Consumer Theory An individual's utility function is U (x, y) = x3y3. Initially, the price of good at is px = 12, the price of good 31 is [03, = 3, and the individual's income is I = 48. Graphically, assume good at is on the horizontal axis and good 3! is on the vertical axis. 1) Determine the budget line. 2) Determine the marginal rate of substitution for any consumption bundle (x, y). 3) Determine the utility maximizing consumption bundle given the individual's budget constraint. 4) Determine the utility level corresponding to the utility maximizing bundle. Suppose the price of y increases from 3 to 12. 5) Determine the utility maximizing consumption bundle after the price increase assuming the individual's income is adjusted so it can maintain its initial utility level (this corresponds to the substitution effect). 6) Determine the utility maximizing consumption bundle after the price increase when both the substitution effect and the income effect have been considered