1. Consider an economy where the production function isY = K0.5 (LE)0.5The 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), incomeper effective worker (y), investment per effective worker (it) andconsumption per effective worker (c2). Also find sg, that is the levelof the savings rate that would lead the economy to the golden rulesteady state.(d) Suppose the government pursues policies that change the savingsrate from s = 0.2 to sg. What is the immediate effect on income pereffective worker and consumption per effective worker? What is thelong run effect on income per effective worker and consumption pereffective worker? (You are asked to compute the effects; show yourwork and provide numbers!)

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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 (i) and consumption per effective worker (c). 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 effective worker and consumption per effective worker? (You are asked to compute the effects; show your work and provide numbers!)

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 (i) and consumption per effective worker (c). 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 effective worker and consumption per effective worker? (You are asked to compute the effects; show your work and provide numbers!)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q4) Production Functions and Growth (a) Time is continuous and the production function of the economy is given by (1) Y¢ = ( K¢ )ª( A¿N; )1-« Total factor productivity evolves according to (2) A = egt Ao such that A where the growth rate of technological progress g is exogenous. Population grows at an exogenous rate n according to (3) N{ = ent No with No = 1 such that = n Find an expression for the growth rate of (i) output per capita (Yt / Ni) and (ii) output per effective worker ( Yt/ (A:N:) ). When is the growth rate of (ii) equal to zero?
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31) Given the narrow interpretation of technology, technology will include which of the following? A) how well firms are run B) the organization and sophistication of markets C) the political environment D) none of the above 32) Suppose there are two countries that are identical with the following exception. The saving rate in country A is greater than the saving rate in country B. Given this information, we know that in the long run A) the growth rate of output per capita will be greater in B than in A. B) the growth rate of output per capita will be greater in A than in B. C) the capital-labor ratios (K/N) will be the same in both countries. D) the growth rate of output per capita will be the same in both countries. 33) Suppose there are two countries that are identical with the following exception. The saving rate in country A is greater than the saving rate in country B. Given this information, we know that in the long run A) the capital-labor ratio…
(a) Two countries, Country A and Country B, are described by the Solow growth model. Both countries are identical, except that the rate of labor-augmenting technological progress is higher in A than in B. i. In which country is the steady-state growth rate of output per effective worker higher? ii. Does the Solow growth model predict that the two economies will converge to the same steady state? p (b) Based on the Solow growth model with population growth and labor-augmenting technological progress, explain how each of the following policies would affect the steady-state level and steady-state growth rate of total output per person: i. an increase in the government's budget deficit poits) inis) ii. grants to support research and development (c) Consider a Solow model where the production function no longer exhibits diminishing returns to capital accumulation. Assume the production function is now Y = AK. What happens to the growth rate of per capita GDP over time? (6pints)
In this problem, we distinguish between labor and population in the Solow growth model. A proportion of the population, a, between zero and one, works. The production function is now written as Y = A(K^1/3)[(aL)^2/3] (a) How does an increase in a from 0.3 to 0.6 change steady state GDP? (b) Does it change the steady-state capital? Explain. (c) Suppose a rises steadily over time. How do you think would affect the growth rate of GDP?
The Solow Growth Model is a model that is often used to explain the theoretical relationship between several factors that determine a country's economic growthcountry.(a) Explain what you know about the Solow Growth Model and what are the most important determinants of a country's long-term growth rate?(b) Within the framework of the Solow Growth Model, how does population growth affect a country's economic growth rate?(c) Still within the framework of the Solow Growth Model, how does technological progress affect a country's growth rate?
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Are there key differences between an increase in the capital stock and an improvement in the level of technology?