Question

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 1

The profit function can be given as:

profit = Total Revenue - Total Cost

profit = P*Q - MC*L

differentiating with respect to L we get

d(profit)/d(labour) = P*(dQ/dL) - MC*(dL/dL)

= P*MP_L - MC = 0

hence we get,

P*MP_L = MC or P*MP_L = w  ....................eq 1.

Now using given equation :

Q = 4L

and differentiating it wrt L we get:

MP_L = 4 ..........................eq 2.

Now using eq 1. :

P*MP_{L =} w

since, (P = 10 - 0.025*Q) , (w = 2+0.05*L) and eq2.

(10 - 0.025*Q)*4 = 2 + 0.05*L

40 - 0.1*Q = 2 + 0.05*L

since Q = 4*L

40 - 0.1(4L) = 2 + 0.05*L

40 - 0.4*L = 2 + 0.05*L

38 = 0.45L

Thus, L = 84.44 units

Comments: there isn't any use of the given statement : price is 300% above marginal cost.