2. Consider an economy which produces output with the following production function: Y = AK 1...
2.
Consider an economy which produces output with the following production function: Y = AK 1 3L 2 3 , where K is the level of capital and L is the level of labor. Please answer the following questions, assuming this production function:
(a) Please express the marginal product of capital and the marginal product of labor as functions of A, K, L:
(b) What fraction of income is rental income from capital? If the level of labor, L, increases, does the fraction of rental income change (and if so, in what direction)?
(c) Compute the demand for labor and demand for capital as a function of W P (real wages), K, & A in case of labor, and R P (real rental rate), L & A in case of capital.
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2.
Consider an economy which produces output with the following
production function: Y = AK 1...
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...
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...
1) An economy has the following aggregate production function: Y= Ak^1/3L^2/3 and capital stock, labour supply...
1) An economy has the following aggregate production function: Y= Ak^1/3L^2/3 and capital stock, labour supply and total factor productivity of 512, 1000, and 5 respectively. a) What is the effect of a 50% change in the capital stock on the marginal product of labour and the marginal product of capital? b) What is the effect of this change in the capital stock on Output and Consumption, if taxes are 800 and the Marginal Propensity to Consume is 2/3? I...
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....
Assume the following Cobb-Douglas production function: Assume the following Cobb-Douglas production function: Y = AK 0.4...
Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4 20.6 If Y=12; K=8; and L=95, answer the following questions (SHOW ALL YOUR WORK): - 1. What is total factor productivity? 2. With your answer in (1), assume L=95 and estimate the production function with respect to K 3. Estimate the marginal product of capital and demonstrate diminishing marginal product of capital 4. Estimate real capital income 5. Estimate the share of capital income...
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?
-e Consider an economy with the production function Y= AK° N In a year in which...
-e Consider an economy with the production function Y= AK° N In a year in which the capital stock grew at rate 4.16, the populati grew at 8.3%, what is the growth rate of k = K/N. (Note: provide answer as a percent growth rate)
2 Endogenous Growth Theory (5 marks) In the AK model with production function Y = AK....
2 Endogenous Growth Theory (5 marks) In the AK model with production function Y = AK. Assume g- is fixed. The saving rate is s and the depreciate rate of capital of. = 0 and p a. What is the growth rate of capital (K) and output (Y)? b. Under what conditions can the economy experience perpetual (positive) growth? c. What is the key factor that drives the perpetual growth? Explain the intuition. (hint: compare the AK model with the...
1. Suppose an economy's production is defined by the following neoclassical production function: Y=50K 1/3L 2/3....
1. Suppose an economy's production is defined by the following neoclassical production function: Y=50K 1/3L 2/3. Suppose further that the economy wide supply of capital and labor are given as 125 and 64. What will be the equilibrium rental rate of capital in this economy? a. 10.67 b. 62.5 c. 1,333 2. Suppose an economy's production is defined by the following neoclassical production function: Y=50K 1/3L 2/3. Suppose further that the economy wide supply of capital and labor are given...
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...
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...
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....
Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4 20.6 If Y=12; K=8; and L=95, answer the following questions (SHOW ALL YOUR WORK): - 1. What is total factor productivity? 2. With your answer in (1), assume L=95 and estimate the production function with respect to K 3. Estimate the marginal product of capital and demonstrate diminishing marginal product of capital 4. Estimate real capital income 5. Estimate the share of capital income...
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?
-e Consider an economy with the production function Y= AK° N In a year in which the capital stock grew at rate 4.16, the populati grew at 8.3%, what is the growth rate of k = K/N. (Note: provide answer as a percent growth rate)
2 Endogenous Growth Theory (5 marks) In the AK model with production function Y = AK. Assume g- is fixed. The saving rate is s and the depreciate rate of capital of. = 0 and p a. What is the growth rate of capital (K) and output (Y)? b. Under what conditions can the economy experience perpetual (positive) growth? c. What is the key factor that drives the perpetual growth? Explain the intuition. (hint: compare the AK model with the...
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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