Company XYZ produces bottled water. Internal consultants estimate the company’s production function to be Q = 300L2K, where Q is the number of bottles of water produced each week, L is the hours of labor per week, and K is the number of machine hours per week. Each machine can operate 100 hours a week. Labor costs $20/hour, and each machine costs $1000 per week.

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Suppose the firm has 20 machines and is producing its current output using an optimal K/L ratio. How many people does the firm employ? Assume each person works 40 hours a week.

 

Recent technological advancements have caused machine prices to drop. Company XYZ can now lease each machine for $800 a week. How will this affect the optimal K/L ratio (i.e., will the optimal K/L ratio be smaller or larger)? Explain why.

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