Population Growth and Technological Progress – Work It Out An economy has a Cobb–Douglas production function: Y = K"(LE)!-« The economy has a capital share of 0.20, a saving rate of 49 percent, a depreciation rate of 4.00 percent, a rate of population growth of 1.50 percent, and a rate of labor-augmenting technological change of 4.0 percent. It is in steady state. . At what rates do total output and output per worker grow?

Population Growth and Technological Progress – Work It Out An economy has a Cobb–Douglas production function: Y = K"(LE)!-« The economy has a capital share of 0.20, a saving rate of 49 percent, a depreciation rate of 4.00 percent, a rate of population growth of 1.50 percent, and a rate of labor-augmenting technological change of 4.0 percent. It is in steady state. . At what rates do total output and output per worker grow?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter20: Economic Growth In The Global Economy

Section: Chapter Questions

Problem 4P

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3. Consider the Basic Solow growth model with a Cobb-Douglas production function and no technological change for the economy china. In this island economy, capital’s share α= 0.3, the annual depreciation rate on capital δ = 0.08 and the annual population growth rate n = 0.02. Suppose that this is the year 2017, and the economy is in the steady-state with GDP (Y) = 200 bananas, and capital stock K = 400 bananas. [Feel free to use any form of exponentiation that works best for you] Project the equilibrium level of GDP for 2050. Calculate the market value of fixed capital (K) in 2050 on a gross basis. Using the steady-state conditions, solve for the saving rate (s*) that is consistent with a stable steady-state.
please answer the following, I have attached an image of the question for better format. Thanks! 3. Suppose that the production function of a country is given by Y=KaL1-a, where 0<a<1, Y is output, L is labour, and K is capital, Derive the equation for steady state capital per worker, output per worker, and consumption per worker in terms of the saving rate (s) and depreciation rate (d).
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.
Consider two developed and developing countries, the population growth rate of developed countries is 2 percent per year and saving rate of 30 percent. The developing country has a population growth rate of 5 percent and saving rate of 10 percent. Suppose that initial technology of the developed country is 10 times higher than that of the developing country and that both countries have the same productivity growth and depreciation rate: g - 0.02 and 5=0.03. Assume that a - 1/ 3. In a steady state, how much is the developed country's GDP per capita larger than the developing country?
(Long Run) The country of Prosperous has: Production function: Y = 2K1/2 (AN)1/2 ; where Y=output;K=capital; A=technology; and N=labor Saving rate (s): 20% per year Depreciation rate (d): 10% per year Labor growth rate (n): 2% per year Rate of technological change (g): 8% per year c. Calculate the growth rate of the following variables when the economy achieves its steady-state: Output per effective worker (Y/AN) Output per worker (Y/N) Output (Y)
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).
(Long Run) The country of Prosperous has: Production function: Y = 2 K1/2 (AN)1/2, where Y=output;K=capital; A=technology; and N=labor Saving rate (s): 20% per year Depreciation rate (d): 10% per year Labor growth rate (n): 2% per year Rate of technological change (g): 8% per year b. Calculate: The steady state level of capital accumulation per effective worker The steady state level of output, consumption and investment per effective worker Graphically illustrate the above steady state condition.
Suppose a country has a capital-output ratio equal to 10, a savings rate equal to 20% of GDP, capital that lasts on average 100 years and population growth of 1% per year. If we assume the country is at its steady state and production is given by the Solow model with labor-augmenting technological change, so Y = K^a(EL)^(1 – a), then the growth rate of technology as measured by the growth rate of efficiency workers is 0% 1% 3% 2% 4%
Based on article "Technology and economic growth: From Robert Solow to Paul Romer" by Rui Zhao, Solow mentioned technology (At) and capital per unit of effective labor (Kt) have a significant influence on a country's ability to “catch-up” or “converge” to a steady-state level (K*). Why did Solow model assume At as a black box in economics? Explain in brief.
Suppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.
Question 1:In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratiois about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has beenin a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-staterelationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the GoldenRule level of capital. What will the marginal product of capital be at the Golden Rule steadystate? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product…
In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of…