A constant elasticity of substitution (CES) production function is one with the general form

where K is capital expenditure; L is the level of labor; and A, α, β are constants that satisfy A > 0, 0 −1. Show that such a function has constant returns to scale: that is, for any constant multiplier s. (Compare with Exercise 42.)

Data from Exercises 42

Suppose output Q is given by the Cobb-Douglas production function Q(K, L) = AK^αL^1−α, where A and α are positive constants and 0

Q(K, L) = A[aKB + (1 - a)L-B-1/B