Suppose the production function for T-shirts can be represented as q =

Suppose the production function for T-shirts can be represented as q = L0.25K0.75. Show that the production function has constant returns to scale.

What will be an ideal response?

ANSWER

When L = L1 and K = K1, q = q1. Let L2 = m ∗ L1 and K2 = m ∗ K1 so that both L and K have increased by the same proportion. Then, q2 = (m ∗ L1)0.25 (m ∗ K1)0.75 = m0.25+0.75 L10.25 K10.75 = m ∗ q1. Thus, for any m, output changes by the same proportion that the inputs changed.