Consider the following data on two fictional countries: 1 and 2. . Country 1 Country 2 Output per worker (y) Physical Capital per Worker, k Human Capital per Worker, h 120 80 75 50 25 75 If the production function is y = Akªh1-a, where a = 0.5., then if all differences in output were due to differences in factor accumulation then country 1 output would be times greater than in Country 2 1.70 0.71 1.00 0.59 O O O
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- The “per person” versions of production functions: Write each productionfunction given below in terms of output per person y ; Y/L and capital perperson k ; K/L. Show what these “per person” versions look like in a graphwith k on the horizontal axis and y on the vertical axis. (Assume A is somefxed positive number.)(a) Y = K 1/3L2/3 and Y = K 3/4L1/4 (on the same graph) (b) Y = K(c) Y = K + AL(d) Y = K − ALConsider the following data on two fictional countries: 1 and 2. . Country 1 Country 2 Output per worker (y) Physical Capital per Worker, k Human Capital per Worker, h 120 100 50 100 50 25 If the production function is y = Akºh'-a, where a = 0.5., then if all differences in output were due to differences in factor accumulation then country 1 output would be %3D times greater than in Country 2 1.70 0.59 1.17 1.461. 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 that a country has a produ ction function, where Lis labour, K is capital and A is total factor produ ctivity, as follows: Y = F(K, L) = A.K0.25L0.75 a) Write the produ ction function in "intensive form" (output per worker as a fun ction of capital per worker). b) Suppose, initially,that A = 4 andits growth rate is zero. The country has a population growth of 1% per year (0.01) and a depreciation rate of 10% (0.10). If the county saves 30% of nation al in come, find the steady state levels of capital per worker, as well as con sumption andincome per worker.Consider the following data on two fictional countries: 1 and 2. . Country 1 Country 2 Output per worker (y) Physical Capital per Worker, k Human Capital per Worker, h 120 80 75 50 25 75 If the production function is y = Akªh1-a, where a = 0.5., then if all differences in output %3D were due to differences in factor accumulation then country 1 output would be times greater than in Country 2 1.70 0.71 1.00 0.59Suppose 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
- 1. 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?Consider the economies of Sporon and Gobbledigook, both of which produce gobs of goo using only tools and workers. Suppose that, during the course of 20 years, the level of physical capital per worker rises by 5 tools per worker in each economy, but the size of each labor force remains the same. Complete the following tables by entering productivity (in terms of output per worker) for each economy in 2015 and 2035. Sporon Year Physical Capital (Tools per worker) Labor Force (Workers) Output (Gobs of goo) Productivity (Gobs per worker) 2015 11 30 1,800 2035 16 30 2,160 Gobbledigook Year Physical Capital (Tools per worker) Labor Force (Workers) Output (Gobs of goo) Productivity (Gobs per worker) 2015 8 30 900 2035 13 30 1,620 Initially, the number of tools per worker was higher in Sporon than in Gobbledigook. From 2015 to 2035, capital per worker rises by 5 units in each country. The 5-unit change in capital per worker…Question 1 The Mankiw-Romer-Weil (1992) model. Assume the production function is given by Y = KaH³(AL)¹-a-B where a and B are constants between zero and one whose sum is also between zero and one. Physical capital is accumulated as K = SKY dk where SK is the constant share of output invested in physical capital. And human capital is accumulated just like physical capital: Н = SHY dH where SH is the constant share of output invested in human capital. The labor force grows at rate n, and the technological progress occurs at rate g. Solve the model for the path of output per worker y=Y/L along the balanced growth path as a function of SK SH, n, g, d, a and B. (Hint: Define state variables such as y/A, h/A, and k/A.)
- Consider the economies of Hermes and Gribinez, both of which produce gaggles of gop using only tools and workers. Suppose that, during the course of 10 years, the level of physical capital per worker rises by 5 tools per worker in each economy, but the size of each labor force remains the same. Complete the following tables by entering productivity (in terms of output per worker) for each economy in 2016 and 2026. **THE TABLE IS ATTACHED** Initially, the number of tools per worker was higher in Hermes than in Gribinez. From 2016 to 2026, capital per worker rises by 5 units in each country. The 5-unit change in capital per worker causes productivity in Hermes to rise by a _________ (LARGER/SMALLER) amount than productivity in Gribinez. This illustrates the _______ (CATCH-UP/NATURAL RESOURCES/TECHNOLOGY/HUMAN CAPITAL) effect. THANK YOU FOR THE HELPEconomics, physical capital represents the uildings or machines used by a business to produce product. The marginal product of physical capital presents the rate of change of output product with spect to physical capital (informally, if you increase e size of your factory a little, how much more Foduct can you create?). articular model tells us that the output product Y is given, a function of capital K, by Y = AKªL'-a ere A is a constant, L is units of labor (assumed to be stant), and a is a constant between 0 and 1. Determine marginal product of physical capital predicted by this del. ned with CamScannerShow graphically on the same x and y axis what happens to this production function if there is a technological advancement in this economy. Don,t copy from anywhere.