Output per worker is given by yt = A¢k% with a = 1/3. In the year 1900 this country had a capital-labor ratio k1900 equal to 1 and in the year 2000 the same ratio was equal to one half of its level in 1900 due to a terrible civil war. What do you know about the marginal product of capital in 2000 compared to 1900? a. It is the same in both years b. It is lower in 2000 than in 1900 c. It is higher in 2000 than in 1900 d. There is not enough information to decide.
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- In Year 1, Y=2,000, K=1,700, N=70, and, in Year 2, Y=2,100, K=1785, and N=75. Suppose that the production function is given by Y=AK0.25N0.75. Between Year 1 and Year 2 the total factor productivity of this economy changed byMa1. 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 comment1. 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.
- 114.) Output in Rumantily is produced using capital and labor. There is initially a fixed amount of capital (K0), but the amount of labor may be varied in accordance with labor market conditions. What will happen to output per worker and total output in Rumantily if immigration rules are changed so that there is a sharp increase in the immigration of workers from other countries? Decrease, increase Decrease. Decrease Increase, increase Increase, decreaseCountry 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?Say that the average worker in Canada has productivity of $21 per hour while the average worker in Australia has productivity of $33 per hour (both measured in U.S. dollars). If worker productivity, over the next 7 years, grows 3% per year in Canada and 3% in Australia. At the end of the 5 years, how much more productive are Australians workers relative to Canadians, in percentage terms. (Do not include the % sign, round your answer to include 2 decimal places).
- 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?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…
- 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 answeredAssume 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?