It could be stated that economics, as a social science, is largely dependent on psychological findings. This is especially true when we consider the subject of consumption satisfaction. From Aristotle’s hints to Jevons and Menger’s propositions of marginal utility theories, the concept of satisfaction in relation to values has been a great area of interest. However, the focus has mostly been directed toward the mathematics of marginal utility diagrams and less to the behavioural reasoning underpinning them. This article tries to develop a revised theory of kinked marginal utility, based on relevant psychological observations and experiments.

Based on the law of diminishing marginal utility, the first unit of a good or service consumed yields the highest additional utility, the second yields lower additional utility, and in a descending order, increased consumption reduces the satisfaction derived from each unit of the same product. As a result, the marginal utility diagram is usually represented by a downward-sloping straight line or curve to emphasise the inverse relationship between quantity and marginal utility.

Although the general logic of the theory is justifiable, it could be argued that initially, marginal utility must increase and as it reaches its stationary point where marginal utility is about to decrease, the quadratic marginal utility function changes to a linear function of negative utilities. These two functions represent two distinct phases of consumer decision-making of “adaption” and “aversion” as displayed in Figure 1 below.

 Figure 1:

Adaption Phase

Based on a cognitive model developed by Richard L. Oliver and experimentally applied by Ram and Jung, in case of normal standard goods, as usage frequency increases, performance disconfirmation diminishes which leads to sustained satisfaction. In other words, as you use (or consume) a product further, your expectations of the quality of the good are more consistent and therefore because of the lowered cognitive dissonance, your satisfaction from the good increases. The increased familiarity with the good, according to Oliver, after the first unit of consumption, leads to higher marginal utility.

This proposition may first seem unrealistic but in fact it is more convincing than the traditional theory. Imagine you are hungry and so you begin eating a whole pizza. As you eat the first slice, you realise how very pleasant it is and how delicious the slice is. You are in a state of mild surprise and adaption to the features of the pizza e.g. taste, smell etc. The only reason you continue to have the second slice is because the next slice gives you a higher marginal utility. By eating the second slice, you are familiarising yourself even more with the pizza, therefore more reassurance of its excellence and lower expectancy of bad slices. This is the adaption phase of the kinked marginal utility diagram.

As presented by Figure 1, the adaption phase is graphically depicted as a concave curve and not a straight-line. This is because as the performance disconfirmation decreases, the expectancy of future disconfirmations decreases as well due to the user’s optimal forecast adjusting fully with his expectations. So, while the marginal utility is rising, the rate at which it is rising, is falling. This can be better shown using the Howard-Sheth equation, where the change in revised satisfaction (final MU) lessens with a smaller difference between anticipated and received satisfaction. The stationary point at the end of this phase implies that the anticipated and revised satisfaction have become fully equal.

Aversion Phase

Once the marginal utility of a good stops increasing at a decreasing rate, i.e. the consumer reaches his maximum marginal utility at the top of its MU curve, there will be a kink situation caused by the adaption function shifting to an aversion function. The reason the functions need to change at this stage is based on a few assumptions. First, as Menger mentions in his book “Principles of Economics”, our decisions are based on marginal utilities not the total utility. Second, as a result, if the marginal utility starts to decrease, a rational economic agent will not slowly adjust his utility to fall proportionately with increasing units of consumption, but that he will see no benefit in consumption at all and therefore prefers to stop consuming. Third, this aversion decision is a separate decision than the initial adaption decision.

In principle, the kink condition occurs because the consumer, using his System 1 thinking, immediately and unconsciously understands that he no longer is enjoying the good at the margin and responds by a preference not to consume more. The traditional model assumes that the process of marginal utility falling is gradual and that only after consuming very many low-satisfaction units, the consumer can make his mind up. This is whilst we know, as introduced by Kahneman and Tversky that a decision to stop consuming is the one that involves System 1 thinking, is very rapid and indeliberate, and is made through survival instincts of like and dislike and thus, is not a gradual process. You do not get satisfaction from continuing to eat a chocolate bar you do not like anymore. The traditional theory inevitably assumes that you cannot make any prompt decision in liking a product and you lack a desirability threshold. In case you intend to attack the present argument by questioning if consumption decision is processed by System 1 at all, Kahneman, in his book “Thinking, Fast and Slow” clarifies that System 1 is the one we share with animals and that are recurring in short intervals. Making decisions about how much to consume is also the one we share with animals and we repeat every day. Monkeys decide when to stop eating banana. Therefore, the kinked marginal utility diagram takes this point into account through representing aversion (dislike) by the negative downward-sloping MU line starting from zero MU.

On the pragmatic front, Herbert A. Simon argues that “smoothing” feature of various economic models in order to account for nuances in reality, is itself a deviation from the reality. The traditional marginal utility theory postulates that there is a nice negative slope to the MU curve and that there are no immediate shifts or rises or falls in the curve, to enable modelling and calculations. However, considering the changeable nature of demand especially due to exogenous and unanticipated events, the marginal utility curve could consist of several different functions and kinks. This concern is largely removed in our kinked model.

Demand Curve

You might be wondering if the Marshallian aggregate demand curve will be affected by this theory and I can assure you that it will not. The aggregate demand is a combination of all marginal utility curves, not only one. In other words, the demand curve that affects a firm or a country is not an individual demand curve, but the demand of all buyers, whereas the marginal utility concept is individual because each person’s satisfaction derived from consumption differs from another’s. Additionally, demand can be affected by the level of income, substitutes, population etc. whilst utility is merely a theoretical notion that is not constrained by, say, the consumer’s budget.

-Ali Hashemifara