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Why does marginal benefit diminish? Intuitively, marginal benefit would be proportional to the input, so for example, if you had 1 worker that could produce 10 units, then 2 workers could produce 20 units, and 3 workers could produce 30 units, so on and so forth. But according to the law of diminishing marginal benefit, that’s not the case. Why exactly does it diminish?

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    $\begingroup$ I think you are confusing production with consumption (utility). Even in production though, think of 1 bakery which employs 5 people. Jamming 50 into the bakery will not simply increase production 10x. $\endgroup$
    – Alex
    Nov 11, 2022 at 22:27

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When studying microeconomics, we usually consider production to have two major factors:

  • Labor (L) which could be measured as the number of employees
  • Capital (K) which is made up of physical stuff such as machines, stores and factories.

What you are saying it’s the intuitive thing to happen would usually be true if the number of stores, factories and machines (the capital) increased in the same proportion as the number of workers (the labor). This property is known as constant returns to scale.

It wouldn’t be of much help to have a ton of workers if you don’t have the tools and the space for them to work.

For a production function $f(L,K)$, returns to scale are defined by: For all $t>1$

  • Decreasing returns to scale: $f(tL,tK) < t f(L,K)$
  • Constant returns to scale: $f(tL,tK) = t f(L,K)$
  • Increasing returns to scale: $f(tL,tK) > t f(L,K)$

An example of increasing returns to scale is cryptocurrency mining. If that wasn’t the case, there would be no incentives to participate in a mining pool rather than mining alone.

What you were stating was diminishing marginal productivity. Marginal productivity is rather defined by:

  • Marginal Productivity of Labor: $MPL = \frac{\partial f}{\partial L}$
  • Marginal Productivity of Capital: $MPK = \frac{\partial f}{\partial K}$

Marginal returns of each factor alone (keeping the other one constant) are most of the time decreasing, a common exception being a company starting up and trying to take advantage of specialization of labor.

Them being decreasing can be described mathematically as:

  • $\frac{\partial^2 f}{\partial L^2} < 0$
  • $\frac{\partial^2 f}{\partial K^2} < 0$

For example in the case of labor, this means that if you keep the number of factories, stores and machines constant, each additional worker would boost production by less than the previous one.

The marginal returns being decreasing can lead them to in fact becoming negative (i.e. $\frac{\partial f}{\partial L}<0, \frac{\partial f}{\partial K}<0$), meaning having more of a factor leading to producing less than before.

For example, having too many workers could lead them to get in the way of each other because of the lack of physical space for all of them.

As an exercise, I invite you to think about this production function:

  • $f(L,K) = 5 L^{\frac{2}{3}} K^{\frac{1}{3}}$
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