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```Imagine a world with two individuals, a rich one denoted by R, and a poor one denoted by
P. Both individuals consume gas, and their demands are given by QR = 100 - 0.5P and
QP = 60 - P respectively, where P is the price of gas, and QR and QP are the quantities consumed. Imagine the price of gas is \$40. The government wants to introduce a carbon tax of \$10 per units of gas consumed, but is concerned about the impact it will have on the poor individual.

(a) Is it possible to collect new tax revenue, and at the same time guarantee that the poor
individual will not be made worse-off by the new carbon tax? Be specific, and make
sure you calculate the final tax revenue. Assume the government is able to observe who is poor and who is rich.
(b) So far, we have assumed that the supply of gas was perfectly elastic. Imagine that the
supply was no longer perfectly elastic, would it be easier or harder to guarantee that the
poor individual is not made worse-off by the new carbon tax? Be specific; using a graph
may be helpful. ```