Question

4. 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: (4 points each) (a) F(K,L) =KİL (b) F(K,L) = min 4K, 2L] + 20 (c) F(K,L) = 4K +3L

Answer 1

4. (a) f(K, L) = Y = ks 15 Double the inputs k and = 12k)' (22) / wel get 24 kls " 3) < 2 f(K, L) Because increasing the inputs k and L increases the output by less than that amount. This implies that the production function exhibits decreasing returns to scele. b) Alk, L) = min (4k, 22) + 20 Double the inputs k and L we getr - min (212k), 2(24)) + 20 - 2 [min (4k, 22 )] + 20 € 26(k, 1) Because increasing the inputs k and I increases the output by less than that amount This implies that the production. function exhibits decolasing returns to scale

(6) f(K, L) = UK + 32 Double the inputs K and Ly we jet = 412k) + 3(2L) = 214k+ 3) = 2 f (k, 2) Because increasing the inputs k and L, increases the output by exactly the same amount. This implies that the production finition exhibits constant returns to scele.