Solution assignment 06 Partial differentiation

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Assignment 6

Calculate the first partial derivatives of the following function.

$Q(L,K)=10L^{0.8}K^{0.2}-3K-2L+2$

Solution

In economics this function is known as a production function. It is quite easy to calculate the first partial derivatives.

$Q_K=10L^{0.8}0.2K^{-0.8}-3=2(\displaystyle\frac{L}{K})^{0.8}-3$

$Q_L=10(0.8)L^{-0.2}K^{0.2}+2=8(\displaystyle\frac{K}{L})^{0.2}+2$

The second partial derivatives are less relevant. In all cases the first derivatives are necessary to find the extremes, by solving the equations $Q_K=Q_L=0$ . Calculating the second and mixed partial derivatives is a lot of work, so we do not calculate them here.

Return to Assignments Partial differentiation

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Solution assignment 06 Partial differentiation

Assignment 6

Solution

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