You are a manager for Herman Miller - a major manufacturer of office furniture.
ID: 1237056 • Letter: Y
Question
You are a manager for Herman Miller - a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is:Q = 2K^(0.5) L^(0.5)
where K represents capital equipment and L is labor. Your company owns 4 units of capital equipment and does not have the flexibility needed to acquire additional equipment (that is, capital is fixed at K = 4). Your company is currently employing 25 units of labor.
a. calculate the following:
i. Average product of labor
ii. Marginal product of labor
iii. Marginal product of capital
iv. Marginal rate of technical substitution.
b. Workers at the firm are paid a competitive wage of $100 and chairs are sold for $200 each.
i. Calculate value marginal product of labor (VMPL).
ii. Is your company currently employing the profit-maximizing level of labor? Why or why not?
iii. How many units of labor should your firm normally employ in order to maximize profits?
Explanation / Answer
i. Average product of labor = Q(K,L)/L = 2K^(0.5)L^(0.5) = 4/5 = 0.8
ii. Marginal product of labor = dQ(K,L)/dL = 2(05)K^(0.5)L^(-0.5) = 2/5 = 0.4
iii. Marginal product of capital = dQ(K,L)/dK = 2(05)K^(-0.5)L^(0.5) = 5/2 = 2.5
iv. Marginal rate of technical substitution(MRTS) = MPL/MPK
= 0.4/2.5 = 0.16
b)
i. Value marginal product of labor (VMPL) = Price x MPL = 200(0.4) = 80
ii. Profit = 200 Q(4,L) - 100L = 100(8L^(0.5) - L)
dP/dL = 0
4L^(-0.5) - 1 = 0
L = 16
Since L=25 now, the company is not employing the profit-maximizing level of labor currently.
P(L = 25) = 1500$
P(L = 16) = 1600$
iii. Only 16 units of L are required for the firm to maximize the profits.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.