# f07 ec51 ps1 answers - Economics 51D Due 3 September 2007...

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Economics 51D Due 3 September 2007 PROBLEM SET 1 ANSWERS 1. Dirty Laundry: PPF of Scandals and Reports A. See the accompanying spreadsheet for the PPF graph. It looks like a PPF… B. There are basically two ways to solve this: first, you could graph the point on the same graph as the PDF, and see whether it was outside the PDF (infeasible), inside the PDF (inefficient), or on the PDF (efficient). This is actually hard to do in Excel, given your information. So we can try a second way. We can find the equation of the line connecting the nearest 2 points on the PPF and see whether the point (130, 2548) lies above, below, or on that line. The two nearest points on the PPF are (112, 2716.4) and (158, 2284). We can find the equation of the line that goes through these two points by first finding the slope of the line (which happens to be the MC of Scandals, since it’s the vertical change divided by the horizontal change), and then solving for the intercept of the line using one of the endpoints. The slope of the PPF between the two points is (2284 – 2716.4) / (158 – 112) = -9.4. Then since the equation for a line is y = m*x + b where m is the slope and b is the intercept, we can take one of the points on the PPF and this slope to solve for the implied intercept. Let y = 2284, x = 158, m = -9.4, so the equation becomes 2284 = (-9.4)*158 + b, so b = 3769.2. Thus, the equation of the line connecting the two points on the PPF is y = -9.4*x + 3769.2. Now all there is to do is to see whether the point (130, 2548) is above, below, or on the line. We can do this by plugging in the x value, 130, and seeing how the true y value, 2548, compares to the y value on the PPF. In other words, the PPF implies that at 130 scandals, there will be y = (- 9.4)*130 + 3769.2 = 2547.2 tons of reports created. The y value we are considering is 2548, which is greater than the implied y-value on the PPF for x = 130 reports, so technically this level of production is infeasible—just barely beyond what the economy is capable of producing. Of course, in reality we think that the PPF is a smooth curve, so this level of production may be actually be on the PPF or even below it. But our best guess, given the information we have, is that this is an infeasible point. C. The accompanying spreadsheet has the details of the calculations and the results, but one issue that is important to understand is how to tell which MC is which. If we let Scandals be the x-variable and Reports be the y-variable, then the slope of the PPF is measured in units of Reports / Scandals, or in other words how many reports you have to give up to get an extra scandal. So the slope of the PPF give the marginal cost of the x-variable, or in other words the marginal cost of Scandals. Then the marginal cost of Reports should be (Change in Scandals) / (Change in Reports), so that the units of measurement are Scandals / Report. 1

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This implies that the marginal cost of Reports = 1 / (Marginal Cost of Scandals), which you can verify by doing the division on the numbers in the spreadsheet, which is what the final column reports.
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