1. Consider Avataria, which can be described by the Solow model with the population growth. Its production function Y(K,L) = 2K¹2L1/2 Its investment rate is 40%, its depreciation rate is 10%, and its population growth rate is 10%. (a) Calculate the capital-labor ratio, output per worker, and consumption per worker in the steady state. (b) Assume that now the population growth slows down to 4%. What happens with the output per worker and consumption per worker in the new steady state? Calculate the exact values.

1. Consider Avataria, which can be described by the Solow model with the population growth. Its production function Y(K,L) = 2K¹2L1/2 Its investment rate is 40%, its depreciation rate is 10%, and its population growth rate is 10%. (a) Calculate the capital-labor ratio, output per worker, and consumption per worker in the steady state. (b) Assume that now the population growth slows down to 4%. What happens with the output per worker and consumption per worker in the new steady state? Calculate the exact values.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

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: %
In the Solow model with technological progress, suppose that the rate of depreciation is 10% per year, the population growth rate is 2% per year, and the growth rate of technology is 3% per year. Which of the following represents the level of investment needed to maintain a constant capital stock (K) in this economy? 0.02K 0.03K 0.05K 0.10K
Consider an economy as per solow model, with a Cobb-Douglas production function with constant returns to scale with respect to K and L. Moreover, you know that the economy is producing 80 units of total output and the productivity parameter is equal to 1. If the depreciation rate is 10%, the investment rate is 10%, and there are 75 workers, the growth rate of GDP per person ____________. a) is equal to zero because the economy is at its steady state b) is negative because the economy is above its steady state c) is positive because the economy is below its steady state d)cannot be determined
= 2. Consider a Solow growth model in which the production function is Yt AK²N₁¹/2, where A = 1. Moreover, assume that the depreciation rate is d = 0.02, the rate of population growth is n = 0.02, and the saving rate is s = = 0.2. a. Compute the value of the capital stock per worker in steady state. b. Draw a graph that represents the steady-state equilibrium of the model. c. Suppose that the capital-labor ration in year t is 90. What will the level of the capital- labor ratio be in year t+1? Will it increase or decrease in future periods? Explain. d. Compute the rate of change of the capital labor ratio between time t and t + 1. How does it compare to the rate of growth of the capital-labor ratio in steady state?
Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.
1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%, a. What is the steady-state level of capital per worker? b. What is the steady-state of output per worker? c. What is the steady-state level of consumption per worker? 2. Now assume population growth is instead-0.5% (approximately the growth rate when every couple has 1.7 children), but that all other parameters stay the same. a. What is the new steady-state output per worker? Is it higher or lower than with faster population growth? [A numerical answer and a 1 sentence response is fine.] b. What is the new steady- state of consumption per worker? Is it higher or lower than with faster population growth? [A numerical answer and 1 sentence response is fine].
Q11
4. Assume an endogenous growth model with a production function that in per capita terms can be written as y = 0.8k. If the savings rate is s = 0.3, the rate of growth of population is n = 0.03, and the rate of depreciation is d = 0.1, how high is the rate of growth of output per capita? A. 14% B. 17% C. 13% D. 11% E. There is not enough information to calculate it.
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 =
Q5) Solow Growth Model Based on Abel, Bernanke and Croushore, 10th edition, Chapter 6, Numerical Problems No. 5. An economy has the per-worker production function Yt = 3k95 where Yt is output per worker and k, is the capital-labor ratio. The depreciation rate is 8 = 0.1, and the population growth rate is n = 0.05. Saving is St = 0.3Y; where S; is total national saving and Y, is total output. a. Define the steady state of this economy. (Hint: see definition in slides.) b. What are the steady-state values of the capital-labor ratio, output per worker, and consumption per worker? c. Repeat Part (a) for a saving rate of 0.4 instead of 0.3.
Q7
Exercise 4: Growth and capital over-accumulationSuppose two countries, A and B, with the same production function Y = KαL1−α. Thevalue of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.a) Show that with price-taking firms the share of labor must be 1 − α.b) Compute the stock of capital, output and consumption per unit of labor in the steadystate if the savings rates were 25% for country A and 35% for country B.c) Compare both economies to the Golden Rule.d) Explain what would happen to both countries if suddenly their savings rate becamethe Golden Rule savings rate.