6. Maximization problem. Let U (3:1, $2) = In 371 + 111372. (a) Suppose that the budget line is I = mm + 192332. Find the optimal bundle of consumption as a function of I , p1, and pg. (1 point) (b) Suppose that I = 2 and p1 = 102 = 1. Suppose that the budget line is 2 = 3:1 + 332 for 1 6 [0,1] and 2 = (1 + 703:; + $2 for :31 > 1. Here, '7' > 0 is a quantity tax imposed on consumption of good 1 beyond the treshold. 1. Find the optimal bundle of consumption. (1 point) ii. Sketch carefully the budget line, the indifference curve, and the optimal so- lution. (1 point) (c) Suppose that I = 2 and p1 = 302 = 1. Suppose that the budget line is 2 = 3:1 + 932 for 331 e [0, 0.5] and 2 = (1 +T)IL'1 + $2 for 351 > 0.5. Here, 7' > O is a quantity tax imposed on consumption of good 1 beyond the treshold. i. Find the optimal bundle of consumption. (1 point) ii. Sketch carefully the budget line, the indifference curve, and the optimal so- lution. (1 point)