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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.
Solution
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.
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