EBK MANAGERIAL ECONOMICS & BUSINESS STR
9th Edition
ISBN: 8220103676267
Author: Baye
Publisher: YUZU
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Question
Chapter 5, Problem 10CACQ
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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A firm produces output according to a production function Q = F(K, L) = min {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 8 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 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?
Chapter 5 Solutions
EBK MANAGERIAL ECONOMICS & BUSINESS STR
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Similar questions
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- Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q= 4K¾L where q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. (K For this production, MP, L and MP = 3 K K The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.)arrow_forwardA firm's production function is Q = min ( K, 2L ) , where Q is the number of units of output per day when the firm rents K units of capital and L units of labor. What is the Long Run total cost curve?arrow_forwardImagine a firm faces a short run function of C(q) = 0.66687q^3 - q^2 +6q +367.23 and a short run production function of (q(L) = -L^3 + 2L^2 +5L. At what level of production is the average variable cost function minimized?arrow_forward
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