You manage a plant that mass-produces engines by teams of workers using assembly
machines. The technology is summarized by the production function
q = 5 KL
where q is the number of engines per week, K is the number of assembly machines, and L
is the number of labor teams. Each assembly machine rents for r = $10,000 per week, and
each team costs w = $5000 per week. Your plant has a fixed installation of 5assembly machines as part of its design.
In the SHORT RUN:
For any given level of output q, write the expression for the number of Labor teams required.
b. What is the cost function for your plant � namely, how much would it cost to produce q engines? (Hint: TC=TFC+TVC, TFC=rK, TVC=wL)
c. What are average and marginal costs for producing q engines? How do average costs vary with output?
d. How many Labor teams are required to produce 250 engines? What is the average cost per engine?
In the LONG RUN:
e. You are asked to make recommendations for the design of a new production facility. What capital/labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q? MPL=5K, MPK=5L.
f. For output q=500, how many L and K should you use in order to minimize cost?
g. What is the minimum cost of production for q=500?
h. What is the minimum cost of product for any output q? (Note: write TC as a function of q).
i. If w is increased to $10,000 per week, how does this change the capital/labor (K/L) ratio if you want to minimize the total cost of production?
j. Given the new wage rate, how many L and K should you use in order to minimize cost for output q=500?
k. Is the expansion path a straight or a curved line? Is it upward or downward sloping? Why?
You manage a plant that mass-produces engines by teams of workers using assembly
machines. The technology is summarized by the production function
q = 5 KL
where q is the number of engines per week, K is the number of assembly machines, and L
is the number of labor teams. Each assembly machine rents for r = $10,000 per week, and
each team costs w = $5000 per week. Your plant has a fixed installation of 5assembly machines as part of its design.
In the SHORT RUN:
For any given level of output q, write the expression for the number of Labor teams required.
b. What is the cost function for your plant � namely, how much would it cost to produce q engines? (Hint: TC=TFC+TVC, TFC=rK, TVC=wL)
c. What are average and marginal costs for producing q engines? How do average costs vary with output?
d. How many Labor teams are required to produce 250 engines? What is the average cost per engine?
In the LONG RUN:
e. You are asked to make recommendations for the design of a new production facility. What capital/labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q? MPL=5K, MPK=5L.
f. For output q=500, how many L and K should you use in order to minimize cost?
g. What is the minimum cost of production for q=500?
h. What is the minimum cost of product for any output q? (Note: write TC as a function of q).
i. If w is increased to $10,000 per week, how does this change the capital/labor (K/L) ratio if you want to minimize the total cost of production?
j. Given the new wage rate, how many L and K should you use in order to minimize cost for output q=500?
k. Is the expansion path a straight or a curved line? Is it upward or downward sloping? Why?
