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# ps1f06s - Economics 101 Problem Set 1 Solutions Alan C...

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Economics 101, Problem Set 1 Alan C. Marco Solutions. 1. Bill’s preferences for goods x and y are given by the following table that lists combinations of goods that make Bill equally well oF. Units of x Units of y 16 6 12 8 8 12 4 24 (a) Graph Bill’s indiFerence curve, with x on the horizontal axis. Assuming that the price of x is \$1.00 and the price of y is \$1.50, and that Bill has \$24 to spend, add a budget line to the graph. 0 5 10 15 20 y 5 10 15 20 x (b) What combination of x and y will maximize Bill’s utility? 12 units of x and 8 units of y , because that combination yields the same utility as the other points, but is the only one that is aFordable. (c) Show that your answer meets the MRS = P x P y rule. [This may not be exact, so explain why if it’s not.] Well, the curves are tangent at that point on the graph, so we know it’s true. However, we want to show it formally: Starting at (12 , 8) should we sell some x and buy some y ? (No.) MRS = P x P y is the same thing as MU x MU y = P x P y . Moving from (12 , 8) to (8 , 12) , the slope of the IC is 4 - 4 = - 1 . The slope of the budget line is - 2 3 . This means that MU x MU y = 1 > P x P y = 2 3 . Put another way, MU x P x > MU y P y which means we should buy more x and less y. Starting at (12 , 8) should we sell some y and buy some x ? (No.) Moving from (12 , 8) to (16 , 6) , the slope of the IC is - 2 4 = - 1 2 . The slope of the budget line is - 2 3 . This means that MU x MU y = 1 2 < P x P y = 2 3 . Put another way, MU x P x < MU y P y which means we should buy more y and less x. Seen another way, the

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ps1f06s - Economics 101 Problem Set 1 Solutions Alan C...

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