"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 t. It = At ( k , ) 3 ( he )3 where y, is the real GDP per capita, k is the real physical capital per capita, h, 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: rgdpa/pop, the average annual growth rate in percent of the real physical capital per capita: mna/pop and the average annual growth rate in percent of 2 the human capital per capita: he (already in per capita units) from 1960 to 1979, from 1980 to 1999 and from 2000 to 2019 in Canada. (18 points) b. 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) C. 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) d. 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) e. 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)Capital stock at constant 2017 national prices (in mil. Population (in Real GDP at constant national prices (in mil. Toggle display / Index of human capital per person, based on years of schooling and returns to 2017US$) education millions 2017US$ Canada 1960 994219.6250 2.6296 17.9513 310435.4375 Canada 1961 1035527.4375 2.6493 18.3131 19221.343 Canada 1962 1083196.2500 2.6691 18.6579 341186.0938 Canada 1963 132801.7500 2.6891 19.0088 358757.9063 Canada 1964 1189864.3750 2.7093 19.370 382187.0000 Canada 1965 261966.2500 2.7296 9.7244 407080.4063 Canada 1966 342327.3750 2.7500 20.0953 434902.4375 Canada 1967 1407980.500 2.7706 20.4602 446616.9688 Canada 1968 1476176.6250 2.7914 20.7779 470046.0625 Canada 1969 1554442.0000 2.8123 21.0776 494939.4688 Canada 1970 1620297.5000 2.8333 21.3743 508118.3438 Canada 1971 1694191.7500 2.8576 21.7235 528291.9375 Canada 1972 1770844.0000 2.8821 22.0722 557399.1250 Canada 1973 1856335.7500 2.9068 22.4153 595501.5000 Canada 1974 1946317.7500 2.9317 22.7459 615035.8750 Canada 1975 2039123.7500 2.9568 23.059 624023.0000 Canada 1976 2135959.7500 2.9821 23.3546 660707.000 Canada 1977 2234432.5000 3.0076 3.634 83423.1250 Canada 1978 333883.5000 3.0334 23.9017 708597.125 Canada 1979 2440192.0000 3.0594 24.1611 734894.3125 Canada 1980 2552616.2500 3.0856 24.4169 750735.250 Canada 1981 2682009.0000 3.1055 24.6682 776816.750 Canada 1982 2778083.5000 3.1255 24.9165 752057.5625 Canada 1983 2867198.7500 3.1457 25.1714 771621.1250 Canada 1984 2957151.0000 3.1660 25.4449 817212.0000 Canada 1985 3060911.0000 3.1864 25.7448 855926.5625 Canada 1986 3168508.2500 3.2070 26.0755 874286.0000 Canada 1987 3292934.5000 3.2277 26.4329 909895.3125 Canada 1988 3434797.7500 3.2485 26.806 950022.6875 Canada 1989 3582253.5000 3.2695 27.1795 972034.5000 Canada 990 712088.7500 3.2906 27.5413 973635.2500