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ECON5102

MACROECONOMICS

Term 3, 2024 - UNSW

ASSIGNMENT 1

DUE: 5pm Friday, 4th of October 2024

Academic Honesty

Academic honesty is a core value of the University, and all students are required to act

honestly, ethically and with integrity. The consequences of engaging in plagiarism and

academic dishonesty, along with the process by which they are determined and applied, are

set out in the Student Misconduct Procedure. Under the same policy, as the lecturer, I must

report any suspected plagiarism or academic dishonesty.

Instructions

• This is an individual assignment which accounts for 10% of your final grade. You may

discuss with your classmates, but please ensure that the submitted work is independent.

• You can either hand-write or type your answers (or both), but please compile all your

answers in one PDF file and submit it via Moodle. Failure to submit a PDF file will

attract a 1-point penalty,

• You can only submit your work once, so please double check before you submit. The

page limit of the submission is 10 pages including appendix (a 2-point penalty will apply

if the page limit is exceeded).

• There are 3 questions (with sub-questions) in this assignment, and please attempt all

questions. Detailed solutions to each question will be provided during seminars after the

assignment is due.

• I will randomly select 4 sub-questions (same 4 sub-questions for everyone) to grade, and

each question is worth 2.5 points. The total point of this assignment is 10. The grading

will be based on the completion and general quality of your submission.

• For all questions, please show your derivations step-by-step. Answers without

intermediate steps will be considered incomplete and marked down.

• Based on the University late policy, a late submission is subject to a penalty of 5% (of the

total points) per calendar day. No submissions will be accepted after Wednesday (09/10),

11.59pm.

• Make sure to include a cover sheet to your submission. They can be found on Moodle.

Failure to include a cover sheet or including an incomplete one will attract a 1-point

penalty.

• Use of any AI aid is strictly prohibited. If found, the student will be given an automatic

zero and referred to the board of education for breach of academic integrity.

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QUESTIONS

1. You work as an analyst at the World Bank, and you have been granted access to a large

dataset containing information on GDP per capita for several countries since 1990. Your

direct manager asks you to study the data and prepare for some questions other analysts

might have about long-term economic growth.

To access the data, visit the Word Bank’s website (https://data.worldbank.org/) and collect

data on GDP per capita (PPP, constant 2021 international $) for all countries in their dataset.

Make sure to collect data for all years they have available. Download the data on Microsoft

Excel1 (or equivalent) and remove all years until 1989 (keep 1990 onwards). The dataset

includes information on regions also (e.g., Arab countries, Low Income, Euro Area). Please,

ignore these regions when answering the questions. Also, feel free to do some data cleaning

and eliminate countries without any data (e.g., Cuba).

The most pertinent questions the analysts at the Bank sent you are below. Answer all of them

to the best of your ability.

1.1) Which country had the highest GDP per-capita in 2023? Which country had the lowest?

What was the value for Australia? Round your answers to 2 decimal places.

1.2) Which country had the highest average growth rate of GDP per capita in the last 10

years from 2022 (i.e., from 2013 until 2023 inclusive)? Provide a short explanation as to why

this country had such a high growth lately. Keep your comments brief here. Notice that some

countries may not have enough data to obtain this information. Ignore these cases. Hint: use

equation (3.9) of the textbook with t = 10.

1.3) Using the average growth rate for China2 and India, indicate how many years would

these countries take to “catch up” to the level of GDP per capita for Australia. Assume that

Australia does not grow over the years.

1.4) Repeat the exercise above assuming Australia grows at its average 10-year rate.

1.5) Provide a brief description of what the rule of 70 is. Create a similar rule to indicate how

many years would the economies of China, India and Australia take to quadruple their sizes,

using their 10-year average growth rate calculated in (1.2).

1.6) In lectures, we compared the case of South Korea and Vietnam over many decades to

provide some motivation to study the Solow-Swan model. Produce a graph using these two

economies with the data you have. Comment on whether the gap between these two countries

have increased or not over the last 3 decades. Keep your answers brief.

1 UNSW students have access to Microsoft Office for free, both for Windows and Mac users. We strongly advise

that you get it installed on your personal computer.

2 The World Bank separates Macao, Hong Kong and other regions out of China. Please, only use the row titled

“China”, i.e., do not add Macao and other regions into the data for China.

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2. Let’s investigate the Solow-Swan model for when the population is allowed to grow at the

constant rate n > 0. We will use a Cobb-Douglas production function

= ̅

1− with

3.

The per-capita equation describing the behaviour of capital over time now changes to +1 =

+ ̅ − ( + ). Notice that small letters in this equation refer to per-capita terms, e.g.,

= /.

2.1) What is the interpretation of

and (1 − ) in this model?

2.2) Find the expression for production function in per capita terms. Plot a graph with the

production function, savings function and depreciation function, all in per capita terms.

Clearly label all curves and axes.

2.3) Find the expression for output per worker (y) at the steady state. Hint: the definition of

steady state is the point at which capital per worker does not grow.

2.4) In 2022, Australia had a GDP per capita level of around $59,100, while Japan’s was

about $46,268. Using the result you found in (2.2), give two reasons that could explain why

these two countries have important differences in standard of living.

2.5) Find the expression for consumption per capita at the steady state in this economy.

Compare this case to the one when the population does not grow (n = 0).

3. Answer the following questions about the Romer model.

3.1) What is the motivation to study the Romer model? I.e., what are some of the issues the

Solow-Swan model had that stimulated economists to look for an alternative? Explain using

at most half a page.

3.2) What does it mean for a good to be non-rival? How is it different from an excludable

good? Explain using at most half a page.

3.3) Why is the Romer model incompatible with perfectly competitive markets? Justify using

at most 3 sentences.

3.4) Why do we not talk about the notion of steady state in the Romer model? Is it possible

for the steady state to be observed in the Romer model? Explain using at most 3 sentences.

3.5) You are the finance minister of a country whose economy works exactly like in the

Romer model we considered in lectures. The prime minister summons you to their office

asking if there is a way to increase economic growth permanently without sacrificing output

in the short run. Provide one recommendation of how this could be achieved. Make sure to

include (i) the economic intuition (simple words); (ii) a diagram illustrating the dynamics of

GDP per capita over time; and (iii) some equations to further support your suggestion.

3 Do not replace alpha for any specific value in this question.

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