Question

Consider the production function given by Q = l^α + k^α where α > 0. At what values of α does the production technology exhibit increasing, decreasing, or constant returns to scale? Prove your answer!

Answer 1

Q=l^a+k^a

Let a constant 't' be multiplied by Q such that,

tQ=t[(l^a)+(k^a)]

=(tl)^a+(tk)^a

=t^a(l^a)+t^a(k^a)

=t^a(l^a+k^a)

=t^a(Q)

since a>1 the production function exhibits increasing returns to scale.