Suppose the production function for widgets is given by = L0.6^20.2L^2 where represents the quantity of widgets produced per hour, represents hourly capital input and L represents hourly labor input. The marginal product of labor, then, is given by = 0.4L . L Suppose further that widgets sell for $5 per widget and workers are paid $20 per hour

1)What is the maximum amount of output that can be produced with 10 units of capital and 20 workers?

2)If your goal is to maximize profits, and in the short run capital is fixed at 10 units, is 20 workers too much, too little, or just the right amount of labor? Why?

3) If capital is fixed at 10 units in the short run, what is the profit-maximizing amount of labor?

4)In the long run, all inputs are variable. Does this production function exhibit constant, decreasing, or increasing returns to scale? Show your work to justify your answer.