A property of a function of one or several variables such that when all variables change by the same factor the value of the function changes less than proportionally. For example, a production function with capital and labour as two factors has decreasing returns to scale if the output with twice as much capital and labour less than doubles. A function of several variables has decreasing returns to one of its variables if it changes less than proportionally to an increase in this variable, holding other variables constant. Formally, consider the function
f(x1, …, xn)
. If the function satisfies the assumption of decreasing returns to scale then
f(λx1, …,λxn) < λf(x1,…, xn)
for any λ > 1.