. Under what conditions on a and b do the following production functions exhibit decreasing, increasing...

. Under what conditions on a and b do the following production functions exhibit decreasing, increasing or constant returns to scale? Mathematically justify and show your work.

a. Q(L,K) = aL + bK

b. Q(L,K) = (La + Ka ) 1/b

Expert Solution

Rahul Sunny answered 1 year ago

Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove...

Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers. • Q = .5L.34 + K.34 • Q = [min (K, 2L)]2 • Q = (0.3L.5 + 0.7K.5)2 • Q = 4KLM where K, L, M are inputs

3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale?...

3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers. • Q = .5L^.34 + K^.34 • Q = [min (K, 2L)]^2 • Q = (0.3L^.5 + 0.7K^.5)^2 • Q = 4KLM where K, L, M are inputs

1: Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to...

1: Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased, and the other factor is held constant? a. q = (L 0.5 + K 0.5) 2 b. q = 3LK2 c. q=L0.3 K 0.6

Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale. a. Q...

Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale. a. Q = 2L + 3K b. Q = L + 5K + 10 c. Q = min (2*L, K) d. Q = 10*K*L e. Q = L2 + K2 f. Q = K.5*L.5/2 + 10

Show whether each of the following production functions exhibit increasing, decreasing or constant returns to scale....

Show whether each of the following production functions exhibit increasing, decreasing or constant returns to scale. Q = 0.5KL [2.5 Marks] Q = 2K + 3L [2.5 Marks] A firm has the following production function Q = 2(XY) 0.5 Where, X is maize and Y is rice. The cost of maize is K10 and the cost of rice Is K40. The firm has a budget of K80 to spend on the two goods. Formulate the firms’ optimization problem. [5...

5. (i) Do the following functions exhibit increasing, constant, or decreasing returns to scale? (ii) Do...

5. (i) Do the following functions exhibit increasing, constant, or decreasing returns to scale? (ii) Do the following functions exhibit diminishing returns to labor? Capital? Show how you know. a. q = 2L^1.25 + 2K^1.25 b. q = (L + K)^0.7 c. q = 3LK^2 d. q = L^1/2 K^1/2

Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L.

Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L. Note: “exponents add up to one, so it CRTS” is not an acceptable answer. a. Y=(K1-a + L1-a ) 1/a b. Y=K/L c. Y=K1/4L3/4

a) Do the following production functions exhibit constant returns to scale, increasing returns to scale, or...

a) Do the following production functions exhibit constant returns to scale, increasing returns to scale, or decreasing returns to scale? For full credit, show why. 1) Q= 10L^ 0.5K^0.3 2) Q= 10L^0.5K^0.5 3) Q= 10L^0.5K^0.7 4) Q= min{K, L} b) Which objects pin down a_LC and a_KC? Explain carefully. c) Why does labor being mobile across sectors automatically imply revenue maximization for firms? Explain carefully.

For the following two functions prove whether each of the production functions has increasing, decreasing, or...

For the following two functions prove whether each of the production functions has increasing, decreasing, or constant returns to scale. Then find whether the MPL is increasing, decreasing or constant with L. A. ? = ?^1/3?^1/3 B. ? = 3?^3/2

Do the following production functions have increasing, decreasing, or constant returns to scale? Which ones fail...

Do the following production functions have increasing, decreasing, or constant returns to scale? Which ones fail to satisfy the law of diminishing returns? ? = min(??, ??) ?=?10.3 ?20.3 ?0.3

Question