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Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4...
Consider the following production functions Y = AK1/2L1/2 Y=AK+3L a. Fixing total factor productivity (A) at...
Consider the following production functions Y = AK1/2L1/2 Y=AK+3L a. Fixing total factor productivity (A) at 2 and labor employment (L) at 16 units, what is the marginal product of capital when capital employment (K) is 25, 35, and 45 for each production function? Do these production functions exhibit diminishing returns to capital employment? Explain. b. Are labor and capital complements under these production functions? Explain. c. Is either production function a “Cobb-Douglas” function? Explain. 3. Describe the difference between...
6. a) Consider the following Cobb-Douglas production function: Q AK°L where Q output, K labour, L...
6. a) Consider the following Cobb-Douglas production function: Q AK°L where Q output, K labour, L labour Express the above function in a logarithmic form
In a Cobb Douglas production function the marginal product of labor will increase if: a. the...
In a Cobb Douglas production function the marginal product of labor will increase if: a. the quantity of labor increases. b. the quantity of capital increases. c. capital's share of output increases. d. average labor productivity decreases.
1. Consider the following production functions. In each case determine if: • the function is Cobb...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
9. (chapter 6) If the Cobb-Douglas production function is 92- , what is the average product...
9. (chapter 6) If the Cobb-Douglas production function is 92- , what is the average product of labor ( 447 ), holding capital fixed (that is, just leaving K alone in the equation)? , what is the marginal |10. (chapter 6) If the Cobb-Douglas production function is 9=- product of labor ( MP4 )?
1. For the Cobb-Douglas production function Y=AKaL1-a, the marginal product of capital is: a. (1-a)(Y/L) b....
1. For the Cobb-Douglas production function Y=AKaL1-a, the marginal product of capital is: a. (1-a)(Y/L) b. a(Y/K) c. a d. aY 2. The principal economic cost of growth is: a. higher interest rates b. consumption sacrificed for capital formation c. higher unemployment rates d. higher inflation rates Countries with a high level of real GDP per person are likely to have: a. low levels of commercial energy use b. superior literacy levels for females compared to males c. females with...
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, ...
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $300 and each unit of capital costs $1,200. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject...
Sheet1 The Cobb-Douglas production function for a product is NIX.Y) - 10(x*O.B)(y^0.2) where is the number...
Sheet1 The Cobb-Douglas production function for a product is NIX.Y) - 10(x*O.B)(y^0.2) where is the number of units of labor and is the number of units of capital required to produce units of the product. What is the marginal productivity of labor and the marginal productivity of capital? What are they when there are 40 units of labor and 50 units of capital? NxIx.) Nx (40, 50) = Nyix,y) Ny 40, 50) If each unit of labor costs $100, each...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
15. Consider an economy, with a production function given by Y-AK03L07. This economy's annual GDP growth...
15. Consider an economy, with a production function given by Y-AK03L07. This economy's annual GDP growth rate is 5%. Also assume that L and Kare both growing at annual rates of 2%. Calculate the growth rate of total factor productivity for this economy. a. 2.0% b. 3.0% 4.0% c. d. 5.0% 16. Suppose output is determined by a Cobb-Douglas production function Y=AK L1 Where 0ca<1. If total factor productivity (A) remains constant, but labour (L) and capital (K) inputs both...
6. a) Consider the following Cobb-Douglas production function: Q AK°L where Q output, K labour, L labour Express the above function in a logarithmic form
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
9. (chapter 6) If the Cobb-Douglas production function is 92- , what is the average product of labor ( 447 ), holding capital fixed (that is, just leaving K alone in the equation)? , what is the marginal |10. (chapter 6) If the Cobb-Douglas production function is 9=- product of labor ( MP4 )?
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $300 and each unit of capital costs $1,200. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject...
Sheet1 The Cobb-Douglas production function for a product is NIX.Y) - 10(x*O.B)(y^0.2) where is the number of units of labor and is the number of units of capital required to produce units of the product. What is the marginal productivity of labor and the marginal productivity of capital? What are they when there are 40 units of labor and 50 units of capital? NxIx.) Nx (40, 50) = Nyix,y) Ny 40, 50) If each unit of labor costs $100, each...
15. Consider an economy, with a production function given by Y-AK03L07. This economy's annual GDP growth rate is 5%. Also assume that L and Kare both growing at annual rates of 2%. Calculate the growth rate of total factor productivity for this economy. a. 2.0% b. 3.0% 4.0% c. d. 5.0% 16. Suppose output is determined by a Cobb-Douglas production function Y=AK L1 Where 0ca<1. If total factor productivity (A) remains constant, but labour (L) and capital (K) inputs both...
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