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4. Andys utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andys optimal consumption bundle is X* -6 and Y = 6. When the prices are Px = 1 and P, = 4, Andys optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of Y increases from $1 to $4. Decompose the uncompensated price effect into income and substitution effects following the steps below. Graph and clearly label by letters (e.g. (a), (b), ...) the following items in the figure provided on the next page. Have X on the horizontal axis and Y on the vertical axis. (Note that the price of Y has changed; this is different from other problems in which the price of X has changed.) (a) The budget line when prices are Px = 1 and P, = 1. (b) The optimal consumption bundle when prices are Px = 1 and P, = 1 (c) The indifference curve on which the optimal consumption bundle in (b) lies when prices are Px-1 and P 1 (d) The budget line when prices are P, = 1 and P, 4 (e) The optimal consumption bundle when prices are Px = 1 and = 4 (f) The indifference curve on which the optimal consumption bundle in (f) lies when prices are Px = 1 and P 4 (g) The uncompensated price effect (represent by an arrow on the graph and label by letter (g)) (h) The optimal consumption bundle when prices are Px-1 and PY -4 that generates the same utility as the optimal consumption bundle in (b) when prices are Px = 1 and PY-1. (You need to solve this optimal consumption bundle; hint: X and Y are both integers). Show your steps (i) The budget line on which the optimal consumption bundle in (h) lies when prices are Px = 1 and P, = 4 (j) The substitution effect (represent by an arrow on the graph and label by letter (k) The income effect (represent by an arrow on the graph and label by letter (k))

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