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Assignment 1

Economic Growth

Term 1 - 2023

Electronic submission via Moodle

Instructions:

Please include a completed and signed cover sheet (available on Moodle).

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

2.1; 3.1 and 4.2.

Presentation, organization and tidiness of the assignment counts towards your mark. Make sure your solutions

are clear and easy to navigate. We are looking for a simple, but well-organized general look for the assignment.

You are free to type or handwrite your solutions. If you prefer to type them, make sure to use Microsoft

Word equations (or equivalent) to write down your equations properly, otherwise reserve a space to handwrite

them. If you prefer to handwrite the whole assignment or parts of it, make sure the handwriting is clear,

well-organised and legible.

Copyright U. of New South Wales 2023.All rights reserved (do not distribute this file).

1

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 1990 (including 1990

in your calculations) for a large group of countries. In your report you need to address the following questions:

1. Which country had the highest GDP per-capita in 2021? 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 2020 (i.e., from

2010 until 2020 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 the country

with the smallest GDP per-capita 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% p.a. 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.

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 (e.g., 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

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 growth 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: ?kt = syt? (n+ δ)kt, where s is the savings rate and δ is the capital depreciation rate. 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.

2. In 2020, Australia had a GDP per capita level of around $48,679 while Algeria’s was about $10,735. 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.

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.

5. Assume A = 10, n = 0.08, δ = 2% and α = 0.2 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.

3

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 growth 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 labour terms) assumes

the following format: ?kt = syt ? (n+ g + δ)kt, where s is the savings rate and δ is the capital depreciation rate.

kt = Kt/(AtLt) and yt = Yt/(AtLt). 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.

2. In 2020, Australia had a GDP per capita level of around $48,679 while Algeria’s was about $10,735. 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.

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, and α = 0.2 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.

4

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? i.e., 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.

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.

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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