Is it possible that a firm\'s production function exhibits increasing returns to
ID: 1123322 • Letter: I
Question
Is it possible that a firm's production function exhibits increasing returns to scale while exhibiting diminishing marginal productivity of each of its inputs? To answer this question, calculate the maginal productivities of capital and labor for U.S. tobacco products, Japanese beer, and Bangladeshi fabricated metal firms using the information listed in the Application "Returns to Scale in Various Industries." The production function for U.S. tobacco products is g-L0.1 8K0.33 where 0.18,-0.67 dq/dk :0.33[ and dq/dL = 0.18L-0.82 K This production function exhibits 0 A, constant returns to scale and diminishing marginal productivity for capital and labor ( B. increasing returns to scale and diminishing marginal productivity for capital and labor C. increasing returns to scale and increasing marginal productivity for capital and labor D. decreasing returns to scale and diminishing marginal productivity for capital and labor E. decreasing returns to scale and increasing marginal productivity for capital and labor ( The production function for Japanese beer is q = L0 60K040 where 0.60 K-0.60 and dq/dL = 0.60L - 0.400.40 dq/dk = 0.40L K This production function exhibits A. decreasing returns to scale and increasing marginal productivity for capital and labor B, increasing returns to scale and diminishing marginal productivity for capital and labor C. decreasing returns to scale and diminishing marginal productivity for capital and labor D. increasing returns to scale and increasing marginal productivity for capital and labor E. constant returns to scale and diminishing marginal productivity for capital and labor (Explanation / Answer
MPL = dq/dL and MPK = dq/dK
(1) [US Tobacco products] Option (D)
q = L0.18K0.33
Let us double both L and K so that new production function is
q* = (2L)0.18(2K)0.33 = 20.18L0.1820.33K0.33 = 20.51L0.18K0.33 = 20.51 x q = 1.41 x q
q* / q = 1.41 < 2
There is decreasing returns to scale.
From MPK function, as K increases, MPK decreases, so there is diminishing returns (to capital).
From MPL function, as L increases, MPL decreases, so there is diminishing returns (to labor).
(2) [Japanese beer] Option (E)
q = L0.6K0.4
Let us double both L and K so that new production function is
q* = (2L)0.6(2K)0.4 = 20.6L0.620.4K0.4 = 2L0.6K0.4 = 2 x q
q* / q = 2
There is constant returns to scale.
From MPK function, as K increases, MPK decreases, so there is diminishing returns (to capital).
From MPL function, as L increases, MPL decreases, so there is diminishing returns (to labor).
(3) [Fabricated metal] Option (D)
q = L0.98K0.28
Let us double both L and K so that new production function is
q* = (2L)0.98(2K)0.28 = 20.98L0.9820.28K0.28 = 21.26L0.98K0.28 = 2.39 x q
q* / q = 2.39 > 2
There is increasing returns to scale.
From MPK function, as K increases, MPK decreases, so there is diminishing returns (to capital).
From MPL function, as L increases, MPL decreases, so there is diminishing returns (to labor).
(4) TRUE
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.