Cap and dividend(adapted from Boyce and Riddle)

Aggregate US demand for carbon emissions (or the marginal benefit of carbon emissions) is approximately:
Q = 1,500,000,000-500,000P.

where Q is measured tons of carbon per year and P is measured in dollars.

Draw a diagram showing the marginal benefit of carbon emissions.

How many tons of carbon will the US emit if there is no cost to putting carbon in the atmosphere?

Suppose the true social cost of a ton of carbon is $200 and that government places a $200
tax on each ton of carbon emissions (which translates into a gasoline tax of about 53 cents per gallon). How much carbon would Americans emit? How much revenue would the tax raise?

Americans hate taxes, so the government decides instead to implement a permit system, in which companies must purchase one permit to emit one ton of carbon. Assuming again that the social cost of carbon is $200, how many carbon permits should the government auction off? What will be the price of a permit? How much money will the government raise from auctioning off its permits?

Does a carbon tax or permit system create any deadweight loss for the economy? Explain.

If the government returns these revenues to the public on an equal per-capita basis, what would each American'sdividend be?

Some Americans emit more carbon than others. The poorest 70% of Americans are
responsible for 40% of emissions, while the richest 30% of Americans are responsible for 60% of emissions. How much tax would the average person in each group end up paying under a carbon tax or cap? If the revenues are distributed on an equal per-capita basis, who will benefit and who will lose from the policy?

Suppose that the government auctioned off the "correct" number of permits (from part 4), but their price was lower than expected.

How would you advise the government to tweak the policy for the following year? Why?