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.
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 ...view middle of the document...
There was a lot going on in this question including different variables that needed clarification, so for the sake of myself and everyone else’s who reads my post I tried to make it as easy as possible to understand. Even though everyone may have used the same method to arrive at the same answer organization and explanation of variables goes a long way.
Shaun, I believe she may have made a simple error in calculating the number of employees as Junaid had discussed which may have thrown her calculation off a bit. Additionally, when calculating the whether the optimal K/L ratio would increase or decrease if Company XYZ were to lease the machine she did not set W/R equal to MPL/MPK hence the reason for the discrepancy.
I believe you may have made an error in the second part of the question when calculating the effect of the decrease in machine cost on the optimal K/L ratio. The ratio for the cost of labor to the cost per machine hour should have been $20/$8 ($8 = $800/100hrs). I’m not sure if this was an error because I noticed you did the calculation in the first part of the question but if not could you explain why you set the ratio equal to 1.
A company manufactures and sells a line of coffee machines. Demand per period (Q) for a particular model is given by the following relationship:
Q = 400 ½ p
where p is price. Total costs (including a "normal" return to the owners) of producing Q units per period are:
TC = 20,000 + 50Q + 3Q2
(a) Express total revenue (TR) and...