Question

Suppose SF shirt Co. is a monopoly on all SF monogrammed shirts. The demand curve the store faces is given by P=200-Q and its cost function is C (Q) = 2Q².

a) (6) What is the monopoly output and price for each shirt?

b) (4) Suppose the store’s loading dock faces the entrance of an apartment building and the discarded boxes and paper (till they are cleaned out at a particular time of the day) generates a negative externality on the apartment residents. The estimated external marginal cost is MC^E= 2Q. The store and the apartment building negotiate to force the store to internalize the negative externality and pay for extra cleaning costs. What is the store’s monopoly output and price after internalizing the external cost?

Answer 1

a) Monopolist maximizes profit where MR = MC.
TR = P*Q = (200-Q)*Q = 200Q - Q²
MR = d(TR)/dQ = 200 - 2Q
MC = dC/dQ = 2(2Q) = 4Q

So, MR = MC gives,
200 - 2Q = 4Q
So, 4Q + 2Q = 6Q = 200
So, Q = 200/6
So, Q = 33.33
P = 200 - Q = 200 - 33.33
So, P = 166.67

b) When negative externality is internalized then social marginal cost, SMC = MC + MCe = 4Q + 2Q = 6Q.
Now, monopolist maximizes profit where MR = SMC. So,
200 - 2Q = 6Q
So, 6Q + 2Q = 8Q = 200
So, Q = 200/8
So, Q = 25
P = 200 - Q = 200 - 25
So, P = 175