a. Country A starts at $30,000 at year t=0, and grows at a constant rate of 2%; country B starts at $1,000 at year t=0, and grows at a constant rate of 6%. In what year will country B catch country A? Derive your answer analytically and show key steps in your work. b. Now turn to Excel. Display the income of countries A and B (described in part a.) over 101 years (t=0,1,2,...,100) on a single graph. For this part, turn in the graph (you can save it as a picture and embed it), report the incomes in year t=100 of countries A and B to the nearest dollar, and answer the following question: On your graph, can you tell which country is growing faster, and does the comparison seem to vary over time? [Hint: For the years data, you can just enter 0 in the first cell and make each subsequent cell equal 1+ the cell above it. For the income data, you can enter the initial income in the first cell and make each subsequent cell equal (1+g)* the cell above it. For the graph, go to Insert and choose a (2-D) line chart. You can right-click on the chart and then Select Data. The "Legend Entries" are the data you want to graph (y-variables), the "Horizontal Axis Labels" tell you what to graph it against (x-variable), both of which you can select in the spreadsheet. These also allow you to name the data in "Series name". You should make sure the two series are labelled, which you can do by clicking on the "+" icon and clicking the "Legend" box. The Chart Title can also be clicked and changed.]
a. Country A starts at $30,000 at year t=0, and grows at a constant rate of 2%; country B starts at $1,000 at year t=0, and grows at a constant rate of 6%. In what year will country B catch country A? Derive your answer analytically and show key steps in your work. b. Now turn to Excel. Display the income of countries A and B (described in part a.) over 101 years (t=0,1,2,...,100) on a single graph. For this part, turn in the graph (you can save it as a picture and embed it), report the incomes in year t=100 of countries A and B to the nearest dollar, and answer the following question: On your graph, can you tell which country is growing faster, and does the comparison seem to vary over time? [Hint: For the years data, you can just enter 0 in the first cell and make each subsequent cell equal 1+ the cell above it. For the income data, you can enter the initial income in the first cell and make each subsequent cell equal (1+g)* the cell above it. For the graph, go to Insert and choose a (2-D) line chart. You can right-click on the chart and then Select Data. The "Legend Entries" are the data you want to graph (y-variables), the "Horizontal Axis Labels" tell you what to graph it against (x-variable), both of which you can select in the spreadsheet. These also allow you to name the data in "Series name". You should make sure the two series are labelled, which you can do by clicking on the "+" icon and clicking the "Legend" box. The Chart Title can also be clicked and changed.]
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
100%
![3. Growth explorations on paper and in Excel.
a.
Country A starts at $30,000 at year t=0, and grows at a constant rate of 2%; country B starts at $1,000 at
year t=0, and grows at a constant rate of 6%. In what year will country B catch country A? Derive your answer
analytically and show key steps in your work.
Now turn to Excel. Display the income of countries A and B (described in part a.) over 101 years
(t=0,1,2,...,100) on a single graph. For this part, turn in the graph (you can save it as a picture and embed it),
report the incomes in year t=100 of countries A and B to the nearest dollar, and answer the following question:
On your graph, can you tell which country is growing faster, and does the comparison seem to vary over time?
[Hint: For the years data, you can just enter 0 in the first cell and make each subsequent cell equal 1+ the cell
above it. For the income data, you can enter the initial income in the first cell and make each subsequent cell
equal (1+g)* the cell above it. For the graph, go to Insert and choose a (2-D) line chart. You can right-click on
the chart and then Select Data. The "Legend Entries” are the data you want to graph (y-variables), the
"Horizontal Axis Labels" tell you what to graph it against (x-variable), both of which you can select in the
spreadsheet. These also allow you to name the data in "Series name". You should make sure the two series are
labelled, which you can do by clicking on the “+” icon and clicking the “Legend” box. The Chart Title can also
be clicked and changed.]
b.
C.
Repeat part b., but graph ln(income) rather than income. For this part, turn in the graph, report the slope
of the In(incomes) line for each country, and answer the following question: On your graph, can you tell which
country is growing faster, and does the comparison seem to vary over time?
[Hint: You can just add these data and a new graph onto the same sheet as in part b. Once you have income, it
is easy to get ln(income) simply by using the In() formula in Excel. The slope can be calculated simply by
checking how much ln(income) rises each year.]
d. Which country is growing faster, and does the comparison vary over time? Why might one of the
graphs appear to give a misleading answer to this question?
e.
Return to part a. In what year will country B reach an average income of $1,000,000? Country A?
Derive your answer analytically and show key steps in your work.
f.
Return to part a. What growth rate would country B need to achieve to catch country A in 50 years?
Derive your answer analytically and show key steps in your work.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F144161ac-559f-4b1a-80a0-0fffa7827db1%2F894bc602-c232-47ed-9986-99dbe29fa9b7%2Fs5lvt9c_processed.png&w=3840&q=75)
Transcribed Image Text:3. Growth explorations on paper and in Excel.
a.
Country A starts at $30,000 at year t=0, and grows at a constant rate of 2%; country B starts at $1,000 at
year t=0, and grows at a constant rate of 6%. In what year will country B catch country A? Derive your answer
analytically and show key steps in your work.
Now turn to Excel. Display the income of countries A and B (described in part a.) over 101 years
(t=0,1,2,...,100) on a single graph. For this part, turn in the graph (you can save it as a picture and embed it),
report the incomes in year t=100 of countries A and B to the nearest dollar, and answer the following question:
On your graph, can you tell which country is growing faster, and does the comparison seem to vary over time?
[Hint: For the years data, you can just enter 0 in the first cell and make each subsequent cell equal 1+ the cell
above it. For the income data, you can enter the initial income in the first cell and make each subsequent cell
equal (1+g)* the cell above it. For the graph, go to Insert and choose a (2-D) line chart. You can right-click on
the chart and then Select Data. The "Legend Entries” are the data you want to graph (y-variables), the
"Horizontal Axis Labels" tell you what to graph it against (x-variable), both of which you can select in the
spreadsheet. These also allow you to name the data in "Series name". You should make sure the two series are
labelled, which you can do by clicking on the “+” icon and clicking the “Legend” box. The Chart Title can also
be clicked and changed.]
b.
C.
Repeat part b., but graph ln(income) rather than income. For this part, turn in the graph, report the slope
of the In(incomes) line for each country, and answer the following question: On your graph, can you tell which
country is growing faster, and does the comparison seem to vary over time?
[Hint: You can just add these data and a new graph onto the same sheet as in part b. Once you have income, it
is easy to get ln(income) simply by using the In() formula in Excel. The slope can be calculated simply by
checking how much ln(income) rises each year.]
d. Which country is growing faster, and does the comparison vary over time? Why might one of the
graphs appear to give a misleading answer to this question?
e.
Return to part a. In what year will country B reach an average income of $1,000,000? Country A?
Derive your answer analytically and show key steps in your work.
f.
Return to part a. What growth rate would country B need to achieve to catch country A in 50 years?
Derive your answer analytically and show key steps in your work.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 2 images
Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education