代做ECON10003 Assignment #2 Introductory Macroeconomics代做留学生SQL 程序

ECON10003

Assignment #2

Introductory Macroeconomics

Due Friday 4 October

Instructions.   You can but do not have to do this assignment in a group. If you work in a group, it can have at most three people. The assignment is due by 4pm on Friday 4 October.

Late assignments.   Late assignments will not be accepted. Please apply for Special Consideration if for some documented reason you cannot submit by the due deadline.

Marking criteria.   The tutors will mark the assignment according to the following criteria:

• Ability to use material discussed in lectures, tutorials, and other sources to answer the assign ment questions in a logical and coherent fashion (100 per cent weight).

• The maximum assignment length is 800 words.

• Please note that the University and the teaching staff take academic integrity seriously. Please be aware that plagiarism and collusion are unacceptable. Further details can be found in the subject guide.

QUESTIONS

1. Exploring the Production Function (6 points)

In this question, you will explore the properties of a standard production function. You will be asked to make some calculations and provide some economic intuition. Be sure to provide all of your working. Correct answers without working will not receive full marks.

Consider the following production function.

Y = KαL1−α

For this whole question, assume α = 3/1.

(a) Complete the following table (rounding to the nearest whole number).

Use the table to explain whether this production function exhibits the following:

(i) Diminishing returns to capital. What about to labour?

(ii) Constant-returns-to-scale.

Define output per worker as y ≡ L/Y and capital per worker as k ≡ L/K.

(b) Write the production function as a relation between output per worker and capital per worker. Use mathematical methods to explain whether this reduced form. function exhibits diminishing returns to capital per worker.

(c) Suppose this production function is used in a Solow-Swan model (with fixed labour). Derive an equation that describes the steady-state condition of capital per worker, and calculate this steady state value assuming the values α = 3/1, s = 0.32, and δ = 0.08.

(Hint: You will need to adapt the equation used in Lecture 15.)

(d) Graph the results of part (c). Include the reduced-form. output function, savings function and the line of depreciation of capital per worker. Mark-up your graph with steady-state capital per worker, and show steady-state output and consumption per worker (you need not calculate these).

2. Estimating the Solow-Swan Growth Model (4 points)

In this question, you will investigate the Solow-Swan growth model empirically. You will derive and estimate a linear regression model, and evaluate your results. This will will require you to download and prepare data in a way that makes sense for your regression model.

Go to the Penn World Tables website, https://www.rug.nl/ggdc/productivity/pwt/, and down-load Australian annual data covering the period 1950-2019 for the following variables:

(i) Real GDP [use ‘Output-side real GDP at chained PPPs (in mil. 2017US$)’]

(ii) Employment [use ‘Number of persons engaged (in millions)’]

(iii) The capital stock [use ‘capital stock at current PPPs (in mil. 2017US$)’]

Let output Yt be governed by the following production function:

Yt = AtF (Kt, Lt)

where:

F (Kt, Lt) = KtαLβt

(a) Derive a Linear Regression Model

Using an appropriate transformation, write down a linear regression model in which there is a constant and two explanatory variables that will allow you to estimate the parameters α, β and the growth rate of At , i.e., gA. You should assume that gA is constant through time. Please make sure to outline the steps in your reasoning.

(Hint: See Appendix B of Lecture 16)

(b) Estimate a Linear Regression

Using the data that you have collected, estimate the model that you have defined in part (a) and provide your estimation results along with an appropriate interpretation of the estimates of gA and α. Do not worry about the statistical significance of your estimates.

(c) Evaluate the Results

Critically evaluate the model that you have just estimated. Does it produce sensible or strange estimates for gA, α and β compared to what has been discussed in the lectures? Does it make any unrealistic assumptions about the nature of production over the sample period? If so, please make sure to explain why the assumptions are unrealistic.

(Hint: Your analysis should include a calculation of the growth rate of output.)

(d) Bonus questions for good students (not for points)

Total factor productivity At is an unobserved quantity in our model as it is used to represent a wide range of disparate factors that affect the productivity of labour and capital. Using words and appropriate equations, outline a method for generating a time series estimate of At using linear regression.

Replication File.   You must be able to replicate your calculations if we ask you to. To that end, you must keep a single spreadsheet recording the Australian data you downloaded and the figures you made using this data. You should not upload this spreadsheet but, if we have questions about your assignment, we will ask you for this file.