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Exercises for ECON 2: Macroeconomics Exercise Sheet-3

(3.1) In this first question we would like you to assess – with a brief explanation – whether the following four statements are correct or false:
(a) The growth rate of nominal GDP always exceeds the real GDP growth rate.
(b) Consider an economy with a population of 1,000,000 and a working-age population of 700,000, 550,000 employed and 40,000 unemployed. The unemployment rate is approximately 5.7%.
(c) If the unemployment rate is high, the participation rate is likely to be high as well.
(d) For consumers, the inflation rate computed from the CPI (HICP) is a more relevant measure of inflation than the inflation rate computed from the GDP deflator.
(3.2) This exercise deals with national income accounts, in particular with calculating GDP from the income rather than the production side. Consider all quantities in nominal terms throughout the exercise.
(a) Explain the following quantities and their differences: GDP, gross national product (GNP), net national product (NNP), national income and disposable personal income (DPI).
(b) Download the data in the table “Income approach of gross domestic product, current prices” from Statistics Austria. Calculate Austria’s GDP, GNP, NNP and DPI for 2020.3
(c) Compute the average annual growth rates of nominal GDP and disposable personal income for 1996–2020.
(3.3) Norway is one of the most important European producers of crude oil and gas. The available overall resource stock in the Norwegian continental shelf is estimated at around 15,864 million standard cubic meters of oil equivalents (scm oe, as of December 2021). A total of 232.79 million scm oe has been extracted from Norwegian oil fields in 2021.
(a) In how many years will the oil and gas resources contained in the Norwegian fields be exhausted under the assumption of a constant production at the level of 2021?
(b) Show that for a real number c 6= 1 the geometric sum is calculated by:
n - cn+1
1 X j c =
1 - c
j=0
Hint: Take the above equality as a starting point, multiply both sides by (1-c) and “see what happens” on the left hand side, i.e., in Pnj=0cj(1 - c).
(c) Discuss why for |c| 1, as n tends to infinity, the geometric sum leads to a convergent geometric series, with:
n 8
lim Xcj = Xcj
n?8j=0 j=0 1 - c
(d) Assume that Norwegian oil and gas production is reduced by 2% every year starting in 2022, compared to the 2021 level. After how many years will the resources be exhausted?
(e) Assume now that Norwegian oil and gas production is reduced by 5% rather than 2% every year starting in 2022, and that the Norwegian parliament has decided to stop the oil and gas production after 30 years. How many standard cubic meters of oil equivalents would be extracted in total?
(3.4) Consider the file Macro Data Ex03.xlsx provided in Moodle that contains annual data on real GDP Y , the unemployment rate u, and the inflation rate p for both the euro area and Austria over the period 1997–2020.
(a) Create two scatterplots, one for the euro area and one for Austria, that illustrate Okun’s law—a relation between the growth rate of real GDP (output growth) gY (on the x-axis) and the change in the unemployment rate ut - ut-1 (on the y-axis). Use the same axis ranges for both the euro area and Austria to facilitate visual comparison. Also include a linear trend line. What do you observe?
Hint: Interpret the slope of the linear trend line individually for the euro area and Austria, and compare them with each other. Also, calculate at which value of output growth the linear trend line crosses the horizontal axis. Interpret this value.
(b) Create two more scatterplots, one for the euro area and one for Austria, that illustrate the (modified) Phillips curve—a relation between the unemployment rate ut (on the x-axis) and the change in the inflation rate pt - pt-1 (on the y-axis). Use the same axis ranges for both the euro area and Austria to facilitate visual comparison. Also include a linear trend line. What do you observe?
Hint: Compare the slope of the linear trend line for the euro area with that for Austria. Also, calculate at which value of unemployment the linear trend line crosses the horizontal axis. Interpret this value.