comment on the contracts you found comparing the expected level of emissions and the expected level of taxes

INSTRUCTIONS TO CANDIDATES

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An environmental state agency must regulate the emissions emanating from a private national firm. To do so, the agency designs a contract which imposes the emission level 𝑒 ≥ 0 that the firm can produce if it pays a fixed tax 𝑡 ≥ 0. Emissions are verifiable so that the firm who accepts the contract cannot pollute more what is stipulated in the contract.

The firm has a profit function given by 𝜋(𝑒,𝑡) = 𝜃𝑒 − 𝑡, where 𝜃 measures the benefits that it gets from being allowed to emit more pollutants. Assume that the firm has either high or low returns from polluting so that we either have 𝜃 = 80 or 𝜃 = 120.

The firm accepts the contract so long as 𝜋(𝑒,𝑡) ≥ 100.

The state agency is utilitarian. Its objective takes into consideration the benefits of collecting the tax revenue, the profits of the firm and the cost of emissions for the society. The amount of taxes that is raised is used to fund public health and education so that €1 tax generates an overall value of €2. Specifically, the objective function of the state agency is given by

𝐵(𝑒,𝑡) = 2𝑡 + 𝜋(𝑒,𝑡) − 4𝑒 ଶ ,

The first component (2𝑡) reflects the fact that a payment of €1 tax by the firm generates a return of €2, the second component captures the profits of the firm and the last component (4𝑒 ଶ) represents the cost of emissions for society.

i. Consider an environment where the state agency can perfectly verify the value of 𝜃. What would be the optimal levels of taxes that the firm would pay to be granted the right to emit 𝑒 = 40?

ii. Find the optimal contracts (taxes and emission levels) that the state agency would propose to the firm when it can verify the true value of 𝜃.

iii. Explain what would happen if the contracts you found in the previous question were used when the state agency cannot verify the true value of 𝜃. (Prove your answer.)

iv. Solve for the optimal taxes and emission levels that should apply when the state agency cannot verify the true value of 𝜃 and when it knows that 𝜃 = 80 with a probability of 1/2. (Feel free to use some shortcuts relying on constraints that bind.)

v. Comment on the contracts you found comparing the expected level of emissions and the expected level of taxes that are raised when information is symmetric and when it is not. Explain, in a short paragraph, whether you think that your conclusions are specific to the model or whether they would arise in a more general setting. 

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