(b) Suppose that our endowments are as specied at the beginning. My tastes can be represented by the utility function M{$1,I2) = 3:2 + 501nm and yours by the utility function HYIIIl, :2) = $2 + 151] in $1 . i. Derive our demand functions and use them to calculate the equilibrium price p dened as the price of {1 given that the price of 1:2 is normalized to 1. ii. How much of :31 do we trade among each other? iii. Now suppose that a per-unit tax t [payable in terms of :32 j is introduced. Let p be the price buyers will end up paying, and let [p t) be the price sellers receive. Derive the equilibrium levels of p and [p t} as a function of t . iv. Consider the case of t = 0.25 . illustrate that the post-tax allocation is inef- cient . v. Suppose the government distributes the 1'2 revenue back to us, giving me half of it and you the other half. Does your previous answer change? vi. Construct a table relating t to tax revenues, buyer price p , seller price {p t) , n1y consumption level of 3:1 , and your consumption level of 3:1 in 0.25 increments from D to 1.25. vii. Would anything in the table change if the government takes the :33 revenue it collects and distributes it between us in some way