Question

In: Economics

QD=40-2P and QS=P-8 represent market demand and supply functions for a good. If each unit of...

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?

Expert Solution

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.

Rahul Sunny answered 1 year ago

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