- #1
Ginnee
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If I'm given a firm's production function of
\(\displaystyle Y=zK^{\alpha}{N}^{1-\alpha}\)
Then assuming \(\displaystyle K\) is fixed and cost free, we can get our profit maximzation problem of
\(\displaystyle \max_{{N}}zF(K^{\alpha}{N}^{1-\alpha})-wN\)
To find the optimality condition, \(\displaystyle {MP}_{N}=w\) , I take the partial derivative and find
\(\displaystyle z{F}_{N}=z(1-\alpha){K}^{\alpha}{N}^{-\alpha}=w\)
Here is where I'm stuck.
I need to show that the optimality condition can be written as \(\displaystyle \alpha=1-\frac{wN}{Y}\)
Any help would be appreciated.
Thank you,
Gin
\(\displaystyle Y=zK^{\alpha}{N}^{1-\alpha}\)
Then assuming \(\displaystyle K\) is fixed and cost free, we can get our profit maximzation problem of
\(\displaystyle \max_{{N}}zF(K^{\alpha}{N}^{1-\alpha})-wN\)
To find the optimality condition, \(\displaystyle {MP}_{N}=w\) , I take the partial derivative and find
\(\displaystyle z{F}_{N}=z(1-\alpha){K}^{\alpha}{N}^{-\alpha}=w\)
Here is where I'm stuck.
I need to show that the optimality condition can be written as \(\displaystyle \alpha=1-\frac{wN}{Y}\)
Any help would be appreciated.
Thank you,
Gin