Suppose that the initial price of good X is $2 (PX0 = $2), the initial price of good Y is $4 (PY0 = $4), and Bobs income is I0 = $200. Suppose that given PX0, PY0, I0, and standard, well-behaved preferences, Bob purchases 20 units of X and 40 units of Y; i.e., Bobs initial consumption bundle is (x0,y0) = (20X,40Y). At this bundle, Bobs marginal rate of substitution between good X and good Y is 2; i.e., MRSXY(x0,y0) = 2. (30 points) (30 points) a) In an indifference curve and budget line graph, illustrate Bobs initial consumption bundle (x0,y0), his budget line, and his marginal rate of substitution between good X and good Y at (x0,y0), MRSXY(x0,y0). At (x0,y0), how much of good X would Bob be willing to exchange for one additional unit of Y? b) Does (x0,y0) maximize Bobs utility? Explain. If (x0,y0) does not maximize Bobs utility, how should he adjust his consumption of X and Y? Explain in detail and intuitively why Bobs utility increases when he adjusts his consumption in the direction you suggest; i.e., why does Bob reach a higher indifference curve when he buys more of one good, but less of the other good? c) Illustrate Bobs utility maximizing consumption bundle (x*,y*) and state explicitly the two conditions that (x*,y*) must satisfy.