A representative firm which only can survive for one period. It has the following technology: Y = zF(K,

where K is the given capital stock (the representative firm owns K but no market value if the firm sells it). NT is labor demand by paying competitive market wage rate w. and z is total factor productivity (TFP). Let's further assume the production fUnction he a continuous concave function. Without loss of generality, let's assume the output good price equals to I.

Write down the representative firm's profit function and graphically determine or (not both) mathematically prove the profit maximization condition.