2. A Sulow Growth Model Augmented with Two Types of Physical Capital {so points} Let us consider a Solow growth model augmented every time t with two types of physical capital namely machines: Ht 2 and robots: it; 2 b. The aggregate output at every time t: 1": is produced according to the following Cobb-Douglas aggregate production function: 1": = AMER-r + 33:11"? wl'tere s E [0,1] stands for the output elasticity with respect to the aggregate stud: of machines where I.: r.- i] represents the human population and its >0 denote productivity parameters. Let w, denote the real wage rate, let pt stand for the real rental rate of machines and let p, represent the real rental rate of robots. In equilibrium, w, = HPLE, p1- = MFA-it, pt: = MFR, where erect, MPH, and MFR: denote the marginal product of human labour, the marginal product of machines and the marginal product of robotsIr respectively. At every time t; the aggregate human population grows at a constant geometric rate: L144 = {1 + "JLE where n a l]. The aggregate sled: of physical capital at every time tis: Kt: Mt+t In equilibrium, the change in the aggregate stock of physical capital from time tbs: time t-r-I is described by the following law of motion: Kt+1 K! = 1't 5K: where i, denotes the aggregate investment and d 5 (13,1) represents the depreciation rate. In equilibrium, the aggregate investment is a constant fraction y s [[1,1] of the aggregate output: It = 1"?! Let m! E ii: denote the machine per capita, let r, a E stand for the robot per capita, let 3: 51;: represent the output per capita and let it: E f: represent the aggregate physical capital per capita