er production function is given by y = as = 0.25, d= 0.1, and n = 0.02. ose that in country A, z = 1. Calculate apita income and capital per worker. -ose that in country B, z = 2. Calculate apita income and capital per worker. easured by GDP per capita, how much r is country B than country A? What this tell us about the potential for rences in total factor productivity to %3D %3D
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- In this problem, we distinguish between labor and population in the Solow growth model. A proportion of the population, a, between zero and one, works. The production function is now written as Y = A(K^1/3)[(aL)^2/3] (a) How does an increase in a from 0.3 to 0.6 change steady state GDP? (b) Does it change the steady-state capital? Explain. (c) Suppose a rises steadily over time. How do you think would affect the growth rate of GDP?In 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…3. An economy described by the Augmented Solow growth model has the following production function with populationgrowth (1+n) and technological growth (1+z):y =p(k)(a) Solve for the steady-state values of capital per capita and output as a function of s, n, z, and δ.(b) A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A lessdeveloped country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In bothcountries, g = 0.02 and d = 0.04. Find the steady-state value of y for each country.(c) What policies might the less developed country pursue to raise its level of income? Graphically demonstrate howyour advised policy would increase income per capita (y).
- 9. Consider a numerical example using the Solow growth model. Suppose that F(K, N) KO.5N0.5, with d = z = 1, and take a period to be a year. (a) Determine capital per worker, income per capita, and consumption per capita in the steady state. 0.1, s = 0.2, n = 0.01, andQ5) Solow Growth Model Based on Abel, Bernanke and Croushore, 10th edition, Chapter 6, Numerical Problems No. 5. An economy has the per-worker production function Yt = 3k95 where Yt is output per worker and k, is the capital-labor ratio. The depreciation rate is 8 = 0.1, and the population growth rate is n = 0.05. Saving is St = 0.3Y; where S; is total national saving and Y, is total output. a. Define the steady state of this economy. (Hint: see definition in slides.) b. What are the steady-state values of the capital-labor ratio, output per worker, and consumption per worker? c. Repeat Part (a) for a saving rate of 0.4 instead of 0.3.(a) Two countries, Country A and Country B, are described by the Solow growth model. Both countries are identical, except that the rate of labor-augmenting technological progress is higher in A than in B. i. In which country is the steady-state growth rate of output per effective worker higher? ii. Does the Solow growth model predict that the two economies will converge to the same steady state? p (b) Based on the Solow growth model with population growth and labor-augmenting technological progress, explain how each of the following policies would affect the steady-state level and steady-state growth rate of total output per person: i. an increase in the government's budget deficit poits) inis) ii. grants to support research and development (c) Consider a Solow model where the production function no longer exhibits diminishing returns to capital accumulation. Assume the production function is now Y = AK. What happens to the growth rate of per capita GDP over time? (6pints)
- The Solow Growth Model is a model that is often used to explain the theoretical relationship between several factors that determine a country's economic growthcountry.(a) Explain what you know about the Solow Growth Model and what are the most important determinants of a country's long-term growth rate?(b) Within the framework of the Solow Growth Model, how does population growth affect a country's economic growth rate?(c) Still within the framework of the Solow Growth Model, how does technological progress affect a country's growth rate?An economy described by the Solow growth model has the following production function: y = Vk A. Solve for the steady-state value of y as a function of s, n, g, and d. B. A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A less developed country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g = 0.02 and d= 0.04. Find the steady- state value of y for each country. C. What policies might the less developed country pursue to raise its level of income?This question is about the Solow model. For 2 countries, 1 and 2 which has the same rate of population growth and depreciation and the same saving rate, and are in initial steady state, their capital have equal importance for production for both countries with the same value of α = 1/2 a. In the initial steady state, country 1 has 2 times the output per capita to country 2 because of its greater productivity A. Please use the steady-state equation to find the ratio of the 2 countries’ ratio of productivity and explain it. b. Find the 2 countries’ ratio of capital per capita and explain it. c. Please explain in detail if the capital owners in country 1 are motivated to move their capital from country 1 which is capital abundant, to country 2 which is more capital scarce? Hint: the 2 countries’ payment per unit of capital d. Does workers in country 2 motivated to immigrate to country 1? Please explain from the perspective of the 2 countries’ wages.
- In a Solow growth model with population growth but no technological change, show graphically that an increase in the rate of depreciation will reduce the steady-state value of capital per worker and output per worker. It is reasonable to expect that depreciation rates differ across countries? Why or why not? Please be specific.Q.2An economy described by the Solow growth model has the following production function: y = Vk. a.Solve for the steady-state value of y as a function of s, n, g, and d b. A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A less developed country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g = 0.02 and d = 0.04. Find the steady-state value of y for each country. c. What policies might the less developed country pursue to raise its level of income?2. Consider the Solow growth model without population growth or technological change. The savings rate is 20% (s = 0.2) and depreciation rate is 5% (8 = 0.05). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. (a) Rewrite production function Y = K1/3 L²/3 in per-worker term. (b) Find the steady-state level of the capital stock, k*.