Problem 1: Uncertainty in Regulation

Suppose that the government is regulating a producer of carbon emissions (a negative externality). Throughout this problem, assume that the government thinks the marginal damage is constant at MDg = 100 per unit of carbon emissions, but the true marginal damage is constant at MD = 180 per unit.

Suppose that the government knows the producer's true cost of pollution reduction is given by MC = 2R, where R is the level of pollution reduction.

A. If the government enforces quantity regulation, what level of reduction will the government choose? What is the deadweight loss?

ANSWER: 180/2 = 90

R = 90 units

B. If the government enforces price regulation, what tax per unit on carbon emissions will the government choose? How many units of reduction does the producer choose? What is the deadweight loss?

ANSWER: $2 tax * 90 units = $180

The tax is $2 because it eliminates the deadweight loss of 90 units.

Part 2:

Now, suppose that the true marginal cost of pollution reduction is still MC = 2R, but the government underestimates and thinks the marginal is MCg = R

A. If the government enforces quantity regulation, what level of reduction will the government choose? What is the deadweight loss?

B. If the government enforces price regulation, what tax per unit on carbon emissions will the government choose? How many units of reduction does the producer choose? What is the deadweight loss?

C. Out of all the outcomes above, which one is most efficient? Provide Intuition that helps you make sense of that result?

(I have part 1, but I need help with part 2. Thank you!)