For each of the following production functions calculate the ( MRTS v L,K )
a. Q = L^2/3 K^1/3 when Q=8
b. Q = 3L + K when Q=3
c. Q = min{3L, K} when Q=3
MRTS_{L,K} = MPL/MPK.
MPL = Q/L.
MPK = Q/K.
MPL = 2/3*L^{-1/3} * K^{1/}^{3.}
MPL = 2/3 * (K/L)^{1/3}
MPK = 1/3 * K^{-2/3} * L^{2/3}
MPK = 1/3 * (L/K)^{2/3}
MRTS = 0.5 * K/L.
b. MPL = 3
MPK = 1.
MRTS = 3/1 = 3.
c. MRTS = 0.
This is so because this production function represents perfect complements, the two inputs are used in fixed proportions. They are used together, and not substituted for each other.
For each of the following production functions calculate the ( MRTS v L,K ) a. Q...
3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital (MRTS ) is diminishing, constant, increasing, or none of these. a. Q=LK b. Q=LVK c. Q=L*K13 d. Q = 3L +K e. Q = min{3L, K} Show transcribed image text 3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital...
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1. Graph the short-run total product curves for each of the following production functions if K is fixed at Ko 4 (a) Q = F(K, L) = 2K + 3L. (b) Q = F(K, L) = K2L2. (c) In the long run, are the above two production functions characterized by constant returns to scale, increasing returns to scale, or decreasing returns to scale?
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,(M)) by a factor of α, where α > 1: (4 points each) a) F(K,L) = K^1/3*L^1/3+2K+3 b) F(K,L) = sqr(K^3+L^3) c) F(K,L) = (K^2/4+L^2/4)^2 d) F(K,L,M) = min(K,L)*M
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
W= Continuing to use the three production functions: q = h(K, L) = K(1/3) [(1/3), q=g(K, L) = min{įK, L}, and q = = f(K, L) = K (1/4) L (3/4). (h) (6 points) What is the Long Run Cost curve for each of these when r = $4 and $16? (i) (6 points) What are the Long Run Average Cost here? How about the Marginal Cost? (j) (4 points) Provide a convincing argument that a firm using with h(K,...
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 (KL) by a factor of a, where a > 1: (3 points each) (a) F(K.L) = (b) F(KL)= min (4K, 2L + 20 (c) F(K,L) = 5K+ 10L