The aggregate production function shown below graphs the relationship between output (Y, or real GDP) and capital inputs (K). The shape of the production function illustrates two important concepts related to economic growth. You will want to refer to the figure for the questions below.
Because the production function has a positive slope, the marginal product of capital is (positive/ negative/ increasing/ decreasing)
Because the slope of the production function becomes flatter as more capital is added, the marginal product of capital is (positive/ negative/ increasing/ decreasing)
As capital increases from one to two units, the marginal product of the second unit of capital is $_____
As capital
increases from three to four units, the marginal product of the
fourth unit of capital is $____
Homework Answers
MPK is the slope of the production function for capital and so in the first case we see that slope is positive so MPK is positive. Secondly it is decreasing as production function becomes flat
As K rises from 1 to 2 units, MP of second unit of capital is 4000 - 2500 = 1500. From 3 to 4 units, MPK is 5500 - 5000 = 500.
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The aggregate production function shown below graphs the
relationship between output (Y, or real GDP) and...
1. (The AK Model) Consider an economy with an aggregate production function given by y =...
1. (The AK Model) Consider an economy with an aggregate production function given by y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com- pute the marginal product of capital....
1. (The AK Model) Consider an economy with an aggregate production function given by Y=F(K) =...
1. (The AK Model) Consider an economy with an aggregate production function given by Y=F(K) = AK of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com pute the marginal product of capital. Does this function satisly the neoclassical assumptions?
The diagram below shows the aggregate production function for a country on the left real in...
The diagram below shows the aggregate production function for a country on the left real in t ons of 2012 dollars and tabor hours in billions, and the national labor market on the rise real wage in 2012 dollars and labor hours in billions). Use the diagram to answer the following questions ste Labor market LOP NOZ LO Q of Laber Qot Lahor a. Assume the economy is as drawn above. Suppose that as time passes, the level of technology...
1.The aggregate production function is Y = F(K, L) where Y = real GDP, K =...
1.The aggregate production function is Y = F(K, L) where Y = real GDP, K = capital and L = labor. For Y = F(K, L) = K1/3Lb where b = 0 there are A.decreasing returns to scale B.increasing returns to scale C.constant returns to scale D.none of the other answers is correct. E. we cannot determine the returns to scale 2.If y = f(x) = ln U(x) then dy/dx = f’(x) = a. none of the other answers is...
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Suppose that the aggregate production is given by , where Y is real GDP, K is...
Suppose that the aggregate production is given by
, where Y is real GDP, K is the total capital stock and L is the
(constant) labour force. Assume that aggregate investment is equal
to aggregate savings and that the depreciation rate is 0.05, hence
the total capital stock evolves according to K=sY − 0.05K, where s
is the savings rate.
1) Under the stated assumptions for this question, what is the
steady-state level of capital per worker when the saving...
For a production function with a diminishing, but positive, marginal product of labor: A. Output increases...
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Use the production function graph to answer the questions. Calculate the marginal product of the first...
Use the production function graph to answer the questions. Calculate the marginal product of the first unit of capital first unit: units Y =f(K) Calculate the marginal product of the second unit of capita o 4 second unit: units What happens to the marginal product of each additional unit of capital, all else equal? 0 1 2 3 456 7 8 9 10 Capital (K) Capital decreases output at a diminishing rate. Capital increases output at a diminishing rate. Capital...
Assume that the aggregate production is given by the following: Y stands for output, K stands...
Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between 0 and 1 a) Derive an analytical expression for the marginal product of capital (MPK), marginal product of labour (MPN), and marginal product...
2. Consider an economy which produces output with the following production function: Y = AK 1...
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1. (The AK Model) Consider an economy with an aggregate production function given by y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com- pute the marginal product of capital....
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The diagram below shows the aggregate production function for a country on the left real in t ons of 2012 dollars and tabor hours in billions, and the national labor market on the rise real wage in 2012 dollars and labor hours in billions). Use the diagram to answer the following questions ste Labor market LOP NOZ LO Q of Laber Qot Lahor a. Assume the economy is as drawn above. Suppose that as time passes, the level of technology...
Suppose that the aggregate production is given by
, where Y is real GDP, K is the total capital stock and L is the
(constant) labour force. Assume that aggregate investment is equal
to aggregate savings and that the depreciation rate is 0.05, hence
the total capital stock evolves according to K=sY − 0.05K, where s
is the savings rate.
1) Under the stated assumptions for this question, what is the
steady-state level of capital per worker when the saving...
Use the production function graph to answer the questions. Calculate the marginal product of the first unit of capital first unit: units Y =f(K) Calculate the marginal product of the second unit of capita o 4 second unit: units What happens to the marginal product of each additional unit of capital, all else equal? 0 1 2 3 456 7 8 9 10 Capital (K) Capital decreases output at a diminishing rate. Capital increases output at a diminishing rate. Capital...
Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between 0 and 1 a) Derive an analytical expression for the marginal product of capital (MPK), marginal product of labour (MPN), and marginal product...
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