2. Claire has a utility function given by U(x1 ,X2 ) = xax, where a > 0 and b > 0. One reason economists care about the MRS condition is that it reveals information about how consumers are willing to trade-off one good for another, which can be useful for designing policy. Suppose you' ve been hired by Rishi Sunak to advise him on tax policy. Rishi plans to impose a $1 tax on either good 1 or good 2; but he would like to do so in a manner that is not too harmful to Claire. As a policy analyst, you don't know the values of a or b. Due to data limitations, you also don't directly observe how many units of good 2 Claire buys. You do, however, observe the quantity of good 1 that Claire buys and, from census data, you also know her income. Suppose that at the prices p1 = 3 and p2 = 5, we observe that Claire purchases 2 units of good 1; her income is m = 10. (a) At the prices p1 = 3 and p2 = 5, how many units of good 2 does Claire buy? What must be the ratio, :? Explain how you know. (b) Would you suggest to Rishi that he impose the tax on good 1 or good 2? Justify your answer mathematically