Question

I understand this question is very long, but please only answer if you can complete all of it. When I posted it the first time I received a-d, which I am including below. I am not sure if they are correct. 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).

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 maximized 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

Answer 1

The answers from A to D are right.

e) L*=220

Q=30*220-0.05*220*220=4180

So firm will produce 4180 To maximize profit at given good price and wage.

f) Profit=Total revenue - total cost

Total revenue=Price* total quantity=5*4180=20,900

Total cost=Wage* labour=40*220=8800

Profit=20,900-8800=12,100

G)

Profit is maximized when MRP = MC

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

So, 150-0.5L = 45

So, 0.5L = 150-45 = 105

So, L = 105/.5

Thus, L *= 210

H)

Profit is maximized when MRP = MC

MRPL = MR*MPL= 8*(30-0.1L) = 240 - 0.8L

So, 240-0.8L = 40

So, 0.8L = 240-40 = 200

So, L = 200/.8

Thus, L* = 250

I) The Increase in wage will shows as a upward movement along labour demand curve .

Increase in marginal Revenue will shows as a shift of labour demand curve to right side.