University of Illinois at Urbana-Champaign
Professor Ron Laschever, ECON 440, Spring 2010
1
Problem set #3 Answer Key
1. Present a formula to calculate the economic loss
using the guidelines that the special master
prescribed.
You may assume that the person is a 28-year-old single male. In your answer, be sure to
address how many additional years you assume an individual would work. Would you discount
earnings that a person would have earned in the future? If so, at what rate? Would your answer
change in the case of a female? Why? [15 Pts]
Let
w
represent a person’s average wage over the past three years (we could find that out by looking at
their tax returns, but if you just assumed some number, that’s fine too). Let
T
represent the number of
additional years a person is assumed to work. Finally, let
r
represent some risk-free interest rate. In the
year after a person died, we assume he would have earned
w
; But the person wouldn’t have received this
for a year. Referring back to our discussion in the previous class, a dollar received in one year is
equivalent to 1/(1+r) today, where
r
is some personal discount rate. Thus,
w
in a year is only worth
w
/(1+
r
) today. Similarly, in two years a person would have been paid
w
, which is worth w/(1+r)
2
today.
That is, a person’s total (economic) compensation can be expressed as:
∑
=
+
=
+
+
+
+
+
+
+
+
=
T
t
t
T
r
w
Total
or
r
w
r
w
r
w
r
w
Total
1
3
2
)
1
(
,
)
1
(
...
)
1
(
)
1
(
1
It would probably be nice to plug in some values. First, what is the value for T? Since we know the
person is 28 the question is really when is a 28-year-old male going to retire? There are calculators that
predict that. Since the average retirement age is falling, it might seem reasonable to assume that younger
workers who died on 9/11 would have retired earlier than older workers who died. It would also seem
reasonable to project different retirement ages for people with different characteristics (i.e. low versus
high education, white collar versus blue collar jobs, etc.). Similarly, even though the gap between them is
closing, men still tend to spend more years in the labor market than do women. On the one hand, we
might want to use all available information about a person to project their retirement age. On the other
hand, we might feel guided by a principle to treat people as similarly as possible – either because it’s a
more fair method, or because it’s a more simple method. The Special Master balanced these ideas and
only used a person’s age to determine a person’s retirement age (younger people were assumed to retire
earlier than older people). Men and women who were the same age were assumed to work the same