Marginal Product (MP) of a Factor:
From the above mentioned production function, immediately we can study the effect on total output when there is a variation in labour utlilisation, keeping the other factor K, fixed. Thus, we have the marginal physical product, which shows the change in output quantity for a unit change in the quantity of an input, (L), when all other inputs (K) are held constant. Mathematically, it is given by the first partial derivative of a production function with respect to labour. Thus,
It is reasonable to expect that the marginal product of an input depends on the quantity used of that input. In the above example, use of labour is made keeping the amount of other factors (such as equipments and land) fixed. Continued use of labour would eventually exhibit deterioration in its productivity. Thus, the relationship between labour input and total output can be recorded to show the declining marginal physical productivity. Mathematically, the diminishing marginal physical productivity is assessed through the second-order partial derivative of the production function. Thus, change in labour productivity can be presented as:
Similarly