II. Growth Accounting Exercise for Canada (50 points) Using the Penn World table version 10.1: (https://www.rug.nl/ggdc/productivity/pwt/), download from 1960 to 2019 the following data for Canada: "Real GDP at constant 2017 national prices (in mil. 2017US$)" denoted by rgdpna. "Capital stock at constant 2017 national prices (in mil. 2017US$)" denoted by rnna. "Population (in millions)" denoted by pop. "Human capital index, based on years of schooling and returns to education" denoted by hc. Let us consider the following per capita production function at time to yt = At ( k t ) 3 (ht ) 3 where yt is the real GDP per capita, kt is the real physical capital per capita, ht is the human capital per capita and A, is the aggregate productivity level. a. Using the above data, calculate the average annual growth rate in percent of the real GDP per capita: rgdpna/pop, the average annual growth rate in percent of the real physical capital per capita: rnna/pop and the average annual growth rate in percent ofthe human capital per capita: hc (already in per capita units) from 1960 to 1979, from 1980 to 1999 and from 2000 to 2019 in Canada. (18 points) Using the per capita production function, show that the growth rate of the output per capita can be approximated as a weighted sum of various other growth rates. (8 points) Using the average growth rates obtained in question a, compute the relative contributions in percent of physical capital per capita growth and human capital per capita growth to output per capita growth from 1960 to 1979, from 1980 to 1999 and from 2000 to 2019 in Canada. (12 points) From the growth decomposition equation found in b. and your answers to c., derive the relative contributions in percent of productivity growth to output per capita growth from 1960 to 1979, from 1980 to 1999 and from 2000 to 2019 in Canada. (6 points) Among the following three factors: productivity, physical capital per capita, and human capital per capita, which one contributed the most and which one contributed the least to output per capita growth from 1960 to 1979, from 1980 to 1999 and from 2000 to 2019 in Canada? (6 points)