Consider the following production (in per capita terms): For capital stocks between 0 and 10, y; 0.5 k. For capital stocks equal and above 10, y; 5 a. Graph the production function in per capita terms (where y, is in the vertical axis and k, in the horizontal axis). b. Graph the average product of capital y./k, as a function of k.
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- 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…Suppose the 50% of the income generated by an economy is paid to workers, thus implying that the remaining 50% is paid to capital. If GDP grew by 4%, capital grew by 1%, and labor grew by 3%, then what was the growth rate in technology? (Record your answer as a whole number, and do not include a "%".)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 comment
- The following graph shows a variety of possible production functions (PFs) in an imaginary economy, assuming constant levels of human capital and technology. Because human capital and technology remain unchanged, each of these production functions represents a different level of the capital stock. Fill in the table with the curve that corresponds to each of the capital stock levels described. Levels of Capital Stock This corresponds to which curve? (PF1, PF2, PF3) Highest Middle Lowest Fill in the blank: The slope of the line connecting the origin to point B is __________ (options: flatter, steeper) than the slope of the line connecting the origin to point A, because the slope of such a line is equivalent to ___________ (options: productivity, the marginal physical product of labor, marginal cost).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…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?
- 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.Suppose a country has a population of 120 people, a working-age population of 100 people, its labor force participation rate is 0.5 (50%), and the quantity of output is 60 units. Suppose that the production function of the economy is given by Y=2N, where Y represents the quantity of output and N represents the number of workers needed to produce the output. I know the answer is 0.4 but I don't understand how to get it. Thank you!The aggregate production function is y=3KL. If they are 30 units of capital and 40 units of labor, what is aggregate output? What is labor productivity? What is capital productivity?
- 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 HELPA CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?Labour-saving technical progress meansa) that marginal productivity of capital increases.b) that marginal productivity of labour increases.c) that marginal productivity of both inputs increases.d) None of the above is correct.
