ECON2040 Problem Set 1
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ECON2040 Problem Set 1
Instruction:
Type your work and submit your assignment via Turnitin submission link on Blackboard. Your submission should consist of only one file compiled in PDF format. You should also submit your Excel file that you used to generate your answers via the separate Blackboard link.
You may work in groups of up to three members. If you do so:
• Make one submission per group.
• Include the names and student numbers of each of the members of the group on the front page of your submission.
The total mark for this problem set is 100.
Question 1: Australian Business Cycle [70 marks]
Visit the Australia Bureau of Statistics websitehttps://www.abs.gov.au/statisticsand download the
following time series A2304402X: Gross domestic product; Chain volume measures, seasonally adjusted. Use data since Q1, 1980 until Q1, 2022. When you report the results, use 4 decimal places.
1. Compute the natural logarithms of GDP time series. Report the results of last 5 periods. (5 marks).
2. Construct the Hodrick- Prescott (HP) trend for the log-series. Report the results of last 5 periods. (Hint: Follow the steps outlined in Tutorial 2). (10 marks)
3. Plot the log of the series along with their corresponding HP trends. (5 marks)
4. Identify the business cycle chronology based on the cyclical component of that time series., i.e., identify the peaks and troughs. (10 marks)
5. Now download series A2304370T (Gross domestic product, percentage changes), identify the recessions (state the onset and the ending quarters of each recession, and the duration of each recession, i.e. how many quarters did the recession last). (5 marks)
6. Now download series A2304110W (Gross fixed capital formation, i.e. Investment) and A2304080V (Government consumption). Compute the cyclical component of those 2 series using HP filter. Report the results of last 5 periods. (10 marks)
7. Plot the cyclical components of all three series in the same diagram. Comment on the diagram. (10 marks)
8. Compute the following statistics:
a) Standard deviations of the cyclical components of GDP and Investment and Government expenditure (Hint: Use the formula STDEV.P in Excel). (6 marks)
b) The correlation between the cyclical components of the Investment time series and the cyclical components of GDP, the cyclical components of Government expenditure time series and the cyclical components of GDP (Hint: Use the formula CORREL in Excel). (4 marks)
9. Interpret your results and compare against the corresponding business cycle regularity discussed in class. (5 marks)
Question 2: The household problem [30 marks].
Consider the static model of the household discussed in Lecture 3. Suppose that instead of being subject to a lump-sum tax, the consumer faces a labour income tax T and a consumption tax TC . For simplicity, we normalize h (total time available) as 1 and there is no dividend income .
a) Write down the household’s budget constraint. (3 marks)
b) Draw the household’s budget constraint. What is the slope? (5 marks)
c) Find the MRSl,C (Hint: using the Lagrange method, first order condition). How do the effects of T and TC relate to each other? Explain. (8 marks)
d) If the household choose C* and l*, how much tax revenue does the government collect? (5 marks)
e) Suppose that the government had originally set TC = 0 and T > 0 and now wants to enact a tax reform that uses consumption taxes instead of income taxes. What would be the level of TC that leaves the decisions of the household unchanged? (5 marks)
f) How much the revenue does the government collect under the new system? How does it compare to the old system? Explain. (4 marks)
2022-08-24