A firm that only employs labor (L) has the following production function: Q = 20L - L2
Let the price of output be one and the price of labor w.
a. Write out the profit function for this firm as a function of labor, L.
b. What is the necessary first-order condition for the firm to maximize profit for L>0?
c. Express the profit maximizing amount of labor as a function of the wage.
d. How would firm's optimal L change if the wage increases? Use calculus to figure this.