On his first day in office, Joe Biden issued an executive order that among other things resurrected the Interagency Working Group, originally formed by the Obama administration to provide an estimate of the social costs of carbon emissions. This cost estimate would be used to inform and evaluate government regulations of carbon, which often need to be justified using a cost-benefit analysis. The IWG report suggested a cost of CO2 emitted in the year 2020 of around $50 per ton. For this problem, suppose that there are two sectors of the economy (for instance transportation and power generation), with each accounting for an equal amount of carbon emissions. We would like to achieve an economy-wide reduction in emissions. The cost of achieving carbon reductions differs across the two sectors. Initially assume that the marginal cost of carbon reduction is equal to 5X1 for sector 1 and 10X2 for sector 2. Total carbon reduction is therefore X = X1 + X2. (a) What is the private marginal benefit of carbon reduction? What about the social marginal benefit? (b) Solve for the efficient amount of reduction from sector 1 and sector 2. Which sector would we want to reduce carbon from more and why? (c) If the government monitored CO2 emissions, and levied a tax based on the number of tons emitted, a tax of $50 per ton would cause the manufacturing plants to emit the socially efficient level. Suppose via lobbying the manufacturing industry convinced the government to set a tax of only $20. How much would the plants reduce by? What would be the deadweight loss compared to the socially efficient level? (d) Suppose now instead of a tax, the government is considering a cap-and-trade policy, and the status quo level of carbon emissions is 100 in each sector. The government knows that the efficient level of carbon reduction could be achieved if the price of permits was $50. If it knew the marginal cost curves for each sector, how many permits would it want to issue? (e) Continuing on from part (d), a new carbon capture technology is invented that cuts the marginal cost of reduction by 20% in each sector. If the government did not adjust the number of permits issued, how much reduction would occur in each sector, and how much would permits sell for?