8.14. Consider a production function of two inputs, labor and capital, given by The marginal products associated with this production function are as follows:

Let w ! 2 and r ! 1.

a) Suppose the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q. Show how the cost-minimizing quantity of capital depends on the quantity Q.

b) Find the equation of the firm’s long-run total cost curve.

c) Find the equation of the firm’s long-run average cost curve.

d) Find the solution to the firm’s short-run costminimization problem when capital is fixed at a quantity of 9 units (i.e.,

e) Find the short-run total cost curve, and graph it along with the long-run total cost curve.

f ) Find the associated short-run average cost curve.