1. Suppose a consumer has an income of 10, and we have pi = P2 = 1. Further, this consumer has 'standard' preferences (decreasing MRS), and chooses zi = 22 = 5 on the resulting budget line. a) Show this utility maximizing choice on a graph of the budget set with an indifference curve. Now suppose that the government imposes tax of $1.00 per unit of X1. The con- sumer chooses point X1 = - 3, 22 = 4 on the resulting budget line. Show this outcome on your graph, including an indifference curve through the new point. b) The tax in a) raises a revenue of $1.00 x 3 = $3. Suppose the government imposes an income tax of $3.00 rather than using a per unit tax on 21. Show this policy on your graph. Which policy is better from the consumer's point of view? Why? c) Now suppose that instead of the above two policies, the government imposes a per unit tax of of $0.50 on both goods. Show the effect of this policy in a graph. How does this policy rank against the other two from the consumer's point of view? d) Are these preferences consisitent with a Cobb Douglas utility function? Explain. 1. Suppose a consumer has an income of 10, and we have pi = P2 = 1. Further, this consumer has 'standard' preferences (decreasing MRS), and chooses zi = 22 = 5 on the resulting budget line. a) Show this utility maximizing choice on a graph of the budget set with an indifference curve. Now suppose that the government imposes tax of $1.00 per unit of X1. The con- sumer chooses point X1 = - 3, 22 = 4 on the resulting budget line. Show this outcome on your graph, including an indifference curve through the new point. b) The tax in a) raises a revenue of $1.00 x 3 = $3. Suppose the government imposes an income tax of $3.00 rather than using a per unit tax on 21. Show this policy on your graph. Which policy is better from the consumer's point of view? Why? c) Now suppose that instead of the above two policies, the government imposes a per unit tax of of $0.50 on both goods. Show the effect of this policy in a graph. How does this policy rank against the other two from the consumer's point of view? d) Are these preferences consisitent with a Cobb Douglas utility function? Explain