Let us consider a Solow growth model in which the aggregate production function at time t for country i E {CAN, USA} is given by: Y = A' (K) (e L) where Y+ is the aggregate real GDP in country i, K is the aggregate physical capital in country i, L 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 i and = (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 to time t+1 in country i can be written as: (1+n) k +1 = vy + (1 8)k where n (-1, +) represents the growth rate of the population of workers parameter in country i, y = (0,1) denotes the investment rate parameter in country i, si = (0,1) is the depreciation rate parameter in country i, y = Y denotes the output per worker in country i and k = K/L stands for the physical capital per capita in country i. a. Write-down the production function in per worker units at time for country i and derive the steady-state physical capital per worker and the steady-state real GDP per worker formulas for country i. (15 points)