A perfectly competitive firm operates in the short-run with labor as its only variable factor. Its production function is:
Q = -L3 + 10L2 + 88L
where Q is output per week measured in tons and L is the number of workers employed. The weekly wage is $324 and the product sells for $3.24 per ton.
(a) At what weekly output is marginal cost equal to average variable cost?
(b) What is the minimum product price at which the firm will operate in the short-run?
(c) How many workers should the firm employ to maximize profits?
(d) find out the firm's point elasticity of demand for labor at the equilibrium in (c) above.