Question

If the production of a firm is given by P = 4LK – L² + K², L > 0, K > 0, Prove that L `(del"P")/(del"L") + "K"(del"P")/(del"K")` = 2P.

Answer 1

P = 4LK – L² + K²

P(K, L) = 4LK – L² + K²

P(tK, tL) = 4(tL) (tK) – t²L² + t²K²

= t²(4LK – L² + K²)

= t²P

∴ P is a homogeneous function in L and K of degree 2.

∴ By Euler’s theorem, L `(del"P")/(del"L") + "K"(del"P")/(del"K")` = 2P.