Would like to check answers -> question is in whole below.

2. Income and SubstitutiOn Effects Preferences are represented by the utility function u(:c1, $2) = ' m1 +332. You may also assume throughout this question that nonnegativity constraints are not an issue. (a) Use a Lagrangian to calculate the consumer's optimal choices (call this bundle (3:0)) at p1 = 1, p2 = 2, m = 1. Also calculate the utility of :5", call it u\". (b) Use the intuitive (bang-per-buck) method to nd the bundle 55 in part (a). (c) Now suppose the price of good 1 increases to 101 = 2, while there is no change in g. i. Calculate 1130 (the bundle that allocates money optimally at the new prices, but is on the same indifference curve as 1:0). ii. Calculate the CV (\"compensating variation\"): how much compensation is needed to afford 330? iii. Calculate {Bf (the optimal bundle at new prices and old income). (d) Finally, calculate the income and substitution effects using your answers to (c)