1. JapanversusSouthKorea(35Points)

LetusconsideraSolowgrowthmodelinwhichtheaggregateproductionfunctiontimetforcountryisgivenby:

\fs'yl + (1 - 81)k; k t+1 1+ nLet us consider a Solow growth model in which the aggregate production function time ffor counby i is given by: i 1' 1/3 1' E 2/3 Yr = (K5) (6 LE) where Y; is the aggregate real GDP in country 1', K5 is the aggregate physical capital in county 1', Li is the aggregate number of workers in country i, at is the average working time of a worker in country i, and 1/3 is the physical capital's share of output. The equilibrium law of motions of the physical capita per worker from time t to time t+1 in country i can be written as: ki+1 = s'yl + (1 - 81 ) k ; 1 + ni where n' E (-1, too) represents the average growth rate of the population of workers in country i, s' E (0,1) is the average investment rate in country i, S' E (0,1) is the average rate of depreciation in country i, k; = # denotes the aggregate stock of physical capital per worker in country i and y! = represents the aggregate output per worker in country i. Using the Penn World table 10.0: https://www.rug.nl/ggdc/productivity/pwt/ get the following data for both Japan and South Korea: "Expenditure-side real GDP at chained PPPs (in mil. 2017US$)" representing the aggregate real GDP. "Number of persons engaged (in millions)" representing the aggregate number of workers. "Average annual hours worked by persons engaged" representing the average working time of a worker in country i "Share of gross capital formation at current PPPs" representing the average investment rate in country i "Average depreciation rate of the capital stock" representing the average rate of depreciation. a. Derive the real GDP per worker in Japan and in South Korea in 2019 and the real GDP per worker real gap between these two counties in year 2019: y2019/12019. (6 points) b. Write-down the production function in per worker units and derive the steady-state real GDP per worker formula for country i: yes. (7 points) C. Calculate the average annual growth rate of employment in Japan and South Korea from 2009 to 2019, the average depreciation rate in Japan and South Korea from 2009 to 2019, the average investment rate in Japan and South Korea from 2009 to 2019 and the average hours worked in Japan and South Korea from 2009 to 2019. (16 points) d. Using your solutions to question c and the steady-state formula found in question b, compute the real GDP per worker real gap between Japan and South Korea predicted by the Solow growth model: yss / VIPN /yBOR. (6 points)