Consider a production function of the form $Q = K ^ { 2 } L ^ { 2 }$ with marginal products $\mathrm { MP } _ { \mathrm { K } } = 2 \mathrm { KL } ^ { 2 }$ and $\mathrm { MP } _ { \mathrm { L } } = 2 \mathrm {~K} ^ { 2 } \mathrm {~L}$. What is the marginal rate of technical substitution of labor for capital at the point where $\mathrm { K } = 5$ and $\mathrm { L } = 5$ ?
A)5
B)25
C)50
D)1

Question

Quizplus · Accepted Answer

The marginal rate of technical substitution (MRTS) is given by the ratio of the marginal products: $\frac{\mathrm{MP}_L}{\mathrm{MP}_K}$. At $K = 5$ and $L = 5$, $\mathrm{MP}_K = 2 \times 5 \times 5^2 = 250$ and $\mathrm{MP}_L = 2 \times 5^2 \times 5 = 250$. Thus, MRTS = $\frac{250}{250} = 1$.

Consider a Production Function of the Form Q=K2L2Q = K ^ { 2 } L ^ { 2 }Q=K2L2

Consider a Production Function of the Form $Q = K ^ { 2 } L ^ { 2 }$