Consider a production function $Q = 3 K + 4 L$, when $L$ is graphed on the $x$-axis and $K$ is graphed on the $y$-axis, the marginal rate of technical substitution is equal to:
A) $4 / 3$ and the isoquant is convex to the origin.
B) $4 / 3$ and the isoquant is a straight line.
C) $3 / 4$ and the isoquant is a straight line.
D) 12 and the isoquant is convex to the origin.

Question

Quizplus · Accepted Answer

The marginal rate of technical substitution is the slope of the isoquant, which is given by the ratio of the marginal product of labor (MPL) to the marginal product of capital (MPK). In this case, MPL is constant at 4 and MPK is constant at 3, so the slope is 4/3. The isoquant is not convex to the origin because the production function exhibits constant returns to scale (doubling both inputs doubles output). Therefore, choice B is correct. The marginal rate of technical substitution (MRTS) is equal to the ratio of the marginal product of capital (MPK) to the marginal product of labor (MPL), which in this case is $MPK/MPL=3/4$. The isoquant for this production function is a straight line because the inputs are perfect substitutes, and the MRTS is constant along this line. Therefore, the correct choice is B, where the MRTS is $4/3$ as given by the ratio of the coefficients of K and L in the production function.

Consider a Production Function Q=3K+4LQ = 3 K + 4 LQ=3K+4L

Consider a Production Function $Q = 3 K + 4 L$