# Math Help - Microeconomics help.

1. ## Microeconomics help.

A production function for output Y=L^0.5(1+K) where L and K are quantities of the two inputs labour and capital needed to produce A.

Suppose the level of K is fixed at 2 in the short-run. Derive the short-term cost mimimising input demand function for L. Since cost minimising is not really an issue in the short run, beause you dont have choice in inputs- K is fixed, so its just a matter of figuring how much labor you need, from the production fucntion.

I got y^2/9=L. Is this correct?

Now substitute the short term L inout demand function from above into the Total Costs function and derive the short- run marginal cost function and write down the short term supply function, assuming the firm is a price taker.

Any ideas on how I do this part?

2. Originally Posted by schoolhelp
A production function for output Y=L^0.5(1+K) where L and K are quantities of the two inputs labour and capital needed to produce A.

Suppose the level of K is fixed at 2 in the short-run. Derive the short-term cost mimimising input demand function for L. Since cost minimising is not really an issue in the short run, beause you dont have choice in inputs- K is fixed, so its just a matter of figuring how much labor you need, from the production fucntion.

I got y^2/9=L. Is this correct?

Now substitute the short term L inout demand function from above into the Total Costs function and derive the short- run marginal cost function and write down the short term supply function, assuming the firm is a price taker.

Any ideas on how I do this part?
$Y=(1+K)\sqrt{L}$

$Y=(1+2)\sqrt{L}$

$\sqrt{L}=\frac{Y}{3}$

$L=\frac{Y^2}{3^2}=\frac{Y^2}{9}$