You are a manager for Herman Miller – a major manufacturer of office furniture.
ID: 1248703 • 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 includes that the relevant production function isQ = 2(K)^1/2 (L)^1/2
where K represents capital equipment and L is labor. Your company has already spent a total of $10,000 on the 4 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 $100 and chairs can be sold for $200 each, what is your profit-maximizing level of output and labor usage? What is your maximum profit?
Explanation / Answer
We know K=4 because it has already been purchased and no new capital can be purchased. $10,000 is a fixed cost. w=100 P=200 This makes our production function: Q = 2(4)^1/2 (L)^1/2 Q = 4(L)^1/2 Profit is (p-c)Q-F, where c is your marginal cost. In this case, the marginal cost is just the wage. This means maximizing profit is equivalent to maximizing quantity subject to a budget constraint. Max 4(L)^1/2 - v(100L) 2*(L)^(-1/2)=100 (L)^(-1/2)=50 L=0.0004 At this labor, Q = 4(0.0004)^1/2=0.0008 profit is (p-w)Q-F (200-100)*0.0008-10000=-$9999.92 Labor=0.0004 Quantity=0.0008 Profit=-$9999.92
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