Question

You are an industry analyst that specializes in an industry where the market inverse demand is P = 250 - 3Q. The external marginal cost of producing the product is MC_External = 10Q, and the internal cost is MC_Internal = 18Q.

Instructions: Enter your responses rounded to the nearest two decimal places.

a. What is the socially efficient level of output?

_______ units


b. Given these costs and market demand, how much output would a competitive industry produce?

_______ units


c. Given these costs and market demand, how much output would a monopolist produce?

________ units

Answer 1

(a)

Market demand curve is as follows -

P = 250 - 3Q

Calculate the Total Revenue -

TR = P * Q = (250 - 3Q) * Q = 250Q - 3Q²

Calculate the marginal revenue -

MR = dTR/dQ = d(250Q - 3Q²)/dQ = 250 - 6Q

MCinternal = 18 Q

MCexternal = 10Q

MCSocial = MCinternal + MCexternal = 18Q + 10Q = 28Q

The socially efficient level of output is that level of output corresponding to which MR equals MCsocial

MR = MCsocial

250 - 6Q = 28Q

34Q = 250

Q = 250/34 = 7.35 units

Thus,

The socially efficient level of output is 7.35 units.

(b)

Market demand curve is as follows -

P = 250 - 3Q

MCinterval = 18Q

A competitive firm produces that level of output corresponding to which price equals MCinternal.

P = MCinterval

250 - 3Q = 18Q

21Q = 250

Q = 250/21

Q = 11.90 units

The competitive industry will produce 11.90 units.

(c)

Market demand curve is as follows -

P = 250 - 3Q

Calculate the Total Revenue -

TR = P * Q = (250 - 3Q) * Q = 250Q - 3Q²

Calculate the marginal revenue -

MR = dTR/dQ = d(250Q - 3Q²)/dQ = 250 - 6Q

MCinternal = 18Q

A monopolist can maximize profit when it produce that level of output corresponding to which MC equals MR.

MC = MR

18Q = 250 - 6Q

24Q = 250

Q = 250/24

Q = 10.42 units

Thus,

The monopolist will produce 10.42 units.