This article assumes you know the importance of falsifiability.
Marginal Utility, Subjective Value and The Labour Theory of Value, those are terms people with any interest in economics and politics probably have come across. They all attempt to answer more or less the same problem, but which one is correct?
The later two are probably more commonly seen online, Subjective Value is often used by proponents of the Austrian school of economics, while The Labour Theory of Value (LTV) is more commonly used by Marxists. Marginal utility is more commonly seen in academic discussion of mainstream economics (the branch of economics most academics agree to be correct). You probably already have some clue of what is about to come lol.
The Labour Theory of Value (LTV) was initially conceived by Adam Smith but nowadays is used mostly by marxists. Originally it stated that the price of a commodity is determined by the number of direct labour input hours that went into making it. Since then it has been modified by marxists to the point of unfalsifiability. For example “direct labour input hours” became “average socially necessary labour time” a concept that is absolutely impossible to test. The LTV has it’s own article.
Subjective Value is completely correct, easily falsifiable and yet almost entirely useless. It basically asserts that each individual has a different function \( P: \{Goods\} \to \R^{*+} \) that associates any object with a positive real number (the price).
That’s so broad a definition that even if correct it’s hard to make anything useful out of it. In fact it makes it entirely possible that all individuals just happen to value goods based on the number of labour input hours, which is just the LTV.
Marginal utility came about during the marginal revolution of economics, an attempt at increasing rigour by building strong mathematical foundations, the name that became famous was Marshall but we can also mention Pareto and Walras. It doesn’t try to assert how people value goods, instead it uses differential equations to describe how the value attributed to goods changes, which has the enormous advantage of being easy to test and actually useful.
The function \( U(g_{1}, g_{2}, g_{3}, …) \) is the total satisfaction or benefit (utility) a consumer derives from certain quantities of goods \( g_{1}, g_{2}, g_{3}, … \). The following partial differential equation describes how total utility \( U \) changes with respect to \( g \) and is called the marginal utility:
\[ \frac{ \partial U }{ \partial g } \]
Where \( g \) is the quantity of a certain good (any good!). Furthermore if we take the second partial derivative we can derive the law of diminishing marginal utility:
\[ \frac{ \partial^2 U }{ \partial g^2 } < 0 \]
Which in lay terms says that how much utility someone derives from a good decelerates for each new unity of such good. (The second derivative of a function is acceleration, it being less than zero means deceleration). This equation is read as: the second partial derivative of \( U \) with respect to \( g \) is negative.
This is known as the law of diminishing marginal utility which can and has been tested. It basically says that after the first unity of a good you are less and less likely to consume another unity.
Notice how the theory of marginal utility doesn’t require that we know \( U() \) to be useful.
It’s important to note that assuming something will be correct simply because it’s written in the form of differential equations is positivism, which is not science and has its own problems. But fortunately, mathematics happens to be very good at explaining the universe and marginalism was actually correct as far as we can tell.