If I'm given a firm's production function of
$$Y=zK^{\alpha}{N}^{1-\alpha}$$
Then assuming $$K$$ is fixed and cost free, we can get our profit maximzation problem of
$$\max_{{N}}zF(K^{\alpha}{N}^{1-\alpha})-wN$$
To find the optimality condition, $${MP}_{N}=w$$ , I take the partial...