Question

MRTSLK decreases as the firm substitutes labor for capital along the isoquant for all production functions below EXCEPT:

A) Q(K, L) = K⁰.⁵L⁰.⁵
B) Q(K, L) = K⁰.⁷⁵L¹.²⁵
C) Q(K, L) = 5K + 5L
D) Q(K, L) = LK + K

Answer 1

The MRTSLK decreases as labor is substituted for capital along the isoquant, except when labor and capital are perfect substitutes. The correct answer is (C) Q(K, L) = 5K + 5L

Step-by-step explanation:

MRTSLK stands for the marginal rate of technical substitution of labor for capital. It measures the rate at which a firm can substitute labor for capital while keeping output constant along an isoquant. The MRTSLK decreases as labor is substituted for capital when the production function exhibits diminishing marginal returns to labor.

Let's analyze each production function to determine if the MRTSLK decreases as labor is substituted for capital:

1. Q(K, L) = K⁰.⁵L⁰.⁵: In this production function, the MRTSLK will decrease as labor is substituted for capital because it exhibits diminishing marginal returns to labor.
2. Q(K, L) = K⁰.⁷⁵L¹.²⁵: Similar to the previous production function, the MRTSLK will also decrease as labor is substituted for capital due to diminishing marginal returns to labor.
3. Q(K, L) = 5K + 5L: In this production function, the MRTSLK does not decrease as labor is substituted for capital because labor and capital are perfect substitutes, and the ratio of their input prices remains constant.
4. Q(K, L) = LK + K: Likewise, this production function also does not exhibit diminishing MRTSLK because labor and capital are perfect complements, and their ratio does not change as labor is substituted for capital.

Therefore, the correct answer is (C) Q(K, L) = 5K + 5L, as it is the only production function where the MRTSLK does not decrease as labor is substituted for capital.