2. Quantitative Effects of Population Aging (18 points)
a. Show that the GDP per capita at time t can be written as the product of the GDP per worker at time t , the employment rate at time t and the working age fraction of the population at time t . (4 points)
b. Show that the GDP per capita growth rate from time t to t+1 can be approximated as the sum of the GDP per worker growth rate from time t to t+1 and the growth rate of the working age fraction of the population from time t to t+1 if the employment rate remains constant. (6 points)
c. In 2021, 65% of the population in Canada was of working age. In 2034, 60% of the Canadian population is expected to be of working age. Calculate the average annual growth rate of the working age fraction of the population from time 2021 to 2034. (4 points)
d. Using you answers to b. and c. how much does the GDP per worker has to grow on average per year until 2034 to keep the GDP per capita constant? (4 points)
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