# Anything written on the process behind "multiplicative" production function?

Intuitively, one might make a naive first guess that the production function of the economy, or of a firm, should be a "leontief" production function: "for example, you need both a factory and a worker to produce cars. A worker by himself, without the help of furnaces, and so forth, cannot construct a car, and the furnace by itself cannot do so either"

Obviously, this argument does not mean that the production function has to be leontief, but intuitively this might be what one expects.

I am looking for something written, that goes into great detail, on what the processes are behind the form of the production function (both firm-level and aggregate). Why would we expect a certain form of production function and not another? E.g. why would we expect a CES production function? why would the elasticity parameter be close to negative infinity, or to 0, or to 1? I hope that someone has written something that answers these questions on the basis of a micro level account (whether mathematical, or narrative).

## 1 Answer

As I understood from my lectures, a multiplicative function means that the marginal product of one factor increases when another factor increases, and decreases when another factor decreases. The extreme cases (leontieff or additive) don't have this property.

At the moment the teacher explained this, it made sense to me. If one factor increases, it expands the capacity of the other to produce more. I think it makes sense.