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 am struggling with these questions. Could someone please help me with these questions thanks ahead
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1) An economy has the following aggregate production function:
Y= Ak^1/3L^2/3 and capital stock, labour supply...
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....
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,...
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?
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...
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...
Consider the following production function for an economy: 1. Y=2K1/4L3/4 (a) Suppose the capital stock is...
Consider the following production function for an economy: 1. Y=2K1/4L3/4 (a) Suppose the capital stock is K = 16 and its labour force is L = 1. Find: (i) GDP; (ii) the marginal product of capital; (iii) the real rental price of capital; (iv) labour's share of income. (b) Suppose further that aggregate consumption (C) is 80 per cent of disposable income, government spending is G = 1, the budget is balanced, and private sector investment is I = 6...
ASSIGNMENT # 3 Actual aggregate expenditure or output (Y) (billions of $) Consumption (C) (billions of...
ASSIGNMENT # 3 Actual aggregate expenditure or output (Y) (billions of $) Consumption (C) (billions of $) Planned investment (billions of $) Government spending (G) (billions of $) Net exports (NX) (billions of $) Unplanned investment (inventory change) (billions of $) 500 300 150 100 50 600 350 700 400 800 450 900 500 For the table shown, answer the following questions: For each level of actual aggregate expenditure, calculate unplanned inventory investment. What is the equilibrium level of aggregate...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by: Y = 6K1/3L2/3 In this economy, workers consume 80% of income and save the rest. The labour force is growing at 2% per year while the annual rate of capital depreciation is 5.5%. a) Solve for the steady state capital-labour ratio and consumption per worker. The economy is in its steady state as described in part (a). Suppose both the stock 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...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of δ, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s. I5 marks] i. Determine the scale of production? Suppose capital is increased by a...
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?
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...
Consider the following production function for an economy: 1. Y=2K1/4L3/4 (a) Suppose the capital stock is K = 16 and its labour force is L = 1. Find: (i) GDP; (ii) the marginal product of capital; (iii) the real rental price of capital; (iv) labour's share of income. (b) Suppose further that aggregate consumption (C) is 80 per cent of disposable income, government spending is G = 1, the budget is balanced, and private sector investment is I = 6...
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...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of δ, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s. I5 marks] i. Determine the scale of production? Suppose capital is increased by a...
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