Y - K"(LE) The economy has a capital share of 0.20, a saving rate of 45 percent, a depreciation rate of 3.75 percent, a rate of population growth of 5.00 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k"), output per elffective worker (y"), and the marginal product of capital. k' - y* = marginal product of capital =
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- What are the advantages of backwardness for economic growth?Population Growth and Technological Progress – Work It Out PLEASE WRITE ANSWERS CLEARLY An economy has a Cobb-Douglas production function: Y = K“(LE)'-a The economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of population growth of 5.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = y* = marginal product of capital =2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (c) Find the long-run growth rate of output per worker. Now the economy has the following production function:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (e) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…
- Population Growth and Technological Progress-Work It Out An economy has a Cobb-Douglas production function: Y = K (LE)¹- The economy has a capital share of 0.20, a saving rate of 49 percent, a depreciation rate of 4.00 percent, a rate of population growth of 1.50 percent, and a rate of labor-augmenting technological change of 4.0 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: Output per effective worker is constant in the steady state and does not change. increases in the steady state. declines in the steady state. % Output per worker growth rate: %2. An economy has a production function: Y 3KtLt. (1) The economy has a saving rate of 24 percent, a depreciation rate of 3 percent, 1 for all period (no population growth). and Lt Yt Lt (a) What is the per-worker production function, yt f(kt)? Define yt Ки Lt and kt (b) Find the equation for the evolution of capital per worker in terms of kt and kt+1 (c) Find the long-run growth rate of output per worker. Now the economy has the following production function: Y 3Kt (2) but savings rate, depreciation rate, and population remain the sameGiven a saving rate of 5%, a depreciation rate of 1%, and a production function in which y = k0.5where y is output per worker and k is capital per worker, calculate the steady state values fori. capital per worker, ii. output per worker, iii. consumption per worker
- 1. Suppose an economy experiences both positive population growth (8 ) and technological progress (84 ). The capital depreciation rate is d . The saving rate is exogenously given as s. (a) Draw a diagram with variables in per effective worker terms to show how a steady state level of capital per effective worker (K/AN) is determined. Also explain your answers in words. (b) We further assume that the aggregate production function is given by Y= K“(AN)™, where oJ 7 Given a production function Yt = AKt1 /3L2 /3 , if K0=8, A = 2, L = 4, s = 0.2, and d = 0.05: (a) Calculate the steady-state level of capital and output. (b) Calculate K1 , I 1 , Y1 and C1 .An economy's production function as follows Y = 8 (K)¹/2 (EL)¹/2 If depreciation rate is 10%, population growth rate is 4%, tech progress grows 6%, and saving rate is 20%. a. b. C. d. e. f. Write production function in term of per effective worker variables. Find steady state capital per effective worker, output per effective worker, consumption per effective worker, investment per effective worker. Find growth rate of capital per worker and output per worker at steady state. Find growth rate of capital stock and total output at steady state. Propose policies to encourage long run growth of total output and living standard? Draw relevant graph for the above questions.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…COISiuci all tconOly utsciiotu vy uit pTouucion TuIcuoll. Y = F(K, L) = K0.45L0.55 a. What is the per-worker production function? y= ()04 Incorrect b. Assuming no population growth or technological progress, find the steady-state capital stock per worker (k* ), output per worker (y*), and consumption per worker (c*) as a function of the saving rate and the depreciation rate. |(2)* k* = Incorrect y* = 2) Incorrect c* =1. Consider an economy where the production function is Y = K0.5 (LE)0.5 The depreciation rate is = 0.04, the savings rate is s = 0.2, the popula- tion growth rate is n = 0.03 and technology growth rate is g = 0.03. (a) What is the 'per effective worker' production function? (b) Find the steady state levels of capital per effective worker (k*), in- come per effective worker (y*), investment per effective worker (¿*) and consumption per effective worker (c"). (c) Find the golden rule levels of capital per effective worker (kg), income per effective worker (y), investment per effective worker (it) and consumption per effective worker (c2). Also find sg, that is the level of the savings rate that would lead the economy to the golden rule steady state. (d) Suppose the government pursues policies that change the savings rate from s = 0.2 to sg. What is the immediate effect on income per effective worker and consumption per effective worker? What is the long run effect on income per…SEE MORE QUESTIONS