Question

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 1

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 + 0.05Q2/16 TC = 0.5Q + 0.003125Q2

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 - 0.025Q2

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