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Q: part C
A: Argentina and Spain are two countries. The table is as follows:
Assume that a country's production function is Y = K1/2L1/2 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
labor ratio.)
d. If the saving rate equals the steady-state level, what is consumption per worker?
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- 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?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.)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?
- 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…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.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
- Write the production function (human capital (H) is included in TFP) and the logarithmic form of this production function then explain why the GDP growth will be at the end ofa given long period lower than at the beginning of this period, assuming that the average contribution of TFP to GDP average growth during the period is constant.1. Over the period from B.C. 10,000 to A.D. 1, the world population is estimated to have increased from 4 million to 170 million, while the level of income per capita was constant over time. Assuming that the quantities of human and physical capital per worker did not change, and that the exponent on land in the production function is one-third, calculate the growth rate in productivity over this period. What was the annual growth rate of productivity, A?Why does adding capital to a production function make the economy more productive? What are diminishing returns to capital? How does technology affect productivity and growth?
- Suppose that total capital and labour both increase by the Suppose that total capital and labour both increase by the same percentage amount so that the amount of capital per worker k does not change. Writing the production function in per-worker terms, y = f(k), requires that this increase in capital and labour must not change the amount of output produced per worker y. Use the growth accounting equation to show that equal percentage increases in capital and labour will leave output per worker unaffected only if aK + aN = 1. Suppose that total capital and labour both increase by the1. 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?Write out the equation for output growth with capital, labor and total factor productivityas determinants of growth. Suppose that the shares of capital and labor are respectively0 .3 and 0.7. If labor supply grows by 10% what would be the growth rate of outputassuming that there is no change in the other determinants? What would happen to percapita output if labor supply growth is entirely due to population growth?