II. A Quantitative Solow Growth Model Exercise (35 Points) Let us consider a Solow growth model in which the aggregate production function at time t for country / is given by: Y = A' (K! ) (e'LL) where Y is the aggregate real GDP in country i, K? is the aggregate physical capital in country i, Ly is the aggregate number of workers in country i, e' is the average working time of a worker parameter in country i, A' > 0 is the total factor productivity parameter in country / and B'e (0,1) is the labour share of output parameter in country i. The equilibrium law of motions of the physical capita per worker from time t to time t+1 in country / can be written as: (1 + n')ki+1 = pyt + (1 -8 )k; where n'e (-1, +co) represents the growth rate of the population of workers parameter in country i, y' e (0,1) denotes the investment rate parameter in country i, &' e (0,1) is the depreciation rate parameter in country / and y; denotes the output per worker in country i. a. Write-down the production function in per worker units at time t for country / and derive the steady-state physical capital per worker and the steady-state real GDP per worker formulas for country i. (15 points)