1. The owner of the Thomas Car Wash believes that the relationship between the number of cars washed and labor input is
Q = - 0.8 + 4.5 L - 0.3 L2,
Where Q is the number of cars washed per hour, and L is the number of people employed per hour. Thomas Car Wash received $5 for each car washed , and the hourly wage rate for each person employed is $4.50. The cost of other inputs like water is trivial, and hence they are ignored.
a. How many people should be employed to maximize profit?
b. What will be the firm's hourly profit?
c. Is the above relationship between output and labor input valid for all values of L? Why or why not?
2. An electronics plant's production function is
Q = 5LK,
where Q: is its output rate,
L: is the amount of labor it uses per period of time,
and K: is the amount of capital it uses per period of time.
The price of labor is $1 per unit of labor, and the price of capital is $2 per unit of capital. The firm's vice president for manufacturing hires you to determine which combination of inputs the plant should use to produce 20 units of output per period.
a. What advice would you give him?
b. Suppose the price of labor increases to $2 per unit. What effect will this have on output per unit of labor?
c. Is this plant subject to decreasing returns to scale? Why or why not?