This is a three-part question: Given the following functions: MPB = 60 – 0.05Q,

Question

This is a three-part question:

Given the following functions:

MPB      =        60 – 0.05Q, MPB is marginal private benefit

MPC      =      0.025Q, MPC is marginal private cost

Calculate equilibrium price and quantity assuming perfectly competitive markets and indicate the free-market equilibrium values. If marginal social cost = MSC = 0.07Q (where the difference between MSC and MC = marginal damage), solve for the socially-efficient level of output (Q*).

How much is the Pigouvian tax per unit?

Calculate the amount of tax revenue collected by the government assuming this tax is imposed.

Explanation / Answer

(a) In free market equilibrium, MPB = MPC.

60 - 0.05Q = 0.025Q

0.075Q = 60

Q = 800

P = 0.025 x 800 = 20

(b) Socially optimal outcome is achieved when MPB = MSC.

60 - 0.05Q = 0.07Q

0.12Q = 60

Q* = 500

P* = 0.07 x 500 = 35

(c) When Q* = 500,

MPC = 0.025 x 500 = 12.5

MSC = 0.07 x 500 = 35

Therefore, Pigouvian tax per unit = MSC - MPC = 35 - 12.5 = 22.5

(d) Tax revenue = Tax per unit x Q* = 22.5 x 500 = 11,250

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