Question

1. Below are production functions that turn capital (K) and labor (L) into output. For each of the production functions below, state and PROVE whether it is Constant/Increasing/or Decreasing Returns to scale. That is, you want to see how production changes when you increase all inputs (K.L) by a factor of a, where a > 1: (3 points each) (a) F(KL)=KL (b) F(K,L) = min (4K, 22] + 20 (c) F(K,L) = 5K+10L

Answer 1

(a) ff K, L) = {23 2245 Double the inputs k and I we get a - (2K) 3 12 % 2% Tkºs,47 > 2 FCK,L) Because increasing the inputs K increases the output by more amount. This implies that the function exhibits increasing scale. and L than that production returns to T5 FLK, 1) = min lyk, 22) +20 Double the inputs K and L, we get = min (462k), 2(22)) + 20 - 2 [min (k, 2 L) + 20 = 2F (k, L) because increasing the inputs k and by

increases the amount. This function exhibits output by the same implies that the production constant returns to scale. (C) F (k, L) - 5K+ lot Double the inputs k and L, we get it <5(23) + 10 (24) - 255k + lol] = 2 FLK, L because increasing the inputs k and L increases the outbut bes. amount. This implies that the production exhibits constant retums to scale,