Question

You are a manager for Herman Millera 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 = 2(K)1/2(L)1/2where K represents capital equipment and L is labor. Your company has already spent a total of $8,000 on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. If workers at the firm are paid a competitive wage of $120 and chairs can be sold for $400 each, what is your profit-maximizing level of output and labor usage?

Answer 1

Answer:

$4000  is the correct answer to the given question .

Explanation:

The marginal cost with compare to the labor can be written as

$MC\ = \frac{dQ}{dL} \\MC =\frac{d\ ( 2(K)1/2(L)1/2\ )}{dL} \\\\MC=\frac{\sqrt{K} }{\sqrt{L} }$

Here K=9 units  putting this value in the previous equation  we get

$MC\ = \frac{\sqrt{9} }{\sqrt{L} }$

$MC=\frac{3}{\sqrt{L} }$

We can find the value of labor by the given formula that are given below

$V *MC=\ W\\400\ *\frac{3}{\sqrt{L} }\ =120\\ L=10$

From the given question that are mention in question

Q = 2(K)1/2(L)1/2

Putting the value of K and L in the given equation we get

$Q\ =2 * \sqrt{9} \ * \sqrt{100} \\Q\ = 60$

So profit maximizing output is =$60 chairs as the chairs can be sold for  the $400 each so = $60 * $400 *10=$24000 chairs

As the competitive wage of $120 for 100 units as well as the total of $8,000 on the 9 units of capital equipment

=$20000

Therefore profit-maximizing level of output =$24000-$20000=$4000