Calculate the cost of capital and units of capital, Cost Accounting

The owner of the Hughes Car Wash believes that the relationship between the number of cars washed and the amount of labor employed is
Q = 0.8 + 4.5 L - 0.3 L2

where Q = the number of cars washed per hour
L = the number of people employed per hour.

The firm receives $5 for each car washed. The hourly wage rate is $4.50. The hourly cost of capital is $15. The firm uses 6 units of capital per hour.
a. How many people should Hughes Car Wash employ to maximize profit?
Decision rule: MRPL = MCL
MRPL = (MR) (MPL)
MRPL = ($5) (4.5 - 0.6 L) = 22.50 - 3 L
MCL = $4.50
22.50 - 3 L = 4.50
3 L = 18
L = 6

b. How many cars will it wash when it maximizes profit?

Q = 0.8 + 4.5 (6) - 0.3 (36)
Q = 17

Note: the cost of capital and units of capital has no impact on the solution. K is not in the production function.

 

Posted Date: 3/29/2013 6:30:07 AM | Location : United States







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