Please explain each work
Problem 1: Taxes \& Substitution/Income Effects [11 Points] Suppose that an individual gains utility from two goods: (i) Cigarettes (C) and (ii) Food (F). This utility is given by the following utility function. For the purposes of figures, assume that Cigarettes (C) is on the x-axis and Food (F) is on the y-axis. U(C,F)=2C1/5F4/5 And this individual has a Budget Constraint given by: 200=4C+6F Now suppose that the government imposes a tax of \$2 per unit on cigarettes. 1. What is this individual's utility-maximizing demand for Cigarettes and Food before this tax is implemented? Show your work. [1 point] 2. What is this individual's utility-maximizing demand for Cigarettes and Food after this tax is implemented? Show your work. [1 point] 3. What part of this change in Cigarettes is the result of the Substitution Effect and the Income Effect using the Slutskian Decomposition? Show your work. [2 points] 4. How much tax revenue does this tax on Cigarettes end up raising? Show your work. [1 point] 5. What is the Equivalent Variation of this tax (i.e. this \$2 price increase on Cigarettes)? Show your work. [2 points] 6. What is the Compensating Variation of this tax (i.e. this $2 price increase on Cigarettes)? Show your work. [ 2 points] Suppose that the purpose of this tax was to raise revenue. The government is considering either the tax on Cigarettes above, or a tax on income, which simply removes an amount from the individual's income equal to the total revenue raised in Q4. Which of the two taxes, i.e. either (i) cigarettes only, or (ii) an individual's income, would lead to the least decline in the individual's utility if both taxes had to raise the same revenue? Show your work. [2 points] Problem 1: Taxes \& Substitution/Income Effects [11 Points] Suppose that an individual gains utility from two goods: (i) Cigarettes (C) and (ii) Food (F). This utility is given by the following utility function. For the purposes of figures, assume that Cigarettes (C) is on the x-axis and Food (F) is on the y-axis. U(C,F)=2C1/5F4/5 And this individual has a Budget Constraint given by: 200=4C+6F Now suppose that the government imposes a tax of \$2 per unit on cigarettes. 1. What is this individual's utility-maximizing demand for Cigarettes and Food before this tax is implemented? Show your work. [1 point] 2. What is this individual's utility-maximizing demand for Cigarettes and Food after this tax is implemented? Show your work. [1 point] 3. What part of this change in Cigarettes is the result of the Substitution Effect and the Income Effect using the Slutskian Decomposition? Show your work. [2 points] 4. How much tax revenue does this tax on Cigarettes end up raising? Show your work. [1 point] 5. What is the Equivalent Variation of this tax (i.e. this \$2 price increase on Cigarettes)? Show your work. [2 points] 6. What is the Compensating Variation of this tax (i.e. this $2 price increase on Cigarettes)? Show your work. [ 2 points] Suppose that the purpose of this tax was to raise revenue. The government is considering either the tax on Cigarettes above, or a tax on income, which simply removes an amount from the individual's income equal to the total revenue raised in Q4. Which of the two taxes, i.e. either (i) cigarettes only, or (ii) an individual's income, would lead to the least decline in the individual's utility if both taxes had to raise the same revenue? Show your work. [2 points]
