Find the marginal rate of technical substitution for the following production functions. a. q =...
Question:
Find the marginal rate of technical substitution for the following production functions.
a. {eq}q = 10L^{1/3}K^{2/3} {/eq}
b. {eq}q = 4L^{0.5} + 2K^{0.5} {/eq}
c. {eq}q = \min \left \{ 2K,4L \right \} {/eq}
d. {eq}q = 3L + 8K {/eq}
Rate of Technical Substitution
The marginal rate of technical substitution is actually the slope given for any type of production function. The slope of the production function is derived by using the marginal product and taking the ratio of each marginal productivity of each input. The ratio of marginal product of labor to that of capital is the marginal rate of technical substitution.
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a.
The marginal rate of technical substitution:
{eq}MRT{S_{L,K}} = \frac{{M{P_L}}}{{M{P_K}}}{/eq}
{eq}\begin{align*} q =...
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Marginal Rate of Substitution: Definition, Formula & Examples
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Chapter 3 / Lesson 13
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The marginal rate of substitution shows how quickly a person will substitute or replace one product for a different one. Study the definition, formula, and examples of the marginal rate of substitution, how producers use it, and differing quantities.
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