The government is considering creating a carbon tax of t per unit of carbon. Suppose we have an idea of the "typical" consumer's preferences for carbon-intensive and carbon-free goods (that is, we know the typical consumer's indifference curves for these two aggregate goods). Suppose the government wants the tax to be welfare neutral, that is, it wants to make sure consumers are not worse off with the tax.

(a) Show graphically how you would estimate the income transfer required for the typical consumer to be equally off as in the initial situation?

(b) How does the consumption of carbon-intensive goods compare with the initial level if no income is provided by the government?

(c) How does the consumption of carbon-intensive goods compare with the initial level if the government hands out enough income so as to maintain the initial utility level?