Question

In the market for Phil Collins albums MPB=MSB=D=17-2q/3. MPC=1+2q and there is a negative production externality of $8 per album produced. (suppose other musicials hear the music and are negatively influenced to make similar music)

a) what is the MSC equation

b) graph MPB, MSB, MPC, and MSC

c) what is the market outcome (q^m and P^m)

d) show part (c) on graph

e) what is the efficient outcome? (q* and p*)

f) show answer from part (e) on graph

g)what should be the PIgouvian tax on the Phil Collins albums to achieve economic efficiency (be specific and include a number)

Answer 1

Solution:

Marginal private benefit, MPB = Marginal social benefit, MSB = Demand, D = 17 - 2q/3

Marginal private cost, MPC = 1 + 2q

Production externality = $8 per album produced

a) Marginal social cost, MSC = MPC + externality cost

So, MSC = (1 + 2q) + 8

MSC = 9 + 2q

b) Graphing the required equations:

c) Market outcome occurs where the marginal private cost equals marginal private benefit (so, where the two curves intersect)

MPC = MPB

1 + 2q = 17 - 2q/3

3 + 6q = 51 - 2q

(6+2)q = (51 - 3)

q = 48/8 = 6 albums

So, pm = 1 + 2*6 = $13

Thus, market outcome is (qm, pm) = (6, 13)

d) Following is the required graph:

e) Efficient outcome occurs where the marginal social cost equals marginal private benefit (or social marginal benefit) (so, where the two curves intersect)

MSC = MPB

9 + 2q = 17 - 2q/3

27 + 6q = 51 - 2q

(6+2)q = (51 - 27)

q = 24/8 = 3 albums

So, pm = 9 + 2*3 = $15

Thus, market outcome is (q*, p*) = (3, 15)

f) Following is the required graph:

g) Optimal Pigouvian tax required to achieve economic efficiency is the cost of production externality (it is the difference in the costs, at socially optimal level of production) = $8. When the tax amounting to this much is imposed, firms take the complete social cost in their profit function, and thus marginal private cost shifts up to the marginal social cost. So, the market outcome, same as efficient outcome is achieved.