Inbox (4,796) - nicholas.volko x -o D2L Homework Assignments - EC D2L ECON3810W24HW2 - ECON courselink.uoguelph.ca/d2l/le/content/864431/fullscreen/3746564/View...

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Inbox (4,796) - nicholas.volko x -o D2L Homework Assignments - EC D2L ECON3810W24HW2 - ECON courselink.uoguelph.ca/d2l/le/content/864431/fullscreen/3746564/View M Gmail ECON3810W24HW2 + U 1 of 3 + 100% Let us consider a production economy endowed with a single perfectly competitive firm renting at every time t both labour and physical capital from the current human population at the real rental rates W, rt, respectively. In equilibrium at time t. W = MPL and r = MPK+ where MPL and MPKt denote the marginal product of labour and the marginal product of physical capital, respectively. The aggregate output/income Yt at every time tis produced according to the following Cobb-Douglas production function: Y = AK-L where A>0 stands for the total factor productivity parameter, K represents the physical capital and Lt denotes the total number of workers with =(0,1) is for the labour share of output. Let us assume that the total number of workers corresponds to the size of the aggregate human population at every time t: Lt = Nt which grows at a constant rate n=(0,+): Nt+1 = (1+n)Nt where yt = Yt/Nt denotes the output/income per capita at time tand k = K/N stands for the physical capital per capita at time t. The change in the aggregate physical capital from time to time t+1 is governed by the following equation of motion: Kt+1 = It + (1 - 8)Kt where Se(0,1) represents the physical capital depreciation rate parameter and It denotes the aggregate investment in physical capital at time t which in equilibrium is equal to the aggregate saving: It = St. a. Derive at time tan expression for the marginal product of labour schedule and an expression for the marginal product of physical capital schedule. (10 points) 1 Finish update: Print Download Inbox (4,796) - nicholas.volko x -o D2L Homework Assignments - EC D2L ECON3810W24HW2 - ECON courselink.uoguelph.ca/d2l/le/content/864431/fullscreen/3746564/View M Gmail ECON3810W24HW2 + U 1 of 3 + 100% Let us consider a production economy endowed with a single perfectly competitive firm renting at every time t both labour and physical capital from the current human population at the real rental rates W, rt, respectively. In equilibrium at time t. W = MPL and r = MPK+ where MPL and MPKt denote the marginal product of labour and the marginal product of physical capital, respectively. The aggregate output/income Yt at every time tis produced according to the following Cobb-Douglas production function: Y = AK-L where A>0 stands for the total factor productivity parameter, K represents the physical capital and Lt denotes the total number of workers with =(0,1) is for the labour share of output. Let us assume that the total number of workers corresponds to the size of the aggregate human population at every time t: Lt = Nt which grows at a constant rate n=(0,+): Nt+1 = (1+n)Nt where yt = Yt/Nt denotes the output/income per capita at time tand k = K/N stands for the physical capital per capita at time t. The change in the aggregate physical capital from time to time t+1 is governed by the following equation of motion: Kt+1 = It + (1 - 8)Kt where Se(0,1) represents the physical capital depreciation rate parameter and It denotes the aggregate investment in physical capital at time t which in equilibrium is equal to the aggregate saving: It = St. a. Derive at time tan expression for the marginal product of labour schedule and an expression for the marginal product of physical capital schedule. (10 points) 1 Finish update: Print Download