constant return to scale and Solow model
Prove through the production function that the shortened function of the Solo model cannot be reached unless the production function has a constant return of volume.
Y = KαLβ
Homework Answers
The marginal product of capital is the output resulting from the use of an additional unit of a capital, keeping all other things constant (ceteris peribus). Mathematically, it is defined as the partial derivative of the production function w.r.t. capital.
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale...
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale and it is explicitly given by: Y = K L l-a a. What is the level of output per capita, y, where y = Y/L? b. Individuals in this economy save s fraction of their income. If there is population growth, denoted by n, and capital depreciates at the rate of d over time, write down an equation for the evolution of capital per...
2. Consider a Solow growth model with Cobb-Douglas production function Y Ko (AN)-a with constant savings...
2. Consider a Solow growth model with Cobb-Douglas production function Y Ko (AN)-a with constant savings rate s, depreciation rate d and no growth in productivity or labor (gA = gN = 0) (a) Suppose A = 1, a = 1/3, s = 0.2 and 5 = 0.1 (annual). Calculate the steady state capital per worker and steady state output per worker (b) Suppose that the real wage w and real return to capital r are equal to the marginal...
returns to scale and The aggregate production function for the Solow growth model assumes returns to either labor or c...
returns to scale and The aggregate production function for the Solow growth model assumes returns to either labor or capital. _marginal increasing; diminishing. constant; diminishing. O decreasing; constant O constant; constant
Prove that in the generalized model of Solow, the ratio of total capital to production is...
Prove that in the generalized model of Solow, the ratio of total capital to production is constant.
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...
Growth rates in the Solow model (I):
(a) Use the production function in equation (5.6) (Y=AK^1/3L^2/3)and the rules for computing growth rates from page 53 of Chapter 3 to write the growth rate of per capita GDP as a function of the growth rate of the capital stock. (Hint:Because the labor force is constant, the growth rates of GDP and per capita GDP are the same.) (b) Combine this result with the last equation in footnote 7 (Section 5.9) to get a solution for the growth rate of per...
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...
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...
Distinguish between the external return to scale and internal return to scale. How does the new...
Distinguish between the external return to scale and internal return to scale. How does the new trade theory of economic returns to scale differ from the traditional trade theories like Ricardian model, and Heckscher - Ohlin model? 3. 4. What is the Rybczynski theorem? How does theorem predict changes in factors usage in production and change in trading volume if there is an influx of immigrant?
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...
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale and it is explicitly given by: Y = K L l-a a. What is the level of output per capita, y, where y = Y/L? b. Individuals in this economy save s fraction of their income. If there is population growth, denoted by n, and capital depreciates at the rate of d over time, write down an equation for the evolution of capital per...
2. Consider a Solow growth model with Cobb-Douglas production function Y Ko (AN)-a with constant savings rate s, depreciation rate d and no growth in productivity or labor (gA = gN = 0) (a) Suppose A = 1, a = 1/3, s = 0.2 and 5 = 0.1 (annual). Calculate the steady state capital per worker and steady state output per worker (b) Suppose that the real wage w and real return to capital r are equal to the marginal...
returns to scale and The aggregate production function for the Solow growth model assumes returns to either labor or capital. _marginal increasing; diminishing. constant; diminishing. O decreasing; constant O constant; constant
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...
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...
Distinguish between the external return to scale and internal return to scale. How does the new trade theory of economic returns to scale differ from the traditional trade theories like Ricardian model, and Heckscher - Ohlin model? 3. 4. What is the Rybczynski theorem? How does theorem predict changes in factors usage in production and change in trading volume if there is an influx of immigrant?
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...
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