ECON2102 Assignment 1
Economic Growth
Term 3 – 2024
Due: Please check Course Outline Instructions:
Due date: Check Moodle and Course Outline.
This assignment is to be completed individually.
You must answer all the questions (ideally), but not all the questions will be marked. We will mark questions 2.3; 3.1 and 4.4.
1 Facing economic growth in real life
As a senior staff member of the Reserve Bank of Australia (RBA ) you are invited to discuss long run economic growth around the world. In particular, you are concerned about the growth rates starting in 2010 for a large group of countries. In your report you need to address the following questions:
- Which country had the highest GDP per-capita in 2022? Which country had the lowest? What was the value for Australia?
2. Which country had the highest average growth rate of GDP per-capita in the last 11 years from 2012 (ie, from 2012 until 2022 inclusive)? Notice that some countries may not have enough data to obtain this information.
Ignore these cases. Hint: pay close attention to the formula discussed in the textbook to calculate average growth rates.
3. Using the average growth rate of the country you found in part (2), calculate how many years Australia would take to “catch up” to the level of GDP per capita of the highest country. Assume that the country with the highest GDP per capita does not grow at all in this period. Round your answer to the highest integer.
4. Calculate the answer to part (3) if the country with the highest GDP per-capita grows at 0.5% pa What
about if the growth rate is 0.9%? Round your answers to the highest integer.
5. Would you say the 0.9 percentage point difference from (3) to (4) in the average growth rate is an important difference? as a policymaker interested in improving the standard of living of the ones you govern, which of these two rates would you prefer?
6. Using the dataset, replicate figure (3.5) of the textbook for Australia. Make sure to use all the years from 1990 onwards. Please discuss your findings in a short paragraph.
To prepare your report, you are advised to visit the Word Bank’s website (https://data.worldbank.org/) and collect data on GDP per capita (PPP, constant 2017 international $) for all countries in their dataset. Make sure to collect data for all years they have available. Download the data on Microsoft Excel(1) (or equivalent) and remove all years until 1989 (keep 1990 onwards). The dataset comes with a few extra information on regions and other administrative regions at the very bottom (eg, Arab countries, Low Income, Euro Area). Be mindful of those when answering the following questions. Note: you do not need to prepare a report, just answer the questions but show all your calculations.
(1)UNSW students can 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 Growth and population– The Treasury is currently estimating the growth level for Australia. They are concerned about population growth and they have ask you to help them to prepare a report that accounts for an increase in the population size over time. You remember your time at UNSW and decide to use the Solow-Swan model to prepare your report. The ABS forecast that population will grow at a constant rate n, where n > 0. When this assumption is made, the capital accumulation equation (in per capita terms) assumes the following format: Δkt+1 = syt− (n+δ)kt, where s is the savings rate and δ is the capital depreciation rate. Output is defined as Yt = AtK
αt L (1−α)t .
In your report you need to answer the following questions:
1. Find the steady-state level of income per capita assuming the production function follows the standard Cobb- Douglas production function. Show your work, step-by-step and explain your procedure.
2. In 2023, Australia had a GDP per capita level of around US$61,305 while Korea’s was about US$33,128. Using the result you found in (1), give two reasons that could explain why this difference exists.
3. Ceteris paribus, what happens to the level of income per capita at the steady state when n increases. Explain why (intuitively) using 1-2 sentences. How do you relate this effect to the output figures reported in Australia over the last few quarters?
4. Find the expression of consumption per capita at the steady state in this economy. Compare this case to the case when the population does not grow. Show your work step by step and provide an explanation.
5. Assume A = 12, n = 0.07, δ = 15% and α = 0.35 for this exercise. Use Microsoft Excel (or equivalent) to plot a graph illustrating the relationship between consumption per worker at the steady state and the savings rate. Hint: use 0.01 increments of the savings rate when plotting your graph.
6. What is the value of the golden rule of savings rate in this economy ? You need to do some research to answer this question. Calculate the exact value. Show your work step by step providing an explanation. How your answer relates to part e)?.
3 Growth, technology and population
Following the report you have prepared for the Treasury, one of the comments you received is that you are not allowing technology to grow over time, so you have decided to prepare a new report allowing for that possibility.
You can assume that the growth level of technology is g > 0, and continue making the same assumptions on population growth you made before.
When these assumptions are made, the capital accumulation equation (in per effective labor terms) assumes the following format: Δkt+1 = syt− (n+ g+ δ)kt, where s is the savings rate and δ is the capital depreciation rate.
Total output can be described using a CES production function, Yt = At (αKγt + (1− α)Lγt )
1
γ . In your report you need to answer the following questions:
1. Find the steady-state level of income per capita assuming the CES production function described above. Show your work, step-by-step providing an explanation.
2. In 2023, Australia had a GDP per capita level of around $61,340 while Korea’s was about $33,128. Using the result you found in (1), give two reasons that could explain why this difference exists.
3. Ceteris paribus, what happens to the level of income per capita at the steady state when n increases. Explain why (intuitively) using 1-2 sentences. How do you relate your answer to the reported figures for Australia over the last few quarters.
4. Find the expression of consumption per capita at the steady state in this economy. Compare this case to the case when the population does not grow (but A still grows).
5. Assume A = 10, n = 0.08, δ = 2%, g = 0.06, γ = .5 and α = 0.3 for this exercise. Use Microsoft Excel (or equivalent) to plot a graph illustrating the relationship between consumption per worker at the steady state and the savings rate. Hint: use 0.01 increments of the savings rate when plotting your graph.
6. What is the value of the golden rule of savings rate in this economy? You need to do some research to answer this question. Calculate the exact value. Show your work, explain and relate to the previous answer.
4 Sustained economic growth
After discussing your report with senior economist at the Treasury, they were impressed about how the model can generate sustained economic growth. Then you decide to explain them the following:
1. What is the motivation to study the Romer model? ie, what are the issues the Solow-Swan model had that stimulated economists to look for an alternative? Explain using at most 3 sentences.
2. Why is the Romer model incompatible with perfectly competitive markets? Justify using at most 3 sentences, and provide an example (different than the one provided in the Lecture and textbook)
3. 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.
4. Using the Romer model discussed in lectures, show (using equations and a diagram) the effect of an increase in the proportion of workers in the research sector on the balanced growth path of output per worker. There is no need to derive the equations again; just use the ones obtained in lectures. Explain the intuition.
5. Using the results above, indicate which parameters would cause only level effects. What about only slope/growth effects? What about both effects at the same time?
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