Economics 302
Summer 2007
Answers to Homework #3
Homework will be graded for content as well as neatness. Sloppy or illegible work will
not receive full credit. You will find it helpful to do this work using Excel.
1.
The total adult population in your country is constant and equal to 500,000
people. In your country there are initially 400,000 people in committed
relationships (C) and 100,000
people who are not in committed relationships (F).
In this example, “C” stands for committed and F for “free”.
There are pros and
cons to being in either group and in your country there is substantial movement
between these two categories.
a.
What is the initial percentage of people in committed relationships in this
country?
Initial percentage of people in committed relationships = (400,000/500,000)
(100) = 80%.
Now, suppose that each year the rate of commitment to committed relationships ,
m, is 10% of the previous year’s free population while the rate of separation, s, is
20% of the previous year’s committed population. Use this information to answer
the following questions. Note: the adult population in your country is unchanging
and should therefore always sum to 500,000.
b.
Calculate the values for the end of the first year given the values of m and
s. You can do this without Excel, but you will find it infinitely easier to do
this problem using Excel.
Committed
Relationships (C)
Free from
Relationships (F)
Total Adult
Population
Initial Levels at
Beginning of Year
400,000
100,000
500,000
Change due to
committing to a
relationship
10000
10000
XXX
Subtotal
410,000
90,000
500,000
Change due to
leaving committed
relationship
80000
80000
XXX
Total
330,000
170,000
500,000
c.
At the end of the first year, what is the percentage of people in committed
relationships in this country?
1
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View Full DocumentPercentage of people in committed relationships = (330,000/500,000)*100 =
66%.
d.
Calculate the values for the end of the second year given the values of m
and s, and the values you calculated in part (b). Use the following table to
report your answers.
Committed
Relationships (C)
Free from
Relationships (F)
Total Adult
Population
Initial Levels at
Beginning of Year
330,000
170,000
500,000
Change due to
committing to a
relationship
17000
17000
XXX
Subtotal
347,000
153,000
500,000
Change due to
leaving committed
relationship
66000
66000
XXX
Total
281,000
219,000
500,000
e.
At the end of the second year, what is the percentage of people in
committed relationships in this country?
Percentage of people in committed relationships = (281,000/500,000)*100 =
56.2%.
f.
Calculate the values for the end of the third year given the values of m and
s, and the values you calculated in part (d). Use the following table to
report your answers.
Committed
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 Spring '07
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