)4) A firm\'s production function is glven by: q- Ls K1. The wage rate is $5 and
ID: 1130797 • Letter: #
Question
)4) A firm's production function is glven by: q- Ls K1. The wage rate is $5 and the rental rate is $10 Fill in the following blank. Suppose the firm is minimizing costs to produce some unspecified q, then if the firm uses 5 units of labor, it will use units of capital. Given the production function, the firm has (circle one) a. b. Increasing Returns to Scale ii. Constant Returns to Scale iii. Decreasing Returns to Scale c. Suppose this firm wants to produce 64 units of output. Determine the cost-minimizinga of labor the firm will hire.Explanation / Answer
a)
Cost would be minimized when MPL/w = MPK/r
MPL = dq/dL = 0.5KL-0.5
MPK = dq/dK = L0.5
w = $5, r = $10 and L = 5
0.5KL-0.5 / L0.5 = 5/10
K = L
K = 5
b)
On doubling the inputs:
q' = (2L)0.5 x (2K) = 21.5 x q (Output more than doubles)
There exist increasing returns to scale.
c)
q = 64
q = L0.5 x K = K1.5 = 64 (Because K = L from the condition derived in part a)
K = 16 and L = 16
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.