3. Consider the balanced-growth path (BGP) of the Solow growth model, with production function Y = K°(L/E)lª . Suppose that E is growing at rate g=.01. and L at rate n=.02. The growth rate of output per effective worker equals.
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![3. Consider the balanced-growth path (BGP) of the Solow growth model, with production
function Y = K°(L/E)lª . Suppose that E is growing at rate g=.01. and L at rate n=.02. The
growth rate of output per effective worker equals](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1cc2e7b-9d6a-424c-9b4f-581c61bca63d%2F99450c11-2ed0-4f81-82e7-fd81f29aefda%2Febbcpid_processed.png&w=3840&q=75)
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- Assume that the production function for output is given by Y = BK&TBEYL¹-a-B-y. Where T is a fixed amount of land, and E represents the energy input into production. ● Derive the steady-state growth rate of output per worker. Analyze the balanced growth path of this model. Explain "growth drag" resulting from the presence of natural resources.9. Consider our graph of the basic Solow growth model. steady state dk y=F(() F() (-7' in LF equilibrium) On the graph above: y represents real output (or income) per worker; y-F(k) is the production function; is the capital stock per worker; s is the savings rate; 8 is the rate of depreciation of capital; 'i' represents business investment (purchases of capital) per worker); 'LF' stands for Loanable Funds. (For purposed of intuition, think of capital as 'machines.) If we started out with a capital (per worker) stock higher than the steady-state stock (above), we would expect to see which of the following happen over time? Positive growth rates while the capital stock increases. Positive growth rates while the capital stock stays less than the steady-state level. Negative growth rates while the capital stock increases. Positive growth rates while the capital stock decreases. Negative growth rates while the capital stock decreases.Consider a standard Solow growth model. Denote capital stock as K, population as N, capital depreciation rate as d, saving rate as s, output as Y. Output is produced by a representative firm according to the production function Y=zF(K, N), where z is current total factor productivity. The law motion for capital is K' = (1 - d)K + I, where K' is the future capital stock. Population grows at a constant rate n, that is N' = (1 + n)N, and household supply labor inelastically, so population equals labor force. (a) In a graph, show the steady state level of capital per worker. Use lower case letters to denote per-capita terms and use * to denote steady state.(b) Suppose a country is initially at a steady state, then a war destroyed some of its capital stock. Determine the long run effects on the quantity of capital per worker and on output per worker in the steady state. Show by a graph. (C)Define golden rule saving rate. What does it maximize? Determine the effects of a decrease in the…
- Consider an economy described by the Solow model with the following production function: Y = F(K, L) = K“ (L)'-« L grows at the rate n, the depreciation rate is 8, and the country saves a constant fraction s of its income. The change in capital per-worker is given by Ak = sy – (n+ 8)k. (a) Derive the per-worker production function. (b) Assuming population growth equals n and the depreciation rate equals 8, find the steady state level of capital per worker. It will depend on a, s, n and 8. Imagine the economy begins at the steady state you found in part b. Then there is a war that destroys a substantial amount of the economy's capital. The war does not affect the size of the labor force, population growth, the depreciation rate, or the saving rate. c) What is the immediate effect of the war on output per worker? Explain. d) After the war, is the growth rate of output per worker higher or lower than it was in steady state? Explain. e) How does the war affect steady state output per…In the Solow growth model with no population growth and no technological change, the output per worker increases when investment per worker is greater than depreciation of capital per worker. Select one: True FalseIn the Solow growth model, suppose that the per-worker production function is given by y = zk 0.4 with s = 0.15, d = 0.1, and n = 0.02. a. Suppose in country A that z= 1. Calculate the steady-state capital per worker and income per capita in country A. The steady-state capital per worker is (Round to two decimal places as needed.) The steady-state income per capita is. (Round to two decimal places as needed.) b. Suppose in country B that z = 2. Calculate the steady-state capital per worker and income per capita in country B. The steady-state capital per worker is|. (Round to two decimal places as needed.) The steady-state income per capita is (Round to two decimal places as needed.) c. As measured by GDP per capita, how much richer is country B than country A? What does this tell us about the potential differences in total factor productivity to explain differences in standards of living across countries? Country B is times richer than country A, as measured by GDP per capita. This…
- = 2. Consider a Solow growth model in which the production function is Yt AK²N₁¹/2, where A = 1. Moreover, assume that the depreciation rate is d = 0.02, the rate of population growth is n = 0.02, and the saving rate is s = = 0.2. a. Compute the value of the capital stock per worker in steady state. b. Draw a graph that represents the steady-state equilibrium of the model. c. Suppose that the capital-labor ration in year t is 90. What will the level of the capital- labor ratio be in year t+1? Will it increase or decrease in future periods? Explain. d. Compute the rate of change of the capital labor ratio between time t and t + 1. How does it compare to the rate of growth of the capital-labor ratio in steady state?Consider the following Solow diagram, indicating two sep-arate savings rates, 0.2 and 0.4: Suppose the savings rate is 0.2. At the steady state, what is capital per worker? What is output per worker? How much is saved per worker? Suppose the population growth rate is equal to the depreciationrate. Solve for n and d.Explain the basic theory of Solow Growth model, highlight the production function and basic assumptions of Solow Growth model. Show the steady-state condition. [Use the production function: = ?? 1/3? 2/3 ]
- In the Solow model with population growth and technological progress, the steady- state growth rate of total output is: On. 0. On+g. 0 g.Consider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.A key assumption of the Solow Growth Model is that: (a) the marginal product of capital diminishes as additional units of capital are added; (b) output per capita declines as a nation’s capital to labor ratio increases; (c) the marginal product of labor tends to rise as additional units of labor are added; (d) capital tends to depreciate at an increasing rate as a nation’s output increases.
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