A small consulting firm is only interested in hiring College graduates (denoted
ID: 1167986 • Letter: A
Question
A small consulting firm is only interested in hiring College graduates (denoted by S), but it does not know how many it should hire in order to be profit maximizing. Assume there is a competitive wage of $20 per hour and the production function is F(S) = 100S – (1/8)S2. Hiring additional workers will increase production F(S) over relevant ranges of S. But is the 51st S more valuable than the 50th S in terms of her additions to overall production? What quantity of college graduates should this firm hire and why does it stop hiring at this level of S? How does your answer change if the production function is F(S) = 200S – (1/8) S2 and the wage increases to $22?
Explanation / Answer
F = 100S - 0.125S2
MPS = dF / dS = 100 - 0.25S
When S = 50, MPS = 87.50
When S = 51, MPS = 87.25
Since increase in S from 50 to 51 results in a decrease in its marginal product, the 51st unit of S is not more valuable.
Firm will hire upto the point when
w = MPS
Or, 20 = 100 - 0.25S
0.25S = 80
S = 320
Firm should stop hiring beyond this point since MPS will become negative & hiring additional unit of S will decrease production.
If
Q = 200S - 0.125S2 & w = 22:
MPS = 200 - 0.25S
Setting w = MPS
22 = 200 - 0.25S
0.25S = 178
S = 712