Machittan Lea Population Growth and Technological Progress - Work It Out An economy has a Cobb-Douglas production function: Y = Ka(LE)-a The economy has a capital share of 0.25, a saving rate of 45 percent, a depreciation rate of 4.75 percent, a rate of population growth of 6.00 percent, and a rate of labor-augmenting technological change of 3.5 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. declines in the steady state. increases in the steady state. % Output per worker growth rate: % de

Machittan Lea Population Growth and Technological Progress - Work It Out An economy has a Cobb-Douglas production function: Y = Ka(LE)-a The economy has a capital share of 0.25, a saving rate of 45 percent, a depreciation rate of 4.75 percent, a rate of population growth of 6.00 percent, and a rate of labor-augmenting technological change of 3.5 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. declines in the steady state. increases in the steady state. % Output per worker growth rate: % de

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter20: Economic Growth In The Global Economy

Section: Chapter Questions

Problem 5P

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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 =
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: %
Consider a Solow growth model with a human capital augmented production function Y, = AK" H N-a- %3D Suppose that both physical and human capital are accumulated with constant savings rates sx and Sy respectively and depreciate at the common rate 8, that is K+1 - K, = sKY, - 8K, and H1 - H, = SKY, - SH, There is no growth in productivity A or raw labor N. "Suppose A = 1, a = ß = 1/4, sx = Sn = 0.12 and ô = 0.06. Let (a) y = YIN, k = KIN and h = HIN denote output per worker, physical capital per worker, and human capital per worker respectively. Let = hlk denote the intensity of human capital relative to physical capital. Calculate y, k, h and o in steady state. (b) . output per worker of the analogous Solow model without human capital (i.e., with Y, = AK" N- and A = 1, a = 1/2, s 0.12 and ô = 0.06. Explain the differences. How does steady state output per worker in this economy compare to the steady state * I Now consider the case a = 1/4 and ß = 3/4 with all the other parameters as in…
Consider the growth model with labour augmenting technological progress. A decrease in the steady state capital per worker may be a result of O Increase in technological growth rate Decrease in savings rate O Increase in population growth rate All other options are correct,
Assume that a country's per-worker production is y = k1/2, where y is output per worker and kis capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10) 2 andthere is no population growth or technological change.a. If the saving rate (s) is 0.4, what are capital per worker, production per worker, andconsumption per worker in the steady state?b. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.6.c. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.8.d. Is it possible to save too much? Why?
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?
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 answered
Explain the Solow Model when there is an improvement of technology
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 =
Solow Growth Model: Cobb-Douglas Production Function. Suppose that production is described by the following constant returns to scale technology: Y a) Derive an expression for steady-state k and steady-state c. b) What value of steady-state k maximizes steady-state c? c) What value of steady-state s, ensures that steady-state c is maximized? KªN1-a
Given 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 forii. output per worker, iii. consumption per worker, iv. Calculate the golden rule steady state level of capital
Why Capital does not Flow from Rich to Emerging Countries? We assume that the production function in country i is 1 1 2 Yi = A ² k², (1) where y, and ki are output and capital per capita, respectively, in country i, and A is a measure of technology in country i. (a) Calculate the marginal product of capital (MPK) denoted by Ri in country i. (b) Express the MPK in terms of output per capita, yi, i.e., eliminate ki from Ri by using the production function (1). (c) We consider two countries, indexed by i 1 and i 2, whose production function is described by (1). Both are assumed to have the same level of productivity, i.e., A₁ A2. We assume y2 50y₁. Calculate the ratio R₁/R₂. (d) We keep assuming that y2 50y1, but now we assume that A2 educational attainment is higher in country 2. Calculate the ratio R₁/R₂ under 10A₁ because these assumptions. FX = - (e) We keep assuming y2 50y₁ but now we consider that technology in country 1 is a function of technology of the more advanced country 2,…