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)

Macroeconomics

13th Edition

ISBN:9781337617390

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter17: Economic Growth: Resources, Technology, Ideas And Institutions

Section: Chapter Questions

Problem 6WNG

See similar textbooks

Similar questions

Ma1. two countries have the same effectiveness of labor production function Y = F (K,LE) = K^0.5 (LE)^0.5 a. what is the per effective worker production function for these countries? b . what is the steady state value of y as a function of s, n, g, and δ only? c. countries A and b are identical in every way except rate of savings. countries A has a savings rate of 17 percent and country B has a savings rate of 10 percent. for both countries the rate of technical progress is g = 0.04 the birth rate is n = 0.05 and depreciation δ = 0.04. find the steady state value of y for each country. compare and comment
Suppose we have the following production function with human capital normalized to 1 (i.e. human capital = 1), total factor productivity represented with A=10, physical capital represented with K=537, and labor represented with L=754 to create GDP represented with Y. What would the size of this economy be for the common production function of Y=A*K0.5*L0.5? This reads as "A times K to the 0.5 power times L to the 0.5 power." However, this is also the same as "A times the square root of K times the square root of L." Round your answer to two digits after the decimal.
In the production function, Total factor productivity = A = 3.5% Labor input = L = 0.75 Capital input = K = 1 – 0.75 = 0.25 Therefore, Y = 3.5% - {(0.25 × 2%) + (0.75 × 2%)} = 3.5% - (0.005 + 0.015) = 0.035 – 0.02 = 0.015 = 1.5% Answer: Contribution to growth by total factor productivity is 1.5%. Does this mean that labour contributes 75 per cent of the increased output? Explain.
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…
Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker? Only D, other option answered
Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker?
Suppose an economy’s production function is Y = AKαL1−α. If the annual rate of economic growth is 3.5 per cent and labour and capital are both growing by 2 per cent annually, what contribution to growth is made by total factor productivity? You can assume that labour receives 75 per cent of the total income generated in this economy.
Assume the production function takes the general form: Y=Z*F (K,L,A)where all marginal products are positive.Which 3 of the following statements are correct?a. If A is fixed, then population growth acts as a drag on growth of output per person.b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that populationgrowth will always reverse the impact of technological improvements.c. Both rises in z and rises in K/L (capital intensity) will boost output per worker.d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), orboth.
Suppose that K(t+5)/N > K(t+3)/N, where K(t+3) is capital in period t+3 and K(t+5) is capital in period t+5. Output per worker, Y/N, in period t+3 is ____ in period t+4. less than equal to greater than
Suppose that in Country 1 the growth rates of multifactor productivity (a), capital (k), and labor (h) are 2.5, 3, and 1 percent per year, respectively, and that capital’s share of output (b) equals 0.25. Initially output per hour equals 40 in Country 1 and 10 in Country 2. (a) Calculate the labor productivity growth rate in Country 1. (b) Calculate output per hour in Country 1 at the end of ten, twenty, and thirty years. (c) Suppose that the labor productivity grows four times as fast in Country 2 as it does in Country 1 for the first ten years, three times as fast for the second ten years, and twice as fast for the third ten years. Calculate output per hour in Country 2 at the end of ten, twenty, and thirty years. (d) Calculate Country 2’s output per hour as a percentage of Country 1’s output per hour at the end of ten, twenty, and thirty years. Are these calculations consistent with the predictions of the Solow growth model?
In 2000, the country of Cobra Island has an initial level of capital set at 10 units. The population of Cobra Island is unknown, but we do know that it grows each year at some constant rate. The level of total income is 500 cobra dollars. Finally, the total production function of Cobra Island can be described as Y=10*L1/2k1/2 What is the initial population of Cobra Island? Let the wage of labor is 0.4, and the rental rate of capital is 0.6. The capital to labor ratio after two years (in 2002) is 50 while the amount of workers is 1000. The growth rate of capital is 6,970%. The growth rate of labor is 100%. Find the GDP of Cobra Island. How much labor is there in Cobra Island one year after the initial year (or in 2001)? The growth rate of income is 1,089%. Find the Solow Residual. Do not give the answer as a percentage. Zackland, a developing country, can be described using the Harrod-Domar Model. The ICOR of Zackland is 0.8. Assume that the economy is stable. In other…
Country A and country B both have the production function Y = F(K, L) = K1/3L2/3 Does this production function have constant returns to scale? Explain. Find Solow’s production function, y = f (k)? 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. Find the steady-state level of capital per worker for each country, then find the steady-state levels of income per worker and consumption per worker. 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, better yet, a computer spreadsheet) to show how the capital stock per worker will evolve over time in both countries. For…