1. A monopsonist has the production function
Q=4⋅L
and faces the following labor supply and product demand equations respectively.
W=2+0.05⋅L
P=10−0.025⋅Q
How much labor should the firm hire in order to maximize profits if they mark their price 300% above marginal cost? Answer is not 10
2.
A monopsonist has the production function
Q=4⋅L
and faces the following labor supply and product demand equations respectively.
W=2+0.05⋅L
P=10−0.025⋅Q
What wage rate should the firm pay in order to maximize profits if they mark their price 300% above marginal cost? Answer is not 2.5
Answer)
Given
P = 10 - 0.025Q+ |
Q = 4L OR L = Q / 4 |
W = 2 + 0.05L |
Total Cost = TC = W x L L = Q /4 TC = (Q / 4) (2 +0.05L) TC = (Q / 4) (2 +0.05 Q/4) TC = 0.5Q + 0.05Q^{2}/16 TC = 0.5Q + 0.003125Q^{2} |
MC = d(TC) / dQ MC = 0.5 + 0.00625Q |
We are given it is 300% above marginal cost
= 400 / 100 (0.5 + 0.00625Q)
New MC = 2 + 0.025Q
TR = P x Q TR= (10 - 0.025Q)xQ TR = 10Q - 0.025Q^{2} |
MR= d(TR)/ dQ MR = 10 - 0.05Q |
For maximum Profit, MC =MR 10 - 0.05Q = 2 + 0.025Q 8 = 0.075Q Q = 8 / 0.075 Q = 106.67 |
L = Q / 4
L = 106.67 / 4
Labour = 26.67
W = 2 + 0.05L
W = 2 + 0.05 x 26.67
Wage Rate = 3.33
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