Why does marginal cost slope upwards after the minimum point?

Question

My textbook writes this on marginal cost:

"The law of diminishing returns refers to the idea that as more of a factor (input) is used, with at least one fixed factor, there is some point at which the increase in output will be at a decreasing rate. Each variable unit produces less when diminishing returns are occurring, so the production of extra units of output will require more of the variable inputs, so MC must increase."

I've got some questions about this

1. What is meant by variable unit?
2. Does marginal cost increase because there is more variable input, or does each worker become less productive when there are too many workers, so there needs to be more variable inputs (so increasing the variable input doesn't decrease productivity, it increases because more input is needed when the workers are less productive).

Answer 1

The variable unit in the quotation is the factor of production that is varied keeping the others fixed. For example it could be the amount of workers hired, while keeping the amount of machinery (capital) fixed. Or it could be the amount of machines reented, keeping the amount of workers fixed.

As for your other question diminishing returns does not refer to workers specifically, although it can.

Suppose we do consider workers as variable input and keep capital fixed. In the beginning usually adding workers will increase output a lot, so the costs of producing an additional unit are low, and might even be decreasing.

However, at some point adding extra workers will increase output only a little. After all the amount of capital is fixed so adding extra workers mean that they e.g. have to wait for another at the machines or get in another's way. So at that point whereas earlier you only needed say 1/2 a worker to produce an additional unit of output, now you need 2 extra workers to produce that one extra unit. That means that the costs of producing an additional unit (the marginal costs) have risen.