A firm that only employs labor (L)has the following production function:
f(L)= 20L - L²
Let the price of output be normalized to one and the price of labor (relative to output price)is 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 when L 0?
c.Compute the profit maximizing amount of labor as a function of the wage.What is the effect of an increase in wage on the firm's optimal employment level? Use calculus to solve this.

Question

A firm that only employs labor (L)has the following production function:
f(L)= 20L - L²
Let the price of output be normalized to one and the price of labor (relative to output price)is 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 when L > 0?
c.Compute the profit maximizing amount of labor as a function of the wage.What is the effect of an increase in wage on the firm's optimal employment level? Use calculus to solve this.

Quizplus · Accepted Answer

The Answer of A firm that only employs labor (L)has the following production function:
f(L)= 20L - L²
Let the price of output be normalized to one and the price of labor (relative to output price)is 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 when L > 0?
c.Compute the profit maximizing amount of labor as a function of the wage.What is the effect of an increase in wage on the firm's optimal employment level? Use calculus to solve this.

A Firm That Only Employs Labor (L)has the Following Production