12. (Originally on Homework >>>Bob has $100 in income that he can spend on either Good X or Good Y. Good X costs $2 per unit while Good Y costs $4 per unit. a. Given the above information, draw a graph of Bob's budget line (call it BLI) and write an equation in slope-intercept form for Bob's budget line measuring Good Y as the Goodon the vertical axis. b. Given Bob's income and the prices of these two goods and given Bob's preferences he finds that he maximizes his satisfaction when he chooses to consume bundle A which consists of 30 units of Good X and 10 units of Good Y. Can Bob afford this bundle given his income and the prices of the two goods? Prove this mathematically. Does consumption of bundle A exhaust Bob's available income? c. Suppose that the price of Good X decreases to S1. Bob's income and the price of Good Y stay constant. Bob now finds that he maximizes his satisfaction when he consumes consumption bundle B which consists of 56 units of Good X. Draw a graph that represents Bob's BLI, his new budget line (BL2) and bundle A. Calculate how many units of Good Y Bob consumes when he consumes consumption bundle B (make sure you show how you found this answer). Mark bundle B in your graph . Suppose that Bob was constrained to stay on his first indifference curve-the one that bundle A sits on-while paying the new price for Good X. We can construct this budget line 3 where Bob's income has been compensated (in this case lowered) so that he can reach the indifference curve that bundle A is on, but he cannot reach a higher level of satisfaction. On budget line 3 Bob finds that he maximizes his satisfaction by consuming bundle C which consists of 36 units of Good X and 8 units of Good Y. Draw a graph that illustrates BLI, BL2, BL3, bundle A, bundle B, and bundle C. Sketch in indifference curve I and indifference curve 2 in your graph. c. How much would Bob's income have to be decreased by in order for him to have the same utility as he had initially but now face the lower price of Good X? You have all the necessary information at hand to calculate this decrease in income. Show how you found your answer. f. What is the amount of the substitution effect for Good X given the above information? What is the amount of the income effect for Good X given the above information? Explain your