Suppose you manage a plant that produces engines by teams of workers using assem
ID: 1197250 • Letter: S
Question
Suppose you manage a plant that produces engines by teams of workers using assembly machines. The technology is summarized by the production function Q = 4KL where Q is the number of engines produced per week, K is the number of assembling machines, and L the number of labor teams. Each assembly machine rents for r = $12,000 per week and each labor team costs w = $3,000 per week. Total engine costs are given by the cost of labor teams and assembling machines plus $2,000 per engine for raw (component) materials. Your plant currently has a fixed installation of 10 assembly machines as a part of its design. You are now asked to make recommendations for the design of a new production facility. What would you suggest? In particular, what capital/labor ratio should the new plant accommodate? If lower average cost per engine was your prime consideration, what would be the optimal capital/labor levels to produce 80 engines? What then would be the average cost per engine? And lastly, should you suggest that the new plant have more or less production capacity than the plant you currently manage? Explain why you chose as you did and the circumstances by which you answered as you did.
Explanation / Answer
The production function is Q = 4KL
If there are 80 engines (Q) of production and 10 machines (K) in use, the required number of labor team (L) would be as below:
Q = 4KL
80 = 4 × 10 × L
L = 2
Therefore, the required capital/labor ratio = Capital / Labor
= 10 / 2
= 5:1
Total cost of 80 engines = Kr + Lw + ($2,000 × 80)
= ($12,000 × 10) + ($3,000 × 2) + $160,000
= $120,000 + $6,000 + $160,000
= $286,000
Average cost per engine = Total cost / Number of engines
= $286,000 / 80
= $3,575
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