8. Consider the following production function: Y A(5K +6L). Does this production exhibit constant returns to...
4. Proving constant returns to scale A production function expresses the relationship between inputs, such as capital (K) and labor (L), and output (Y). The following equation represents the functional form for a production function: 9=f(K, L). If a production function exhibits constant returns to scale, this means that if you double the amount of capital and labor used, output is twice its original amount. more than Suppose the production function is as follows: less than equal to f( KL)=5K+9L...
A firm’s production function is given by Q = 2K2 + 6L. Does this production function exhibit constant returns to scale?
Returns to scale in production: Do the following production function exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume A is some fixed positive number.) (a) Y= K1/3L1/2 (b) Y=AK2/12/3 (c) Y= K1/2L1/2 (d) Y=K+ L (e) Y = K1/2L1/2 + L 2/3TI/3 2/3TI/3
Returns to scale. A production function has constant returns to scale with respect to inputs with inputs K and L if for any z > 0: F(z · K, z ·L) = zF(K, L), For example, for a production function with constant returns to scale, doubling the amount of each input (i.e., setting z = 2) will lead to a doubling of the output from the production function. A production function has increasing returns to scale if for any z >1: F(z ·...
1. Suppose that output is generated by the production function Y = F(K, L, M = AK1-0-BL M. where M is the quantity of raw materials used in production. What condition is necessary for the production function to exhibit constant returns to scale? 2. Suppose instead that output is generated by a "constant elasticity of substitution" (CES) production function, Y = F(K,L) = A(Kº + L), where a < 1. What condition is necessary for the CES production function to...
Given the following production functions, determine if they exhibit increasing, decreasing, or constant returns to scale. Be sure to mathematically prove your answer and show your work. Y = K + L Y = 4(K + L)0.5 Y= 10(KL0.5)
8.5. Consider the Cobb-Douglas production function Y = BILB2 KB where Y= output, L = labor input, and K = capital input. Dividing (1) through by K, we get (Y/K) = B.(L/KB2 KB2+B3-1 Taking the natural log of (2) and adding the error term, we obtain In (Y/K) = Bo + B2 In (L/K) + (B2+ B3 - 1) In K+u; (3) where Bo = In BI. a. Suppose you had data to run the regression (3). How would you...
Briefly show whether the following production functions exhibit increasing, decreasing, or constant returns to scale: Y = K2/3 + L2/3 Y = min {2L+K, 2K+L} Y = 20*L1/5*K4/5
2) Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale (or none of these) a) Y=K+L^1/3 b) Y= aln(L) + bIn(k)
Consider the production function given by Q = l^α + k^α where α > 0. At what values of α does the production technology exhibit increasing, decreasing, or constant returns to scale? Prove your answer!