7. A country's GDP is expected to grow at a constant rate of 3%, and population grows at rate of 2%. Productivity grows at rate of 1%, and capital share is 1/2. Approximately how many years would it take for a country's per capita income to double? Assume population is equal to labor force, and the production function is Y = AKªL'-a. a) 14 b) 23 c) 35 d) 70
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- Why dues productivity growth in high-income economies not slow down as it runs into diminishing returns from additional investments in physical capital and human capital? Does this show one area where the theory of diminishing returns fails to apply? Why or why not?Would you expect capital deepening to result in diminished1etmns? Why or why not? Would you expect improvements in technology to result in diminished returns? Why or why not?An economy starts off with a GDP per capita of 5,000. How large will the GDP per capita be if it grows at an annual rate of 2 for 20 years? 2 for 40 years? 4 for 40 years? 6 for 40 years?
- 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?The current population of the United States is 327.2 million with 2.2% of the population is engaged in R&D at an efficiency rate of 1/375 per million persons per year. If R&D is the only source of total-factor productivity growth what is the growth rate of total factor productivity in the United States?
- 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 commentAssume that total output is determined by this formula: number of workers × productivity = total output Hint: Assume there are 100 workers and each worker produces $100 of output. If productivity increases by 3 percent and the number of workers increases by 2 percent a year, how fast will output grow?The “graying of America” will substantially increase the fraction of the population that is retired in the decades to come. To illustrate the implications for U.S. living standards, suppose that over the 56 years following 2016 the share of the population that is working returns to its 1960 level, while average labor productivity increases at the same rate as it did during 1960–2016. Under this scenario, what would be the net change in real GDP per person between 2016 and 2072? Year Average labor productivity Share of population employed 1960 47,263 36.4% 2016 110,384 46.8% Instructions: Enter your response as whole numbers for dollar values and rounded to one decimal place for percentages.Real GDP per person in 2016: $51,660 (need help) Real GDP per person in 2072: $ (need help) Net change in real GDP per person between 2016 and 2072: $____________ , which is an increase of___________ % from 2016.
- The “graying of America” will substantially increase the fraction of the population that is retired in the decades to come. To illustrate the implications for U.S. living standards, suppose that over the 56 years following 2016 the share of the population that is working returns to its 1960 level, while average labor productivity increases at the same rate as it did during 1960–2016. Under this scenario, what would be the net change in real GDP per person between 2016 and 2072? Year Average labor productivity Share of population employed 1960 47,263 36.4% 2016 110,384 46.8% Instructions: Enter your response as whole numbers for dollar values and rounded to one decimal place for percentages.(need help)Real GDP per person in 2016: $ (need help) Real GDP per person in 2072: $ (need help) Net change in real GDP per person between 2016 and 2072: $____________ , which is an increase of___________ % from 2016.Provide intuitive economic to explain why equal percentage increase in savings rates and population growth rate appears to nullify each other in the equation y*= 1000( √s/n) ( where per capita income is unchanged)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.