** Please show your work! THANK YOU! 3. You are a manager for Office Depot, a ma
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** Please show your work! THANK YOU!
3. You are a manager for Office Depot, 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 = 2K1/211/2 where K represents capital equipment and L is labor. Your company has already spent a total of S8,000 on the 9 units of capital equipment it owns. Due to current cconomic conditions, the company does not have the flexibility needed to acquire additional equipment. Workers at the firm are paid a competitive wage of $120 per day and chairs can be sold for $400 cach What is the Marginal Product of Labor? a. b. What is your optimal labor usage? c. What is the output created with K-9 and optimal L calculated from part b d. What is your maximum profit? **Thinking through Question 3 For part a: Since K9 is fixed, if we plug it in the production function Q-2(9)1/211/2-611/2 . Now, Q is simplified and only in terms of L. Take a derivative with respect to L to find MPL **This is where producer determines labor productivity For part b: P * MPL = w Substitute for P, w (given in the problem) and MPL (from part a). Solve for optimal L This is where producer decides on how many L to hire. For part c: Plug K9 and Lfrom part b) to find Q **This is where producer determines output produced. For part d: Total revenue = P * Q Total cost = Fixed capital cost (8000) + w * L Profit = Total Revenue-Total Cost **Producer will be happy if his business decisions produces profitsExplanation / Answer
a) K = 9
Q = 6L0.5
MPL = dQ/dL = 3L-0.5
b) Optimal labour use would require P x MPL = wage rate
w = $ 120, P = $ 400
400 x 3L-0.5 = 120
L = 100
c) Q = 6L0.5 = 6 x 10 = 60 chairs
d) Profit = P x Q - 8000 - w x L
Profit = 60 x 400 - 8000 - 100 x 120 = $4000
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