Problem 13
Suppose the long-run total cost function for an industry is given by the cubic equation \(\mathrm{TC}=\mathrm{a}+\mathrm{b} q+\mathrm{c} q^{2}+\mathrm{d} q^{3}\). Show (using calculus) that this total cost function is consistent with a U-shaped average cost curve for at least some values of \(a, b, c\), and \(d\).
Problem 14
A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units \(H\) and software programs \(S\) is given by \\[\mathrm{TC}=a H+b S-\mathrm{cHS}\\] where \(a, b,\) and \(c\) are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale? With economies or diseconomies of scope?
Problem 16
Suppose that a paving company produces paved parking spaces \((q)\) using a fixed quantity of land \((T)\) and variable quantities of cement (C) and labor (L). The firm is currently paving 1000 parking spaces. The firm's cost of cement is \(\$ 4,000\) per acre covered, and its cost of labor is \(\$ 12 /\) hour. For the quantities of \(C\) and \(L\) that the firm has chosen, \(M P_{C}=50\) and \(M P_{L}=4\) a. Is this firm minimizing its cost of producing parking spaces? How do you know? b. If the firm is not cost-minimizing, how must it alter its choices of \(C\) and \(L\) in order to decrease cost?
