Suppose a firm has the following production function Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8 = (16/Q)+ 4√? (b) Draw the SRAC curve (c) By solving the first order conditions that the global minimum of production is 4 (d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path (e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.
Suppose a firm has the following production function Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8 = (16/Q)+ 4√? (b) Draw the SRAC curve (c) By solving the first order conditions that the global minimum of production is 4 (d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path (e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Suppose a firm has the following production function
Q = f(K,L) = (1/2)L(2/3)K(1/3)
and a total cost function TC = wL + rK
The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process.
(a) Show that the firm’s short-run average cost (SRAC) is SRACK=8 = (16/Q)+ 4√?
(b) Draw the SRAC curve
(c) By solving the first order conditions that the global minimum of production is 4
(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path
(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.
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