How does marginal utility and marginal product differ?

The marginal utility is, in plain English, the additional benefit (utility) that an individual gets by consuming an additional unit of a good or service. According to the Law of Diminishing Marginal Utility, the utility of an additional unit of a good is inversely related to the number of units consumed already. In turn, the marginal productivity (or marginal product) is the production gain got by a given plant when a given input is increased by one unit. It is often argued - with some reason, I must add - that the productivity gain got by applying extra input units will increase only marginally from one unit to the next, which is known as the Law of Diminishing Marginal Productivity.

I am not an Economist but, for me, it is clear that both Marginal Utility and Marginal Product are one and the same concept. Indeed, the former is derived from a demand perspective and the latter from a supply perspective. See, if you write down the phrase "the additional X got when an additional unit of Y is consumed" and replace "X" by "utility" and "Y" by "a good or service", you have defined "marginal utility". Similarly, if you change "X" and "Y" by "productivity" and "an input", this phrase becomes a decent definition of marginal productivity. Judging by the graphs I've seen here and there, even the underlying mathematical models that describes both concepts look indistinguishible.

Is that impression correct? Are marginal utility and marginal productivity two different perspectives of the same concept? Does that make any sense?

• They both use calculus sure, but I don't see why they're the same. Production is not the same as Utility. If you produce things no one wants (as historically many command economies have done), no one's utility is increasing. I think you're making the mistaking of thinking more production = more utility. You could use the same argument for m/s^2 and kg/cm^2, they're obviously not the same units. Commented Mar 6, 2022 at 13:30
• @ShaikhAmmar Fair point, Ammar! Notwithstanding, what I meant is that both concepts are closely related, semantically speaking. According to Turgot, as increasing quantities of capital and labor are applied to a given land, the output will increase monotonically to a certain point, after which it will steadily decrease tending to zero ("law of the diminishing returns"). If you pick the (infamous) example that relates the consumption of ice creams to the marginal utility, the idea is pretty similar: as you consume more and more ice creams, the marginal utility becomes progressively smaller. Commented Mar 6, 2022 at 19:18
• It is important to distinguish between ordinal and cardinal utility concepts here. In consumer theory economists use ordinal utility, where there is no such thing as a Law of Diminishing Marginal Utility. Commented Mar 9, 2022 at 13:37

Indeed there is a phrase called "diminishing returns" which covers both of these ideas. I find it is misleading to call this a "Law", but it is very frequent.

If you are familiar with partial derivatives:

Denoting the utility function by $$U$$, and the two goods consumed by $$x_1,x_2$$, the marginal utility of good $$x_1$$ is defined as $$MU_1(x_1,x_2) = \frac{\partial U(x_1,x_2)}{\partial x_1}.$$ Denoting a production function by $$f$$ and its two inputs by $$z_1,z_2$$, the marginal product of input $$z_1$$ is $$MP_1(z_1,z_2) = \frac{\partial f(z_1,z_2)}{\partial z_1}.$$

Thus the two concepts are indeed mathmetically identical.

Some notes:

According to the Law of Diminishing Marginal Utility, the utility of an additional unit of a good is inversely related to the number of units consumed already.

1. This is not necessarily true, as "inversely related" is a precise term that would require $$MU_1(x_1,x_2) \sim \text{constant} \cdot \frac{1}{x_1}.$$

the productivity gained from each subsequent unit produced will only increase marginally from one unit to the next

1. The statement is about units of inputs used, not units of goods produced.
• You're right, I've used the expression "inversely related" colloquially, which is certainly misleading. I meant that the greater the amount of goods consumed, the smaller is the increment in the overall utility - but they don't have to be inversely related as you properly pointed out. Commented Mar 6, 2022 at 19:23