data for questions :

U.K. (Population = 67.5m) (data) GDP Per Capita ( 70.7) and Per Worker ( 69.7) 0.2 Growth Rate (Average is 2.09) 80 0.15 0.1 70 0.05 60 -0.05 50 0.1 1950 1960 1970 1980 1990 2000 2010 2020 1950 1960 1970 1980 1990 2000 2010 2020 30 Investment/GDP (24.7) and GovtConsump/GDP (19.8) 100 Human Capital Index (100.6) 25 90 80 20 70 15 1950 1960 1970 1980 1990 2000 2010 2020 60 1950 1960 1970 1980 1990 2000 2010 2020 NetExports/GDP (-5.4) and X+M/GDP ( 57.6) 180 0.8 Exchange Rate per Dollar ( 0.78) 0.7 -5 0.6 -10 140 0.5 0.4 -15 20 1950 1960 1970 1980 1990 2000 2010 2020 1950 1960 1970 1980 1990 2000 2010 2020Question 1 In this exercise we will try to make sense of why economic growth is so important. We will do a counterfactual analysis of economic growth in the UK, to try and understand the implications of different growth rates for living standards in the long run. You can use Excel or another tool for your calculations. 1. Download the data for the UK from the webpage used last week. a. Calculate the average annual growth rate of GDP per capita in UK over the period spanned by the data (1950-2019). b. At this rate, how long does it take to the GDP per capita to double? (Hint: you can use the rule of 70) 2. We will now think about what could have happened if the average annual growth rate would have been different. Starting from the GDP per capita in 1950, calculate what the GDP per capita in 2019 would have been for the UK if the average annual growth rate was: a. 1% b. 3% o. 5% d. 415% {negative growth rate!) 3. Plot the GDP per capita from I950 to 2019 as it happened, in the same graph add the 4 scenarios in question 2, Comment on the differences with respect to the actual 20| 9 GDP per capita in the different scenarios. Question 2 Let's think oftwo countries, Richdonia (indicated with subscript or superscript R) and Poorland {indicated with subscript or superscript P). These countries do not trade with each other, therefore neither output nor capital can cross the borders, but there is freedom of movement. Le. workers of each of these countries can freely move to the other country and work there. Output is produced in both countries with the following aggregate production function: YI- = AjKiaLi'\Question 3 For each of these production functions, establish if they have constant, increasing or decreasing returns to scale. (assume that B is a positive constant). (Hint: notice that part of this exercise is solved on the textbook by Chad Jones, have a look!) a. Y = KI/21 1/2 b. Y = K2/3[2/3 c. Y = KI/3/1/2 d. Y =K+L Y =K+ K1/3[1/3 f. Y = KV/312/3 + B g. Y = K1/312/3 - B