3. (25%) This question applies the concept of indirect utility to study migration and voting decision. 30 Suppose there are 99 households in a country. The households consume two goods in their leisure time. Good 1 is books and good 2 is guns. The household i's preference can be represented by U' (11, 12) = (x1) 10 (12)-100 For example, U30(11, 12) = (x1) 10 (12) to represents the preference of the household i= 30. (a) i. What percentage of household i's expenditure is spent on books? ii. Show that the household i's indirect utility function, the maximal level of utility she may attain, is proportional to m' (P1) 100 (p2)-100 where pi and P2 denote the prices of the two goods and m denotes the after-tax income level. The country is composed of two municipalities, the Blue state and the Red state. The two states are run by different governors and have different fiscal policies. Red state enacts a flat income tax rate 10% Blue state enacts an ad valorem subsidy 25% on books and a flat income tax rate 20% We assume that the two states are identical in every other aspect. In particular, the good prices p and p2 are the same in the two states and the households will receive the same before-tax income level M in both states. For simplicity, we also assume that the households may settle in any one of the states without incurring any moving costs, so where they grew up is irrelevant to the migration decision. (b) Find out who will live in the Red state and who will live in the Blue state using the indirect utility function. Hint: Think about how the tax and subsidy in each state affect a household's budget line. You can then modify the indirect utility function accordingly. You may find the following fact helpful: If 1 > A >0 then Ai>Bi A >0 then Ai>Bi