Mj O Macmillan LearningPopulation Growth and Technological Progress-Work It OutAn economy has a Cobb-Douglas production function:Y = K*(LE)¹-The economy has a capital share of 0.30, a saving rate of 50 percent, a depreciation rate of 5.25 percent, a rate of populationgrowth of 4.25 percent, and a rate of labor-augmenting technological change of 4.0 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.marginal product of capital =

The Cobb-Douglas production function is an economic model that represents the relationship between…

O Macmillan Learning Population Growth and Technolo An economy has a Cobb-Douglas p Y = K (LE)¹-a The economy has a capital share of growth of 4.25 percent, and a rate on b. Solve for capital per effective work k" == = marginal product of capital =

O Macmillan Learning Population Growth and Technolo An economy has a Cobb-Douglas p Y = K (LE)¹-a The economy has a capital share of growth of 4.25 percent, and a rate on b. Solve for capital per effective work k" == = marginal product of capital =

Exploring Economics

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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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O Macmillan Learning
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 0.30, a saving rate of 50 percent, a depreciation rate of 5.25 percent, a rate of population
growth of 4.25 percent, and a rate of labor-augmenting technological change of 4.0 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.
marginal product of capital =

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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…
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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?
3 pts in the Solow model, the economy reaches a steady-state because as capital per worker increases O savings per worker is constant, while the population growth rate is contare and the depreciation rate of capital decen, ing that the economy w gro endogenously while the population growth rate and the depreciation rate of capital are comitant implying that the economy will converge to a sady O marginal savings per worker diminishes, while the population growth rate and the depreciation rate of capital are constant implying that the economy will gro endogenously Osaving perv state. O marginal savings per worker diminishes, while the population growth rate and the depreciation rate of capital are constant, implying that the economy will converge to a steady-state
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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