The owner of the Hughes Car Wash believes that the relationship between the number of cars washed and the amount of labor employed isQ = 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 = MCLMRPL = (MR) (MPL)MRPL = ($5) (4.5 - 0.6 L) = 22.50 - 3 LMCL = $4.5022.50 - 3 L = 4.503 L = 18L = 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.