Production function and marginal productivities of two variables

Applications of partial derivatives

In this section we solve problems on partial derivatives which have direct impact on Industrial areas.

Production function and marginal productivities of two variables

(i) Production function:

Production P of a firm depends upon several economic factors like capital (K), labour (L), raw materials (R),machinery (M) etc… Thus P = f(K,L,R,M,…) is known as production function. If P depends only on labour (L) and capital (K), then we write P=f(L,K).

(ii) Marginal productivities:

Let P = f(L,K) be a production function. Then ∂P/∂L is called the Marginal productivity of labour and ∂P/∂L is called the Marginal productivity of capital.

Euler’s theorem for homogeneous production function P(L,K) of degree 1 states that