2. Suppose a firm has the following production function 1 9 = f(K, L) = LiK! and a total cost function as 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 + 4/9 (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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Your Question:
2. Suppose a firm has the following production function
1
9 = f(K, L) = LiK!
and a total cost function as
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
+ 4/9
Transcribed Image Text:2. Suppose a firm has the following production function 1 9 = f(K, L) = LiK! and a total cost function as 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 + 4/9
(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
Transcribed Image Text:(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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