Max has preferences represented by utility function U (x1; x2) = min x1;1/2x2 : His income is m =

900 dollars. The price of good 1 is p1 = 2 and the price of good 2 is p2 = 1. (a) Find a bundle (x1; x2) that belongs to the same indifference curve of bundle (x1 = 2; x2 = 3): (10 Points) (b) Suppose the government imposes an income tax of $100. Find the optimal levels of consumption for Max (x1* and x2*). (10 Points)

(c) Suppose the government does not allow Max to consume more than 100 units of good 1. Find the highest utility level that Max can achieve. (10 Points)