(e) Suppose that later, with the tax still in place, you give back to the con- auiner the amount of money that was raised by the tax. 1With the rebate and the tax in place, what would be the new optimal consumption bun- dle? What would be the consumer's utility? Ev how much does the consumer's utility change relative to the pre-rebate level? Explain the economic intuition for the change in weliare you found from the rebate relative to the original (pre-tax) level of utility. A consumer has preferences um) = 23:? + 62.- The price of good 1 is pl 3,. and the price of good 2 is 1. You may restrict your attention to interior solutions throughout. (a) Explain whether these preferences are i) monotonic, ii} quasilinear, iii) essential and! or iv) convex. (b) Find the consumer's Mar-shaman} demand functions and indirect util- ity mction. Use a Lagrangian and show your work. (c) Suppose that there were a a tax of t per unit on good 1. How much revenue would be raised {in terms of the exogenous variables)? How much worse off does the consumer become, in dollars, from such a tax (in terms of exogenous variables}? (d) Suppose that p, =1f2 and the tax is also t = 1f2. What was the original amount of good 1 purchased? What would be the values of revenue and consumer welfare loss from the formulas that you calculated in part (c). Which is larger? Brieyr explain why