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All questions are in the attached docx file. DO NOT USE AI. Make sure to follow the instructions on question 1-3 very closely. Lecture 7 & 8 mentioned in the homework is also attached for reference.
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Attached.
Intermediate Macroeconomics
Complete the following questions. Submit an individual Word or PDF document on Canvas. Use
this document to create your final submission. Try using Lectures 7 and 8 as much as possible to
support your answers.
1. (10 points) Using data for the USA from https://fred.stlouisfed.org, do the following:
a. Using FRED’s “Edit Graph” feature, graph the nominal interest rate (series DTB3)
and inflation (series CPIAUCSL) on the same plot. Make sure the units for the
nominal interest rate are “Percent” and for inflation are “Percent Change from Year
Ago”. The frequency for both should be “Annual”, and the aggregation method
should be “Average”.
Answer:
Source: FRED and author’s calculations.
b. On the same plot, graph the real interest rate using the nominal interest rate,
inflation, and Fisher equation. Make sure the units are “Percent”, the frequency is
“Annual”, and the aggregation method is “Average”.
Answer:
Source: FRED and author’s calculations.
c. Comment on what you see.
Answer:
The graph makes it clear that real interest rates can change noticeably over time
in response to changes in inflation and nominal interest rates, which reflect the
effects of economic events such as recessions or expansions. This dynamic affects
important financial choices like saving and investing.
d. Download your work as a CSV or Excel file. In the file, remove rows/years where
any of the 3 variables are missing. You should be left with data for 1954 to 2023.
Using this data, calculate the present discounted value (pdv) of $1,000,000 in 1954
if the money is received in 2023.
Answer:
observation_date
1954-01-01
1955-01-01
1956-01-01
1957-01-01
1958-01-01
1959-01-01
1960-01-01
1961-01-01
1962-01-01
1963-01-01
1964-01-01
1965-01-01
1966-01-01
1967-01-01
1968-01-01
DTB3_CPIAUCSL_PC1
0.57640
1.98180
1.14728
-0.16812
-0.96347
2.45403
1.38069
1.28213
1.59629
1.89996
2.22365
2.37039
1.86635
1.50890
1.09291
CPIAUCSL_PC1
0.4
-0.3
1.5
3.4
2.7
0.9
1.5
1.1
1.2
1.3
1.3
1.6
3.0
2.8
4.2
Discount rate (%)
0.5764
1.9818
1.14728
-0.16812
-0.96347
2.45403
1.38069
1.28213
1.59629
1.89996
2.22365
2.37039
1.86635
1.5089
1.09291
1969-01-01
1970-01-01
1971-01-01
1972-01-01
1973-01-01
1974-01-01
1975-01-01
1976-01-01
1977-01-01
1978-01-01
1979-01-01
1980-01-01
1981-01-01
1982-01-01
1983-01-01
1984-01-01
1985-01-01
1986-01-01
1987-01-01
1988-01-01
1989-01-01
1990-01-01
1991-01-01
1992-01-01
1993-01-01
1994-01-01
1995-01-01
1996-01-01
1997-01-01
1998-01-01
1999-01-01
2000-01-01
2001-01-01
2002-01-01
2003-01-01
2004-01-01
2005-01-01
2006-01-01
2007-01-01
2008-01-01
2009-01-01
2010-01-01
2011-01-01
2012-01-01
2013-01-01
2014-01-01
2015-01-01
2016-01-01
2017-01-01
2018-01-01
1.23134
0.50731
0.10770
0.78889
0.77672
-3.16529
-3.35521
-0.79829
-1.20860
-0.45160
-1.19876
-2.10984
3.65787
4.44505
5.45811
5.17208
3.94323
4.02535
2.19915
2.56840
3.32047
2.07726
1.15977
0.38969
0.02747
1.65665
2.68418
2.06873
2.72451
3.22895
2.44527
2.45312
0.58272
0.00965
-1.28964
-1.29293
-0.21667
1.50791
1.49140
-2.44364
0.47088
-1.49812
-3.08681
-1.98559
-1.40889
-1.58274
-0.06911
-0.95124
-1.19732
-0.50269
5.4
5.9
4.2
3.3
6.3
11.0
9.1
5.8
6.5
7.6
11.3
13.5
10.4
6.2
3.2
4.4
3.5
1.9
3.6
4.1
4.8
5.4
4.2
3.0
3.0
2.6
2.8
2.9
2.3
1.5
2.2
3.4
2.8
1.6
2.3
2.7
3.4
3.2
2.9
3.8
-0.3
1.6
3.1
2.1
1.5
1.6
0.1
1.3
2.1
2.4
1.23134
0.50731
0.1077
0.78889
0.77672
-3.16529
-3.35521
-0.79829
-1.2086
-0.4516
-1.19876
-2.10984
3.65787
4.44505
5.45811
5.17208
3.94323
4.02535
2.19915
2.5684
3.32047
2.07726
1.15977
0.38969
0.02747
1.65665
2.68418
2.06873
2.72451
3.22895
2.44527
2.45312
0.58272
0.00965
-1.28964
-1.29293
-0.21667
1.50791
1.4914
-2.44364
0.47088
-1.49812
-3.08681
-1.98559
-1.40889
-1.58274
-0.06911
-0.95124
-1.19732
-0.50269
2019-01-01
2020-01-01
2021-01-01
2022-01-01
2023-01-01
0.24922
-0.89445
-4.63717
-5.96691
0.94261
1.8
1.2
4.7
8.0
4.1
PDV
0.24922
-0.89445
-4.63717
-5.96691
0.94261
660,274.6234
2. (10 points) Suppose a college education raises the average person’s wage by $30,000 per
year, from $40,000 to $70,000. Assume the interest rate is 3% and there is no growth in
wages, then answer the following.
a. Suppose you are a high school senior deciding whether or not to go to college.
What is the present discounted value (pdv) of your labor income if you forgo
college and start work immediately, assuming you work for 50 years?
Answer:
40,000 is the annual wage,
R is the interest rate (3% or 0.03),
50 is the total number of years worked.
𝑝𝑑𝑣 = $40,000 𝑥
1
)〗50
1+0.03
1
1−(
)
1+0.03
1−(〖
= $1,060,066
b. As an alternative, you could pay $20,000 per year in college tuition, attend for 4
years, and then earn $70,000 per year after you graduate. What is the present
discounted value of your labor earnings under this plan? (Compute this value from
the point of view of a high school senior.)
Answer:
(pdv) of total income is:
𝑝𝑑𝑣 = $70,000 𝑥 (〖
1
1+0.03
)〗4
1
)〗46
1+0.03
1
1−(
)
1+0.03
1−(〖
= $1,587,113
Need to substract (pdv) of total tuition paid for four years from this:
𝑝𝑑𝑣 = $20,000 𝑥
1
)〗4
1+0.03
1
1−(
)
1+0.03
1−(〖
= $76,572
Thus, (pdv) of total net income is:
(pdv) = $1,587,113 − $76,572 = 1,510,541
c. Discuss the economic value of a college education.
Answer:
A college education increases lifetime earnings by $450,475 compared to starting
work immediately after high school, even after accounting for tuition costs and
delayed entry into the workforce (The net PDV of income after attending college is
$1,510,541,...
