Answered: Suppose labor productivity increased by…

Suppose labor productivity increased by 4% last year. If technological progress was 3%, by how" much must have the capital-to-labor ratio increased? A) 3%. B) 2%. C) 1%. D) 0%.

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Production And Growth

Section17.1: Economic Growth Around The World

Problem 1QQ

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1. Over a period of 10,000 years, the population of Brobdingnag is estimated to have increased from 4 million to 170 million. Assuming that the level of income per worker was constant, there are only two factors of production, Land (X) and Labour (L), and the exponent on land in the production function is one-third, what was the annual growth rate of productivity, A? a) 0.17% b) 0.42% c) 0.03% d) 0.01%
3. Capital labor ratio is denoted by the equation K/L where K=capital and L=labor. If the total amount of capital remains constant over a certain period of time but the number of workers L grows in the same period, will the value of K/L rise or fall? Justify your answer.
3(a) A firm's production function is initially Q=VKL. Over time, the production function changes to Q=KL^2 (Assume that L21 and K21). Verify that this change represents technological progress.
I need help with parts (f) and (g) of question 2
Suppose the production function is Y = AK0.3N0.7. Suppose in 2010, K = 1000, N = 100, and Y = 199.5. In 2020, capital, labor, and output have doubled, so K = 2000, N = 200, and Y = 399. (a.) By what percentage did productivity grow from 2010 to 2020? (b.) If output had risen to 798 instead of 399, and capital and labor doubled, by what percentage would productivity have grown from 2010 to 2020?
Suppose that the per-worker production (labour productivity) function in South Korea is Y over L equals A open parentheses K over L close parentheses to the power of 0.4 end exponent open parentheses H over L close parentheses to the power of 0.6 end exponent. South Korea's labor productivity rises 6% per year, capital-labour ratio rises 5% per year, and human capital per worker rises 2% per year. This information suggests that total factor productivity grows at _________ per year.
2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (c) Find the long-run growth rate of output per worker. Now the economy has the following production function:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (e) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…
11. Country A and country B both have the production function Y=F(K, L) = K¹/2 [1/2 a. Does this production function have constant returns to scale? Explain. b. What is the per-worker production function, y = f(k)? Hint, do not overthink this one, just use algebraic manipulation. c. Assume that neither country experiences population growth nor 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. Then find the steady-state levels of income per worker and consumption per worker.
10. Labour-saving technical progress means a) that marginal productivity of capital increases. b) that marginal productivity of labour increases. c) that marginal productivity of both inputs increases. d) None of the above is correct. CHOOSE ONE ANSWER ONLY.
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.
Assume that a country's production function is Y = K/2*L/2 and there is no population growth or 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 is Y? 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? c. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary 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 rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital- labor ratio.)
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…