Returns To Scale - Formal Example

Formal Example

The Cobb-Douglas functional form has constant returns to scale when the sum of the exponents adds up to one. The function is:

where and . Thus

But if the Cobb-Douglas production function has its general form

with then there are increasing returns if b + c > 1 but decreasing returns if b + c < 1, since

which is greater than or less than as b+c is greater or less than one.