Assume all markets are competitive, the product price is p = $2 per unit, the wage rate is w = $16 per hour and the firm's production function is q=E(36?E), where E is the level of employment and the firm's fixed costs are zero.
a) Write down the firm's profit in terms of E.
b) What is the value of the marginal product of labor? [Hint: MPE=36?2 E. ]
c) Use your answer to (b) to calculate the profit maximizing level of employment, denoted E*. What are the firm's maximum profits?