Consider the production function for a closed economy: Y = 4K0.5 (AN) 0.5 - where Y is aggregate output, A is technology, K is capital stock and N is labour. Capital evolves according to Kt+1 = sYt + (1 − 8)Kt. Also, assume so = 0.2, 2%, technology growth gA = 3%, and depreciation labour force growth gn = 8 = 3%.
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- Hello I need help to find the answer for my econ 101 hw for a question as follows: Assume that the production function for a country is given by ?=√K and annual investment is given by the function ?=?×? where γ=0.270, and that the yearly depreciation rate is 4.50%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking. I will be also attaching the original problem for your reference as I just need to find the time that it would take the country's output to catch up with its neighbor's output. Thank You and please refer to the image to further assist with the question that I want answered.An economy has the per-worker production function yt=f(kt)=4kt)0.4, where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04. Saving is St=0.5Yt, where St is total national saving and Yt is total output. The slope of the per worker production function is given by f' (kt)=1.6kt-0.6 . What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.A 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)∗?
- Consider the Human Capital Accumulation model with a production function given by Y = AK0.5 H0.5, saving rates sã 0.16 and SH 1. Which of the following is false? 8 - 0.05 and A = = - = 0.09, a common depreciation rate is the long-run intensity of human capital relative to physical capital will fall when SH falls the long run growth rate of physical capital will fall when SH falls the long-run intensity of human capital relative to physical capital is 9/16 the long-run growth rate of physical capital is 0.12Solve for the steady state of K with: An Investment (I) function with a rate of growth of 0.4 times the square root of K and a depreciation (D) function of 0.03 * K. Now graph what this looks like. Hint: you need to set the production function equal to the depreciation function and solve for k.Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.
- Consider an economy that has access to a production technology Y = AKαL1−α where Y is output, A is the level of technology, K is capital and L is the amount of labor in the economy. Capital evolves according to K˙ = sY (thus, the depreciation rate δ = 0). The x˙ population growth rate is n. (Throughout, gx = x , where x can be any of the variables in the model.) (a) Assume that technology is determined by A = BKφ What sort of endogenous growth model is this? Find K/K in terms of the K, L, and other parameters of the model.Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].da qaoudon Suppose that the production function is given by Y=05/K √N, where Y is output, K is capital, and N is the number of workers. The steady-state level of capital per worker in terms of the saving rate, s, and the depreciation rate, 6, is KIN= (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g. a superscript can be created with the character.) The steady-state level of output per worker in terms of the saving rate, s, and the depreciation rate, 6, is VIN= (Property format your expression using the tools in the palette.) The equation for steady-state consumption per worker in terms of the saving rate, s, and the depreciation rate, 6, is CIN=(Property format your expression using the tools in the palette.)
- Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is yt = 2.2kt^0.5, where y is output per worker and k is capital per worker. The depreciation rate of capital is 10% per year a- Households initially consume 80% of income and save the remaining 20% of income. There is no government spending. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker? b-Suppose saving rate decreases to 10% permanently. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?Question 1 Consider the following economy with production function: Y = AK"L-a where Y is total output; K is capital; L is labour force; A is the level of technology (exogenous); s is the saving rate; n is the population growth rate; 0 < a < 1. Assume the rate of capital depreciation (5) to be zero. Hence, capital accumulation equation is: K = sY (a) Does this production function exhibitconstantreturns to scale to capital and labour? Explain. Derive production function per worker. (b) Derive an equation showing how the growth rate of capital per worker depends on s, n, and A. Explain its growth implications and use a graph to support your answer. (c) Find out the expression for the steady state capital per worker andoutputper worker. How do they depend on s, n, and A? Explain. (d) Instead of assuming saving rate (s) to be a constant, suppose we assume that "s" depends on y,y =(equivalently on k, k = . In particular, s = e is constant. Find the expression for the growth rate of capital…An economy has production function Y = K¹/2L¹/2, a savings rate of 60 percent. There is no technological progress or labour force growth. The depreciation rate initially 10 percent, increases to 40 percent. There are 400 workers in this economy. When the depreciation rate is 40 percent, output will be equal to dollars.