Question

I understand this question is very long, but please only answer if you can complete all of it. Thank you so much in advance!!

1. Suppose a short-run production function is described as Q = 30L - 0.05L² where L is the number of labors used each hour.

1. Derive the equation for Marginal Product of labor (MP_L):   
2. Determine how much output with the 200^th worker contribute:
3. Determine the amount of labor (L) where output (Q) is maximized (known as L_max):
4. If each unit of output (Q) has a marginal revenue (price) of $5 and the marginal cost of labor is $40 per labor unit (L), how many units of labor (L) should be hired to maximize profit?
5. Given your answer to the previous question, what output (Q) will the firm produce?
6. Assuming no other cost than labor costs, what is the profit at this level of output:
7. Suppose that the marginal revenue (price) for the product is unchanged at $5, but that the cost of hiring labor increases to $45 per hour. How many labor units (L) will the firm employ?
8. Suppose that labor costs is back to $40 but that the marginal revenue (price) received per unit of output increases to $8. How many labor units (L) will the firm now employ?
9. In terms of the demand (curve) for labor, how would we see (what is the difference between) the changes in parts g and h above?
10. Using the terminology from class and this question, briefly explain why manufacturing-jobs such assembling TVs are no longer highly compensated (and therefore moved overseas).

Answer 1

A. MPL = dQ/dL = 30 - 2(0.05L) = 30 - 0.1L

B. At L = 200, MPL = 30 - 0.1(200) = 30-20 = 10

C. Output is maximized when MPL=0

So, 30-0.1L = 0

So, 0.1L = 30

So, L = 30/.1 = 300

Lmax = 300

D. Profit is maximised when MRPL = MC

MRPL = MR*MPL= 5*(30-0.1L) = 150 - 0.5L

So, 150-0.5L = 40

So, 0.5L = 150-40 = 110

So, L = 110/.5

Thus, L = 220

(Note: As HOMEWORKLIB's policy, 4 subparts are to be answered at a time.)