2. Consider the Cobb-Douglas utility function, u($1, 2) = NIK In x1 + - In x2. In what follows you will be asked to solve for demand for both goods for different levels of prices and income. In all cases use the MRS condition and the budget constraint to find these solutions. (a) Suppose first that the budget constraint specifies p1 = 3, p2 = 1, m = 12. Solve for demand for both goods, x1, $2, and illustrate this in the standard indifference curve and budget constraint pic- ture introduced in the lectures. (b) If p1 changes to 2 (keeping p2 = 1 and m = 12), find the new optimal allocation and illustrate your solution. (c) If instead, m changes to 24 (keeping p1 = 3 and p2 = 1) find the new optimal allocation and illustrate your solution. (d) How would you classify goods 1 and 2 in terms of income effects (i.e. normal, luxury, or inferior) and price effects (Giffen or or- dinary)? How general do you think this classification is for all Cobb-Douglas utility functions, and why