Due 3 September 2007
PROBLEM SET 1 ANSWERS
PPF of Scandals and Reports
See the accompanying spreadsheet for the PPF graph.
It looks like a PPF…
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.
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.
The accompanying spreadsheet has the details of the calculations and the results, but
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
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.