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There is an externality of $18 per unit of production. The market demand and supply functions...

There is an externality of $18 per unit of production.

The market demand and supply functions are

Pd = 125 - 0.3 Q

Ps = 11 + 0.9 Q

(Note: 1. if needed, round to 2 decimal places and 2. do not include comma in your answer )

What is the Total Social Welfare after implementing the Pigouvian tax?

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Answer #1

Optimal Pigouvian tax will increase Ps by the amount of unit externality cost to equate to marginal social cost function.

Marginal social cost (MSC) = Ps + 18 = 11 + 0.9Q + 18 = 29 + 0.9Q

Socially optimal output is obtained by equating Pd and MSC.

125 - 0.3Q = 29 + 0.9Q

1.2Q = 96

Q = 80

P = 125 - (0.3 x 80) = 125 - 24 = 101

From demand function, when Q = 0, Pd = 125 (vertical intercept of demand curve)

Consumer surplus (CS) = Area between demand curve and price = (1/2) x (125 - 101) x 80 = 40 x 24 = 960

From MSC function, when Q = 0, MSC = 29 (vertical intercept of MSC curve)

Producer surplus (PS) = Area between MSC curve and price = (1/2) x (101 - 29) x 80 = 40 x 72 = 2880

Total social welfare = CS + PS = 960 + 2880 = 3840

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