8.14. Consider a production function of two inputs, labor and capital, given by The marginal products associated
Question:
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.
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