Answer to Question #56859 in Macroeconomics for Tom

Question

Derive the demand for labor if the production function is given by f(L)=L^0.5
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Illustrate the labor market graphically

Answer 1

In the short-run, the quantity of labour demanded depends on the wage rate (W), the price of output (P) and the marginal productivity of labour (MPL), so in the short run labour demand depends on the real wage rate (W/P) and the (the first derivative of the) production function.
So, if the demand for labor if the production function is given by f(L)=L^0.5, then the demand for labor will be DL = f(L)' = 0.5/L^0.5.