ased on a aggregate production function model where capital and labor are the only factors of production, we can be certain output ill increase if O the total factor productivity increases while the amount of labor and physical capital stock of the country remain constant O the physical capital stock of the country decreases, the total factor productivity remains constant, and the amount of labor increases

ased on a aggregate production function model where capital and labor are the only factors of production, we can be certain output ill increase if O the total factor productivity increases while the amount of labor and physical capital stock of the country remain constant O the physical capital stock of the country decreases, the total factor productivity remains constant, and the amount of labor increases

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

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14. If output is described by the production function Y = AK0.2L0.8, then the production function has: Select one: A. Constant returns to scale and the share of labor in GDP is 0.2. B. increasing returns to scale and the share of labor in GDP is 0.2. C. Decreasing returns to scale and the share of labor in GDP is 0.8. D. constant returns to scale and the share of labor in GDP is 0.8.
Farmland is a developing country with the following production function:Y = 24L2/3K1/3with Y = Output levelL = Quantity of laborK = Quantity of machinesa. Find the real rate of return for labor. Show your calculation. b. Suppose Farmland is granted some extra machines for production.How would this affect the real rate of return for labor? Explain by using theresult in (a).
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…
In class we argued that if people could accumulate human as well as physical capital, the production function would look like the “AK” production function. • (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and populati on growth are δ and n respectively, what would the growth rate of the economy be? • (b) What would be the macroeconomic consequences of decreasing the savings rate in this economy? • (c) What would be the consequences of an increase in fertility in this economy? • (d) Would the consequences of decreasing fertility be UNAMBIGUOUSLY GOOD? • (e) Can human capital grow without bounds? Explain why or why not (make sure you discuss the physical nature of human capital). • (f) What is the growth rate of the economy (in the absence of technological progress) if human capital cannot grow without bounds?
Ecuador's economy has a production function that is as follows: Y = K2/5L3/5 The men in Ecuador generally stay home performing household chores while women work. Since the Ecuadorian state television stopped airing soap operas, many men decided to join the workforce and thus the labor force increased by 6.5%. However, recent storms have destroyed much of the capital stock of the country and thus the capital stock shrank by 2.5%. A. Assuming there is no change in total factor productivity in Ecuador, how would the output of Ecuador's economy change? B. How would labor productivity (output per worker) be affected by the increase in labor and decrease in capital stock? Explain. C. Assuming instead that Ecuador's economy grew by 4.9%, what would be the change in total factor productivity in the economy?
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.
The relation between technology and the quantity of factor inputs to Real GDP is specified by the production function. O True O False Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.
Assume that Economyland’s production function is Y = F (K, L) = K 0.5 L 0.5Where Y is output level, K is the amount of capital input, and L is the amount of laborinput. a) What is the per-worker production function, y= f (k) for Economyland? b) Assume that 10 percent of capital depreciates each year and savings rate is 20 percent,find the steady-state level of capital per worker for Economyland. Then find the steady-state levelof income per worker and steady-state level of consumption per worker. c) Is it possible to save too much? Why?
Consider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.
Consider an economy in which the labour force grows by 2.7 percent per annum, physical capital grows by 4 percent per annum and human capital grows by 1.8 percent per annum. Suppose 45 percent of national income goes to labour and 40 percent to capital. Use a constant returns to scale production function to answer the following growth accounting questions: (a) If the Solow residual were zero what rate of growth would the economy achieve? (b) The country's actual rate of growth has been 4.5 percent per annum, which is faster than the growth rate generated by the accumulation of capital and labour stocks. Calculate the value of the residual.
7. 1. Consider a neoclassical growth economy described by the following.•Yt = K0.3t ·L0.7t (aggregate production function)•s = 0.35 (saving rate)•δ = 0.10 (depreciation rate)•n = 0.01 (population growth rate)•L1 = 120 (initial population)•K1 = 160 (initial capital stock)•g = 0 (technological growth rate)Compute K, Y , k, y, and c for the first three periods. Please report numerical answersto two decimal points. (a) K1 = ; Y1 = ; k1 = ; y1 = ; c1 =(b) K2 = ; Y2 = ; k2 = ; y2 = ; c2 =(c) K3 = ; Y3 = ; k3 = ; y3 = ; c3 =
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.