程序代写案例-ECON5102-Assignment 1

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ECON5102 - Macroeconomics
Assignment 1
Lecturer: Gonzalo Castex
T1 - 2021

Instructions
- Due date 8th of March at 9.00am. Electronic submission through Moodle.
- Please include a completed and signed cover sheet (available on Moodle).
- This assignment is to be completed individually.
- You must answer all the questions, but only one or two of the questions will be marked. Please note
that only two assignments will be marked. Please see Course Outline for details. You will know in
advance if this assignment will be marked.
- We advise you to firstly attempt all questions on your own then meet other students to discuss your
individual solutions. Write down your own answers using your own words. Discussion with your
peers is beneficial for everyone, please do not copy and do not let other students to copy from your
solutions. Academic misconduct will be reported.
- Presentation, organisation 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-organised 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 equations1 (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.






1 Click on the “Insert tab” then “Equations”.
QUESTION 1
You have been appointed as a senior advisor of the Finance Minister. You are requested to give a
presentation about Australian economic growth using the Cobb-Douglas production function that you
learned in your ECON5102 class (Production Model). = !"#"
Further, assume the assumptions made in lecture 1 hold. Answer the following questions:

a) Provide an interpretation for the exponent of the labour input.
b) Find expressions for the marginal product of capital (MPK) and labour (MPL) in this economy. Would
you say the assumption of diminishing return to inputs is satisfied? Why? (you can add a plot if you want)
c) Derive the demand for capital from a typical firm in this economy. What can you say about the supply of
capital in the simple model of production?
d) Now, suppose there is a sudden increase in the supply of capital in this economy (ie, an exogenous
change in the level of capital). What do you expect to happen to the real rental rate and the real wage in this
economy? Provide both mathematical and graphical explanations and economic intuition.


QUESTION 2
This question aims to explore some of the points discussed in Topic 2 (Solow-Swan model). It is also
designed to test your understanding of Chapter 5 of the prescribed textbook.
Consider an economy with the general Cobb-Douglas production function: $ = $%$!&% .
Answer the following questions assuming that labour grows at the rate n = 0 and adopting the assumptions
made in lecture. The equation describing capital dynamics is: $'! = $ + $ − $
where d is a constant parameter.

a) Obtain the steady state levels of the capital stock (K), output (Y), capital per worker (k), output per worker
(y), consumption per worker (C/L), total savings (S), private investment (I), real wages (w) and real interest
rates (r). Make sure to show all your work.
b) Assuming that s = 0.4, d = 0.1, α = 0.4 and ̅ = 1, calculate the steady state values of the variables in (a).
Now, assume the policy-maker successfully implemented a policy that resulted in the increase of the total
factor productivity level to 2 (i.e., ̅ = 2), ceteris paribus.
c) Using the help of the Solow-Swan diagram developed in lectures and tutorials, explain the effect of this
policy on the standard of living of the economy. Make sure to include:
i) The economic explanation of why the economy experienced a change in the steady state level of
capital per worker;
ii) A diagram illustrating what happened to the relevant curves.
iii) Another diagram illustrating the dynamics of the stock of capital in the economy (before, at and
after the technological shock).
iv) What must have happened to the growth rate of output per worker in the transition between the
initial equilibrium and the final one?
e) Is the current savings rate (s = 0.7) the golden rule of savings? Hint: you don’t need to calculate the actual
golden rule, just to show that the current one is not the golden rule.


QUESTION 3
This question aims to explore some of the points discussed in Topic 3 (Romer model). It is also designed to
test your understanding of Chapter 6 of the prescribed textbook.
Consider the simple Romer model developed in lectures with the following values for parameters: ̅ = 0.003 = 0.25 = 900 ( = 7

a) How fast are ideas growing in this economy in percentage terms? How many workers are being employed
in the goods sector?
b) Find what the stock of ideas in this economy will be in periods 200 (t = 200) and 400 (t = 400).
c) Find an expression for the output per worker in the balanced growth path. What will be the standard of
living in periods 200 and 400?
d) On a clear graph, plot the trajectory of the log of output per worker through time.
e) Now, assume the policy-maker decides to allow 100 extra workers to come from overseas, leading to an
increase in the total labour force to 1,000. Show the effects of this change on the growth rate of ideas, as
well as the effect on the plot you drew in part (d). Do you notice both a level effect and a slope effect?




QUESTION 4
This question aims to explore some of the points addressed on our discussions surrounding unemployment
issues. It is also designed to test your understanding of Chapter 7 of the prescribed textbook.
Using the help of a diagram and clear economic explanation, discuss the effects on the equilibrium wage and
employment level of an economy given the following shocks:
a) A strong increase in Australian exports, leading to a strong increase in GDP.
b) The breakout of a new disease leads to a strong fall in consumer and business confidence, leading to a
strong fall in overall production (please note this is pure fiction!). Does your answer change if wages are
rigid downwards? If so, present the solution when wages are fully flexible and contrast it with the rigid case.
If not, please explain in detail.
c) The Australian government decides to increase the wage-related taxes to increase the chances of achieve a
surplus in the next Budget.
d) A natural disaster hits the Australian economy causing a large contraction on the country’s GDP, and at
the same time the government announces new legislation to lower the tax rate on Superannuation
contributions.


QUESTION 5 (Optional)
This question aims to empirically explore some of the points addressed when studying growth theory and the
labour market.
a) Using Australian data, download time series for output, investment, stock of capital, hours
worked, female labour participation, and the unemployment rate (aggregate and by gender). Plot
them and provide a short explanation of what you obtained, please also compute average levels,
average growth rates, and other statistics. (explain your calculations).
b) Using the ‘law of motion’ of capital described in class, generate the time series for capital starting
in t0 (you can define t0 by yourself, for example 1970, 1980, 1990, or any other date). Assume that
the depreciation rate is 4% and compare your generated time series of capital with the actual one
observed in the data. Add a discussion about similarities and differences.
c)Using the Solow-Swan model compute a measure of TFP and discuss your findings. Justify the
values of your parameters (alpha).


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