Assume that a country's production function is Y = KO4 LO.6 and there is no population growth or technological change. a. What is the per-worker production function y=f(k)? (NB: Write out only your final answer) b. Assume that the country possesses 4,000 units of capital and 1,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function?ls this value the same as labor productivity computed from the original production function? (leave your answer to 4 decimal places where applicable) (NB: Write out only your final answer)

Assume that a country's production function is Y = KO4 LO.6 and there is no population growth or technological change. a. What is the per-worker production function y=f(k)? (NB: Write out only your final answer) b. Assume that the country possesses 4,000 units of capital and 1,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function?ls this value the same as labor productivity computed from the original production function? (leave your answer to 4 decimal places where applicable) (NB: Write out only your final answer)

ECON MACRO

5th Edition

ISBN:9781337000529

Author:William A. McEachern

Publisher:William A. McEachern

Chapter8: Productivity And Growth

Section: Chapter Questions

Problem 2.4P

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1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change What is the per-worker production function y = Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What is Y? f (k)? а. b. and What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function?
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.
ı need only c and d option
Suppose the per-worker production function is: y = A(1-ga) Where ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the following equation growth of A = (ga/m)(L) Suppose L = 1 and m = 7, and that initially ga = 0.7. If g, fell to 0.8 the level of output per worker would: Impossible to say fall stay the same O rise
1. O LounchPad • Country A and country B both have the production function Y = F(K, L) = K/³L²/3. a. Does this production function have constant returns to scale? Explain. b. What is the per-worker production function, y = f(k)? c. Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per work- er for each country. Then find the steady-state levels of income per worker and consumption per worker. d. Suppose that both countries start off with a capital stock per worker of 1. What are the levels of income per worker and consumption per worker?
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Country A and country B both have the production function Y = F(K, L) = K^0,5L^0,5 A. Does this production function have constant returns to scale? Explain. B. What is the per-worker production function, y = f(k)? C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Theen find the steady-state levels of income per worker and consumption per worker. D. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator or a computer spreadsheet…
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…
Assume that a country's production function is Y= AKº³Lº7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Capital is paid its marginal product. a. What is the marginal product of capital in this situation? (Hint: The marginal product of capital may be computed using calculus by differentiating the production function and using the capital-output ratio or by using the fact that capital's share equals MPK multiplied by K divided by Y.) b. If the economy is in a steady state, what must be the saving rate? (Hint: The saving rate multiplied by Y must provide for gross growth of (8 + n + g)K, where 8 is the depreciation rate.) c. If the economy decides to achieve the Golden Rule level of capital and actually reaches it, what will be the marginal product of capital? d. What must the saving rate be to achieve the Golden Rule level of capital?
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In the Cobb-Douglas production function, Y = K°L!-a, if a = 1/4, then O labor's share of GDP is half. O capital's share of GDP is one-fourth. capital's share of GDP is three-fourths. capital's share of GDP is four.
Suppose that there is a constant technological growth (g) and population growth (n) in a sample economy. Production function is given as Y; = F(Kt, A¿N¿) = /KEJA;N: b) Write the output per effective worker as a function of capital per effective worker.