1. A Solow Growth Model Augmented with Automation (65 points] Let us consider a Solow growth model in which the aggregate stock of physical capital at every time f denoted by A, can be either a labour-complementing machine: M, or a labour-replacing robots: &. The aggregate output at every time & Y, is produced according to the following Cobb-Douglas aggregate production functions where 1-a 6 (0.1) stands for the output elasticity with respect to the aggregate stock of machines, N, E 0 represents the human population, i> / denote the constant time allocated to work and A.a 20 denote productivity parameters. The change in the aggregate stock of physical capital from time / to time fol is described by the following law of motion: where I, denotes the aggregate investment and & e (0,1) represents the depreciation rate. In equilibrium, the aggregate investment is a constant fraction y @ (0,1) of the aggregate output: The aggregate human population grows at a constant rate a >: 0 per period: Nin = (1+ 8) N Let m, denote the machine per capita, let r, I stand for the robot per capita, let y - represent the output per capita and let it, .represent the aggregate physical capital per capita. a. Would production possible at time & (1, >: 0) without machines: (M, = 0)? Under which condition production would be possible at time & (1, >:0) without human labour (e = 0)? (5 points) b. Write down the aggregate production function in per capita units. (5 points)