In a market for a dirty good, the inverse demand function is given by p 100 y an

Question

In a market for a dirty good, the inverse demand function is given by p 100 y and the private marginal cost of production is given by MC = 10 + The pollution enerated by this industry creates external damages given y the constant marginal external cost of 2 dollars. (1) Find the competitive equilibrium without requlation (Hint: p MC) (2) Find the socially optimal output(Hint: p = MC + 2) (3) Determine the Pigovian tax that would result in a competitive market producing the socially efficient output.

Explanation / Answer

(1) In free market competitive equilibrium, price equals MC.

100 - y = 10 + y

2y = 90

y = 90/2 = 45

p = 100 - 45 = 55

(2) Socially optimal quantity is obtained by equating price with marginal social cost (MSC), where

MSC = MC + external cost = 10 + y + 2 = 12 + y

Equating price and MSC,

100 - y = 12 + y

2y = 88

y = 88/2 = 44

(3) When y = 44,

MC = 10 + 44 = 54

MSC = 54 + 2 = 56

Pigouvian tax = MSC - MC = 56 - 54 = 2

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