Question

Q_D=40-2P and Q_S=P-8 represent market demand and supply functions for a good. If each unit of the good produced involves external costs of $4 (i.e. MEC=4), then
(a) what amount of good is produced in the market equilibrium?
(b) What are marginal social benefits(MSB) and marginal social costs (MSC) at the market equilibrium quantity?

Answer 1

a) QD =40 -2P

=> P = (40 - Q) / 2

=> P = 20 - 0.5Q

=> Marginal private benefit: (MPB) = 20 - 0.5Q

QS = P -8

=> P = Q + 8

=> Marginal private cost: (MPC) = Q +8

At market equilibrium, MPB = MPC

=> 20 - 0.5Q = Q + 8

=> 20 - 8 = Q + 0.5Q

=> 12 = 1.5Q

=> Q = (12 / 1.5)

=> Q = 8

8 units of good is produced in the market equilibrium.

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(b) Marginal social benefit (MSB) = Marginal private benefit (MPB) + Marginal External benefit (MEB)

note: MEB = 0

=> MSB = MPB + 0

=> MSB = 20 - 0.5Q

Put Q = 8

=> MSB = 20 - 0.5 (8)
=> MSB = 16

Marginal social benefit at market equilbrium quantity is 16

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Marginal social cost (MSC) = MArginal private cost (MPC) + Marginal external cost (MEC)

=> MSC = Q + 8 + 4

=> MSC = Q +12

Put Q = 8

=> MSC = 8 +12

=> MSC = 20

marginal social cost at the market equilibrium quantity is 20.