Returns to scale
Suppose we multiply the amount of each input the firm uses by the same number. For example, we double the amount of every input, or multiply it by three. How does output change?
- If, when we multiply the amount of every input by the number
, the resulting output is multiplied by , then the production function has constant returns to scale (CRTS). More precisely, a production function F has constant
returns to scale if, for any > 1,
F (z1, z2) = F (z1, z2) for all (z1,
z2).
- If, when we multiply the amount of every input by the number , the factor by which output increases is less than , then the production function has decreasing returns to scale (DRTS). More precisely, a production function F has decreasing returns to
scale if, for any > 1,
F (z1, z2) < F (z1, z2) for all (z1,
z2).
- If, when we multiply the amount of every input by the number , the factor by which output increases is more than , then the production function has increasing returns to scale (IRTS). More precisely, a production function F has increasing returns to
scale if, for any > 1,
F (z1, z2) > F (z1, z2) for all (z1,
z2).
Notes:
- Note that there is no direct connection between returns to scale (increasing, constant, decreasing) and the rate change of the marginal product of an input! Returns to scale tells us how the output changes as all inputs change by the same factor; the marginal product concerns how output changes as one input changes, holding all other inputs fixed. In particular, a production
function can have increasing returns to scale even though the marginal product of every input decreases as more of that input is used. (Check out the production function defined by F (z1, z2) =
z13/4z23/4.)
- A production function may have IRTS for some range of outputs, DRTS over another range, and CRTS in some other range.
Examples and exercises on returns to scale
Copyright © 1997 by Martin J. Osborne