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A competitive firm has a production function given by, Q = f(L) = 6L2 - 0.2L3 where L is the labor used for the production.
(a) Find the level of labor L* that maximizes output. What is the maximum output that can be produced? Graph the production function indicating all the critical points (intercepts and extrema points).
(b) Find the level of labor L* that maximizes the average product of labor. Calculate the marginal product of labor and the average product of labor at that level. What do you observe? Graph the average production function and the marginal production function.
(c) Suppose now that the product sells for p = $1 and the wage per unit of labor is w = $45. Write the profit function π(L) and find the profit maximizing level of labor L*. What is the maximum profit?
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