1. Suppose the firm's cost minimization problem is: min L,K wL + rK subject to Q = 4KL First, suppose the firm is in the short run, so that K is fixed at K = K . Solve for the firm's optimal amount of labor (L ). Now suppose the firm is in the long run and can adjust capital and labor. Solve for the firm's optimal amount of labor (L ) and capital (K ) needed to produce any level of output (Q) given the cost of labor (w) and cost of capital (r).

b) Suppose a firm's production function is given by Q = L. Does this production function exhibit diminishing marginal product of labor? Explain.

C) (3 points) Suppose a firm's production function is given by Q = KL. Does this production function exhibit constant, increasing, or decreasing returns to scale? Explain.

2). Suppose a firm experiences an increase in technology. All else equal, will this allow the firm to produce the same level of output at a lower cost? Explain.