I need just question number 3 done
ECON 2203 Assignment #4 Assigned: March 24, 2021 Due: April 12, 2021 1. This question allows us to look at whether there has been economic convergence in the world. To do so we will be making use of a database known as the Penn World Tables. To access this data go to https://www.rug.nl/ggdc/productivity/pwt/. Click on the blue excel button to download version 10.0 of the dataset. This dataset has infor- mation on the GDP and population for a large number of countries. a) We only need the following two variables: rgdpe (Expenditure-side real GDP at chained PPPs (in mil. 2017US$)) pop (Population (in millions)). b) We are going to look at convergence from 1990 to 2019, so you can delete every year that is not those two from your dataset. c) You can also delete any country from your dataset whose GDP or population is missing from either year. Additionally, remove the following four countries who are large outliers: United Arab Emirates, Cayman Islands, Brunei, and Venezuela. Note that in general, we must be careful when removing data points like this. We may bias our results by doing so. However, in this case, their inclusion would obscure the main results. In the end, you should have 177 countries. d) Divide the real GDP by the population in both years to determine the GDP per capita in each country. e) Calculate the average yearly growth rate of real GDP per capita for each country. To do this, you need to find the rate of growth for each country that if it grew by that percentage every year starting in 1990, it would achieve the calculated level of GDP per capita you calculated for 2019. As a hint, Canada’s GDP per capita in 1990 was $33,249.12. In 2019 it was $49,359.25. This means that over this 29 year span Canada grew on average by 1.3717% (0.013717) each year. Obviously some years were faster and some slower, but this was the average. Calculate this value for all countries. In other words, you must find the value for g that solves the following equation for each country: GDP/Capita2019 = GDP/Capita1990 × (1 + g) 29 f) (10 Marks) On a graph with GDP per capita in 1990 on the horizontal axis and the average growth rate on the vertical axis, create a scatter plot for all 177 countries in the dataset. Add a linear trendline to this graph. 1 g) (10 Marks) What does this graph tell you about whether there has been conver- gence in the world between 1990 and 2019? h) (10 Marks) There may be a reason to suspect that convergence may be region specific. Separate the countries by region using the list provided below. Recreate the same graph as in part f) for each of these five regions. Important: In order to make your analysis easier, ensure each graph has the same range for each scale. The horizontal axis should run from $0 to $50,000, while the vertical axis should run from -4% to 10%. i) (10 Marks) What do these fives graphs tell you about whether there has been convergence in different parts of the world between 1990 and 2019? 2. Suppose Canada’s aggregate production function is given by the following: Y = 200K 1 2N 1 2 Variables are defined as they were in class. Suppose the savings rate in Canada is 25% (s = 0.25) and the depreciation rate is 10% (δ = 0.10). Assume that Canada is not currently experiencing any technological change. a) (5 Marks) Calculate the steady-state level of capital per worker and output per worker in Canada’s economy. b) (5 Marks) Determine the annual growth rate of output per worker in Canada. The government wants to grow the economy by encouraging more savings. Suppose they successfully persuade Canadians to increase the savings rate to 35% (s = 0.35). c) (10 Marks) Graph the resulting annual growth rate of GDP per worker for the following 100 years. What is the new steady state level of GDP per capita? Has increased savings led to a large growth in the economy? d) (10 Marks) Calculate the golden-rule savings rate for this economy. e) (5 Marks) Explain what your result from part d) say about the desirability of Canada’s increased savings policy. 2 3. Suppose Canada’s aggregate production function is given by the following: Y = K 2 3 (AN) 1 3 Variables are defined as they were in class. Suppose the savings rate in Canada is 15% (s = 0.15), the depreciation rate is 5% (δ = 0.05), the population growth rate is 3% (gN = 0.03), and the growth rate of technology is 2% (gA = 0.02). a) (10 Marks) Solve for the equilibrium level of capital per effective worker ( K AN ) and output per effective worker ( Y AN ). Solve for the equilibrium growth rates of the following variables: A, N , K, Y , Y N , K N , Y AN , and K AN . Use a table to summarize your answers. b) (10 Marks) Suppose the population growth rate slowed to 1%. Solve for the new equilibrium level of capital per effective worker ( K AN ) and output per effective worker ( Y AN ). Solve for the new equilibrium growth rates of the following variables: A, N , K, Y , Y N , K N , Y AN , and K AN . Use a table to summarize your answers. c) (5 Marks) Discuss whether this fall in population growth rate was a positive change, negative change, or neutral change for the growth rate of the Canadian economy. 3 Table 1: Africa Europe Central and South America Asia Algeria Albania Argentina Bangladesh Angola Austria Belize Bhutan Benin Belarus Bolivia (Plurinational State of) Cambodia Botswana Belgium Brazil China Burkina Faso Bosnia and Herzegovina Chile China, Hong Kong SAR Burundi Bulgaria Colombia China, Macao SAR Cabo Verde Croatia Costa Rica India Cameroon Czech Republic Ecuador Indonesia Central African Republic Denmark El Salvador Japan Chad Estonia Guatemala Kazakhstan Comoros Finland Guyana Kyrgyzstan Congo France Honduras Lao People’s DR Côte d’Ivoire Germany Mexico Malaysia D.R. of the Congo Greece Nicaragua Maldives Djibouti Hungary Panama Mongolia Egypt Iceland Paraguay Myanmar Equatorial Guinea Ireland Peru Nepal Eswatini Italy Suriname Pakistan Ethiopia Latvia Uruguay Philippines Gabon Lithuania Republic of Korea Gambia Luxembourg Middle East Singapore Ghana Malta Armenia Sri Lanka Guinea Montenegro Azerbaijan Taiwan Guinea-Bissau Netherlands Bahrain Tajikistan Kenya North Macedonia Cyprus Thailand Lesotho Norway Georgia Turkmenistan Liberia Poland Iran (Islamic Republic of) Uzbekistan Madagascar Portugal Iraq Viet Nam Malawi Republic of Moldova Israel Mali Romania Jordan Mauritania Russian Federation Kuwait Mauritius Serbia Lebanon Morocco Slovakia Oman Mozambique Slovenia Qatar Namibia Spain Saudi Arabia Niger Sweden State of Palestine Nigeria Switzerland Syrian Arab Republic Rwanda Ukraine Turkey Sao Tome and Principe United Kingdom Yemen Senegal Seychelles Sierra Leone South Africa Sudan Togo Tunisia U.R. of Tanzania: Mainland Uganda Zambia Zimbabwe 4