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...
Select the components or inputs associated with the production function where gross domestic product (GDP) is...
Select the components or inputs associated with the production function where gross domestic product (GDP) is the output. capital deepening aggregate supply technological knowledge human capital aggregate demandLabel the regions of capital stock, K, with their corresponding descriptions of output growth. Answer Bank terminus zero negative positive infinite
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 second question In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4)...
the second question
In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4) Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing (Round responses to two decimal places.) The MPK at 5 units of capital is 156.12 The MP at 6 units of capital is 144.02 The MP at 50 units of labor is 8.84 The MP...
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...
Select the components or inputs associated with the production function where gross domestic product (GDP) is the output
Select the components or inputs associated with the production function where gross domestic product (GDP) is the output. capital deepening aggregate demand aggregate supply physical capital technological knowledge
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...
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...
For a production function with a diminishing, but positive, marginal product of labor: A. Output increases at an increasing rate as more workers are employed B. Output increases at a decreasing rate as more workers are employed. C. Output declines as more workers are employed. D. The effects on marginal product are unknown.
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
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) = 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 second question
In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4) Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing (Round responses to two decimal places.) The MPK at 5 units of capital is 156.12 The MP at 6 units of capital is 144.02 The MP at 50 units of labor is 8.84 The MP...
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...
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