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, ifĀ = 2,Ī = 4 3. (24 pts) Solow Model: Given...
4. Given a production function Y4 = ĀK;'2/3, if Ā= 2, I = 4, 5 =...
4. Given a production function Y4 = ĀK;'2/3, if Ā= 2, I = 4, 5 = 0.2, and d = 0.05. (a) Calculate the steady-state level of capital. (b) Does the above production function exhibit constant returns to scale? Or does it exhibit diminishing marginal returns? Explain, including defining the difference between these two concepts.
Solow Growth Model: Consider an economy with the following features: • Y = K 0.25 0.75...
Solow Growth Model: Consider an economy with the following features: • Y = K 0.25 0.75 • 8 = 0.02 • n=0 . g=0 i. Does the production function exhibit decreasing, constant, or increasing returns to scale? How do you know? ii. Determine MPK. Tii. Does the production function exhibit increasing, constant, or diminishing marginal product of labour? How do you know? iv. Re-express the production function in per worker terms. v. Determine the value of k in three periods...
Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α...
Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α = 0.33; d = 0.05; A = 2; s = 0.5; n = 0.25 a) Calculate the rate of capital accumulation (law of motion) b) Calculate the steady state level of capital? c) Calculate the steady state level of real output/income? d) Calculate the steady state level of investment? e) Calculate the steady state level of consumption? f) What effect does a higher productivity...
1) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters:...
1) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α = 0.33; d = 0.05; A = 1; s = 0.5; n = 0.25 a) Calculate the rate of capital accumulation (law of motion) b) Calculate the steady state level of capital? c) Calculate the steady state level of real output/income? d) Calculate the steady state level of investment? e) Calculate the steady state level of consumption? f) What effect does a higher...
4. A country is described by the Solow Model, with production function y - Aki where y is Output ...
4. A country is described by the Solow Model, with production function y - Aki where y is Output per Worker (Y/L) and k is Capital per Worker (K/L). Suppose k- 400. The fraction of output invested is 50% (s-05) and the depreciation rate is 5% (6-0.05). A, the overall productivity parameter equals 1. Is the country at its steady state level of output per worker, above the steady state or below the steady state? Show how you reached your...
Consider a country described by the Solow model. The production function is y = 29, where...
Consider a country described by the Solow model. The production function is y = 29, where 0 <a < 1. Assume that capital depreciates at a rate 8 € (0,1). a) Write down this production function in levels instead of in per capita terms. Does it display constant returns to scale? Show it. What about if a = 1? b) Find the value of c (per capita consumption) in steady state. c) Find the level of per capita capital that...
Question 5. (4 points each) Consider the Solow model in Chapter 6. Production function is given...
Question 5. (4 points each) Consider the Solow model in Chapter 6. Production function is given by Y = A_KENZ The notations of variables are the same as the slides for Ch.6.The depreciation rate d is 0.1, the population growth rate n is 0.1, and the saving rate s is 0.2. The level of productivity is constant, so At = 2 all the time. (1) Compute the steady-state level of capital per person k*. (2) Compute the steady-state level of...
Given the Solow model, a production function y = Ak1/3; depreciation =δ , and an investment...
Given the Solow model, a production function y = Ak1/3; depreciation =δ , and an investment rate=γ. (a) Draw the basic Solow model from class, labeling all lines, axes, and the steady state. (b) Start a new diagram. Assume a country in its steady state is hit by an earthquake that destroys physical capital but does not kill anyone. Draw a Solow model that describes the transition of the country from (1) its original steady state to (2) its immediate...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function F(K, L)KoL1-a, economy 2 has a production function G(K, L)-aK(1-a)L. For both economies capital grows according to (1). a) Write output per worker as a function of capital per worker for both economies. b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show graphically that it...
1.The Golden Rule in a Solow Model without a Cobb-Douglas Production Function Suppose that the per-worker...
1.The Golden Rule in a Solow Model without a Cobb-Douglas Production Function Suppose that the per-worker production function is: 4k tk +3 where yt = Yt/L and kt = Kt/L A.Does this production function exhibit diminishing marginal product of capital? Illustrate and explain. Note that you can use calculus, but you can also create a table. Note that AKt+1- Akt+1 and: B.Suppose that the savings rate in this economy is 36 percent (s- 0.36) and the depreciation rate is 6...
4. Given a production function Y4 = ĀK;'2/3, if Ā= 2, I = 4, 5 = 0.2, and d = 0.05. (a) Calculate the steady-state level of capital. (b) Does the above production function exhibit constant returns to scale? Or does it exhibit diminishing marginal returns? Explain, including defining the difference between these two concepts.
Solow Growth Model: Consider an economy with the following features: • Y = K 0.25 0.75 • 8 = 0.02 • n=0 . g=0 i. Does the production function exhibit decreasing, constant, or increasing returns to scale? How do you know? ii. Determine MPK. Tii. Does the production function exhibit increasing, constant, or diminishing marginal product of labour? How do you know? iv. Re-express the production function in per worker terms. v. Determine the value of k in three periods...
4. A country is described by the Solow Model, with production function y - Aki where y is Output per Worker (Y/L) and k is Capital per Worker (K/L). Suppose k- 400. The fraction of output invested is 50% (s-05) and the depreciation rate is 5% (6-0.05). A, the overall productivity parameter equals 1. Is the country at its steady state level of output per worker, above the steady state or below the steady state? Show how you reached your...
Consider a country described by the Solow model. The production function is y = 29, where 0 <a < 1. Assume that capital depreciates at a rate 8 € (0,1). a) Write down this production function in levels instead of in per capita terms. Does it display constant returns to scale? Show it. What about if a = 1? b) Find the value of c (per capita consumption) in steady state. c) Find the level of per capita capital that...
Question 5. (4 points each) Consider the Solow model in Chapter 6. Production function is given by Y = A_KENZ The notations of variables are the same as the slides for Ch.6.The depreciation rate d is 0.1, the population growth rate n is 0.1, and the saving rate s is 0.2. The level of productivity is constant, so At = 2 all the time. (1) Compute the steady-state level of capital per person k*. (2) Compute the steady-state level of...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function F(K, L)KoL1-a, economy 2 has a production function G(K, L)-aK(1-a)L. For both economies capital grows according to (1). a) Write output per worker as a function of capital per worker for both economies. b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show graphically that it...
1.The Golden Rule in a Solow Model without a Cobb-Douglas Production Function Suppose that the per-worker production function is: 4k tk +3 where yt = Yt/L and kt = Kt/L A.Does this production function exhibit diminishing marginal product of capital? Illustrate and explain. Note that you can use calculus, but you can also create a table. Note that AKt+1- Akt+1 and: B.Suppose that the savings rate in this economy is 36 percent (s- 0.36) and the depreciation rate is 6...
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