Please solve with steps (calculations) included

Exercise 7 Due Wednesday 11/2. it the United States decided to try to reduce carbon dioxide emissions in order to slow global warming, one policy it might use would be a tax on fossil fuels. A central question that has been a subject of very intense debate is how damaging a tax like that would be to the US. economy. Believe it or not, i This exercise will explore why. 11 part the debate really boils down to an argument about what people's preferences look like. To keep the problem manageable, we'll focus only 011 households and will ignore the fact that energy is also used by rms. Also, households: we'll use one big aggregate household to represent everyone together. we won't worry about the fact that there are lots of individual Suppose households buy two goods: energl, E, and all other goods, 0. In 2022, total househnl PsQB = $850 billion) and $16,150 billion was on everything else (POQD just means we're choosing the units of E and 0 so that one unit of each d spending, M, was about $17 trillion ($17,000 billion), About $850 billion of that was on energy (50 billion units, respectively (units, not dollars). = $16,150 billion). For convenience, we'll let the 2022 prices of energy and other goods, PE and Po, both be $1; formally, that costs exactly $1 in 2022. Using the prices and the initial expenditures, Q? and (2,, are initially 850 billion units and 16,150 1. Suppose that household preferences between goods can be represented by a Cobb-Douglas utility function. The general form of the function and the corresponding demand equations are shown in the table below: Utility Demand E Demand 0 _ 9 ~ M (1 _ g). M U = 9. 1 9 _ = \" Qe 0 Q FL 00 P 0 Use the data given earlier in the problem to determine the appropriate value of 9. Then, derive the expenditure function for a household with these preferences. 2. Suppose the govemment imposes a 25 does the policy raise? What is the corn % tax on energy so that P, rises to $1.25. How much does energy demand decrease? What happens to the demand for other goods? How much revenue pensating variation? Setting aside climate impacts and comparing only the CV and revenue raised, how costly is the policy overall? Now suppose that the utility function in part (1) is wrong and that households really regard cnerm' and other goods as perfect complements. In particular, suppose that they always want exactly b units of O for each unit of E. Using the data at the beginning of the problem, please determine the value nfb derive the corresponding demand equations, Be sure to show the steps in the derivation, not just the result. Suppose the government imposes the 25% tax on enery from part (2) when consumers have the demand for other goods? How much revenue does the poli original amount of E and 0 and overall? . Then use the information about preferences and the budget constraint to preferences from part (3). How much does ener Cy raise? What is the CV? (Calculate the CV, gy demand decrease? What happens to the , in this case by nding the increase in income needed to allow consumers to buy their explain why that approach is appropriate.) Again setting aside climat e impacts and comparing only the CVand revenue raised, how costly is the policy 5, A lot of the debate over climate and energy policy is essentially about whether preferences look more like household preferences is important for climate change polic part (1) or part (3). Compare the results from (2) and (4) and explain why the form of y. Don'tjust write down the numbers, think a Additional Information bout What they really mean for the policy. Compensating Variation Web note giving graphical and numerical e xamples of compensating variation calculations. Other Resources on Compensating Variation Additional information on expenditure functions and compensating variation