MANAGERIAL/ECON+BUS/STR CONNECT ACCESS
9th Edition
ISBN: 2810022149537
Author: Baye
Publisher: MCG
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Question
Chapter 5, Problem 9CACQ
a)
To determine
To calculate:The output when capital is 2 and labor is 3.
b)
To determine
To calculate:The cost minimizing input mix.
c)
To determine
To calculate:The cost minimizing input mix.
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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.
A firm produces output according to the production function
Q = F(K, L) = 4K + 8L.
a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour?
Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?
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MANAGERIAL/ECON+BUS/STR CONNECT ACCESS
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