Answer to Question #199205 in Microeconomics for Ishaq Mubarak

Question

Cobb Doglas production function is given by y=10(LK)^1/2.find the expression for the total differential.

Answer 1

 Differentials of output with respect to labor and capital are the marginal product of capital and marginal product of labor respectively. The differential represents a small change.

$y=10(LK)^{0.5}$

$\frac{\delta y}{\delta K}=10\sqrt{L}(\frac{1}{2\sqrt{K}})$

$=5\sqrt{\frac{L}{K}}$

$y=10\sqrt{LK}$

$\frac{\delta y}{\delta L}=10\sqrt{K}(\frac{1}{2\sqrt{L}})$

$=5\sqrt{\frac{K}{L}}$