Answer to Question #221182 in Microeconomics for Vickie

Question #221182
Given the following cobb-douglas production function
Q=2k2-30L+200
Calculate the marginal product of labour calculate the marginal product of capital calculate the marginal rate of technical substitution
1
Expert's answer
2021-07-29T10:38:01-0400

For the production function given,

the marginal product of labour will be,

δQδL=01×30×L11+0=30\frac{\delta Q}{\delta L}=0-1\times{30}\times{L^{1-1}}+0=-30

and the marginal product of capital will be,

δQδK=2×2×K210+0=4×K\frac{\delta Q}{\delta K}=2\times{2\times{K^{2-1}}}-0+0=4\times{K}

now, for finding the marginal rate for technical substitution(MRTS)

we use,

Q=2K230L+300Q=2K^2-30L+300

or,

K=(Q+30L3002)1/2K={(\frac{Q+30L-300}{2})}^{1/2}

on differentiating with respect to L, we obtain

MRTS(K,L) =δKδL=1/2×15×(Q+30L3002)1/2\frac{\delta K}{\delta L}=1/2\times15\times{(\frac{Q+30L-300}{2})}^{-1/2}


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