Production function is an equation that asserts the relationship between the quantities of productive factors used and the maximum amount of product obtained at certain technological level.
It states the amount of product by every possible combination of factors, assuming the most efficient available methods of production. The production function can thus measure the marginal productivity of a particular factor of production and determine the cheapest combination of productive factors.
Dozens of production functions are applicable under different circumstances, usually taking the form of:
Q = f(X1,X2,X3,…,Xn)
where Q is the quantity produced, and X1, X2, X2, …, Xn are the factors of production.
Marginal product is a *product* of the law of diminishing returns. As a result of diminishing returns that an additional unit of inputs is responsible for a handful of outputs that’s smaller than the outputs previous unit of inputs is responsible for.