Question 1The Mankiw-Romer-Weil (1992) model.Assume the production function is given byY = KaH³(AL)¹-a-Bwhere a and B are constants between zero and one whose sum is also between zero and one. Physical capital isaccumulated asK = SKY dkwhere SK is the constant share of output invested in physical capital. And human capital is accumulated just likephysical capital:Н = SHY dHwhere SH is the constant share of output invested in human capital.The labor force grows at rate n, and the technological progress occurs at rate g. Solve the model for the path ofoutput per worker y=Y/L along the balanced growth path as a function of SK SH, n, g, d, a and B.(Hint: Define state variables such as y/A, h/A, and k/A.)

Production functionY=KαHβ(AL)1-α-β α and β are constant between 0 &1Physical capital…

The Mankiw-Romer-Weil (1992) model. Assume the production function is given by KaH³(AL) ¹-a-B where a and B are constants between zero and one whose sum is also between zero and one. Physical capital is accumulated as = K = SKY - dk where SK is the constant share of output invested in physical capital. And human capital is accumulated just like physical capital:

The Mankiw-Romer-Weil (1992) model. Assume the production function is given by KaH³(AL) ¹-a-B where a and B are constants between zero and one whose sum is also between zero and one. Physical capital is accumulated as = K = SKY - dk where SK is the constant share of output invested in physical capital. And human capital is accumulated just like physical capital:

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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1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.
This is a really straightforward problem of human capital acquisition. Let ht stand for generation t's human capital (i.e., human capital of people born in year t). Assume that education spending, represented by x and quantified in $1,000 US dollars, builds human capital. If x = 30, the entire expenditure is 30,000 dollars, and the individual's human capital is ht = 2x.Assume that everyone has the same amount of human capital and that production per person is the same.Individual is yt = Aht, where A > 0 is a constant technological parameter.Find yt's (long-term) growth rate. Display all of your work and explain how you arrived at your conclusions.
Please no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain. (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k). (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6. (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…
(a) Consider an economy that is initially in a steady state equilibrium. Assume that in this equilibrium it has a saving rate of 50 per cent and a depreciation rate of 2 per cent. Further assume that the population growth rate is 3% and that the level of output produced can be represented by the following production function: = where A = 1 and = 0.5. Use the Solow-Swan model to determine the level of capital per worker and output per worker in this economy. (1 mark) (b) Now suppose the government introduces a set of policies to improve the institutional set up as well as better production technique which increases total factor productivity by double. What is the new steady state level of capital per worker and output per worker? (1 mark) (c) Use a Solow-Swan diagram to show the qualitative effects of this new government policy upon steady state output per worker and capital per worker. Briefly describe the intuition behind this result. (1 mark) (d) Now suppose, population growth rate…
Some resource-rich countries have succeeded in converting resource wealth into longterm and equitable economic development, while many others have not. Naturalresources have played a fundamental role in the growth of several industrializedeconomies, including Germany and the United Kingdom, where coal and iron ore depositswere a precondition for the Industrial Revolution. The United States was the world’sleading mineral economy from the mid-nineteenth to the mid-twentieth century and in thesame period became the world’s leader in manufacturing (van der Ploeg 2011). Morerecently, countries such as Botswana, Chile, and Norway have used abundant oil andmineral resources as the foundation for economic growth. However, in many othercountries, resource extraction appears to have undermined governance, fed corruptionand capital flight, and increased inequality.Required:(a) Discuss the main challenges posed by resource revenues; and(b) Discuss the special fiscal institutions and mechanisms…
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Consider the following (made-up) statistics for some econ-omies. Assume the exponent on capital is 1/3 and that the labor composition is unchanged. For each economy, compute the growth rate of TFP.(a) A European economy: gY/L = 0.03, gK/L = 0.03.(b) A Latin American economy: gY/L = 0.02, gK/L = 0.01.(c) An Asian economy: gY/L = 0.06, gK/L = 0.15.
Two countries, X & Y both have the production function f(k) = k0.5 but X starts with an initial k of 4 while Y starts with initial k of 16. Both of the countries have the same values for these exogeneous variables: s = 0.2, A = 1, depreciation rate = 0.05, n = 0, L0 = 10. As you can see, X starts out with just 25% as much capital as Y. How many periods does it take before X has at least 50% as much capital as Y? (A spreadsheet will help a lot with this)
Country Has Cobb-Douglas production function: Y(it) = A(it) x K(it)1/3L(it)2/3 Where: Y(it) = realGDP K(it) = Capital L(it) = No. workers employed in country (i) on date (t) Suppose multiple countries share the same alpha = 1/3 but different levels of totalfactorproductivity (A(it)). Now Instead of the above function the production function changes to: Y(it) = A(it) x K(it)1/3 x (H(it)L(it))2/3 Y(it) = realGDP K(it) = Capital H(it) = Average hours worked p/worker (This is so the labour input is total hours opposed to employment) L(it) = No. workers employed in country (i) on date (t) These multiple countries share the same alpha = 1/3 but different levels of totalfactorproductivity (A(it)). How does this new variable in the formula impact TFP growth? What happens if the country has higher average hours per worker? what happens if the country has lower average hours per worker?
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).
y=zk^2/3 For this economy, derive the competitive equilibrium, and derive the equation that solves for a steady state capital stock per worker.
Consider the economies of Sporon and Gobbledigook, both of which produce gobs of goo using only tools and workers. Suppose that, during the course of 20 years, the level of physical capital per worker rises by 5 tools per worker in each economy, but the size of each labor force remains the same. Complete the following tables by entering productivity (in terms of output per worker) for each economy in 2015 and 2035. Sporon Year Physical Capital (Tools per worker) Labor Force (Workers) Output (Gobs of goo) Productivity (Gobs per worker) 2015 11 30 1,800 2035 16 30 2,160 Gobbledigook Year Physical Capital (Tools per worker) Labor Force (Workers) Output (Gobs of goo) Productivity (Gobs per worker) 2015 8 30 900 2035 13 30 1,620 Initially, the number of tools per worker was higher in Sporon than in Gobbledigook. From 2015 to 2035, capital per worker rises by 5 units in each country. The 5-unit change in capital per worker…