Suppose that the economy's production function is: Y = (K) 0.5 (AN) 0.5, that the savings rate s is equal to 16%, andthat the rate of depreciation d is equal to 10%. Suppose further that the number of workers grows at 2% per year andthat the rate of technological progress is 4% per year. a) Find the steady state values of the variables listed below: i) Thecapital stock per effective worker. ii) Output per effective worker. iii) The growth rate of output per effective worker. iv)The growth rate of output per worker. v) The growth rate of output. b) Suppose that the rate of technological progressdoubles to 8% per year. Recompute the answers in part a). Explain the differences. c) Now suppose that the rate oftechnological progress is still equal to 4% per year, but the number of workers now grows at 6% per year. Recompute theanswer to part a). Are people better off in part a) or c)? Explain.

The objective of the question is to find the steady state values of the variables in the given…

Answered: Suppose that the economy's production…

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?
if real GDP grows at an annual rate of 3.4% and the population grows at an annual rate of 1.6% then at approximately what rate is the real GDP per capital growing?
The productivity of a country is given by f(x,y)=15.21x0.438y0.562, where x is the amount of labor and y is the amount of capital. (A) Find fx(x,y) and fy(x,y). (B) Find fx(67,55) and fy(67,55), and interpret the results.
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) Consider two countries that have the same parameters and exogenous variables (i.e. they have the same values for s¯, d¯, L¯ etc). Country A starts with a level of capital above the steady state. Country B starts below the steady state. First, plot the Solow diagram, explain why country B will grow but country A will shrink. b) Solve for steady state level of capital per person, k∗.
Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].
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Consider the Solow model with a production function Y(t) = A*K(t)αL(t)1-α, Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and the population growth rate n?
Given the following aggregate production function: Y = K0.25 (AL) 0.75, where technology A grows at a fixed rate: A=g>0 (f) Find the steady state solution algebraically for output per efficiency worker, ỹ, where (i = 1,2). Show all workings. (g) Outline and explain the behaviour of per worker variables along the model's balanced growth path.
Suppose that two countries share identical technology, depreciation rate, saving rate, and population growth. However, these two countries started off with different levels of capital stock. Which of the following is/are true? (i) The country with initially smaller capital stock grows more quickly to reach the steady state compared to the country with initially larger capital stock. (ii) The country with initially smaller capital stock will have a smaller capital stock in the steady state compared to the country with initially larger capital stock. (iii) Both countries will grow at the same rate in reaching the steady state. O a. Both (i) and (ii). O b. Only (iii). O c. Only (i). O d. Cannot tell. Need more information.
The answer should be step by step and the answer should be no plagiarism.
You are given the production function Y= AK H14 N 2, where A = 4. The population growth rate n is 0.025, the depreciation rate d is 0.075 (both physical and human capital depreciate at the same rate), and the growth rate of autonomous factors is zero. Investment 1 is the sum of two components, investment in physical capital Ig and investment in human capital Iµ. The fraction of GDP that goes to physical capital investment is SK = 0.05 and the fraction of GDP that goes to human capital investment is SH = 0.05. (i) Convert the production function to a function relating Y/N to both K/N and H/N. (ii) Find the steady-state physical capital-labor ratio and the steady - state human capital - labor ratio. (iii) Find the steady – state per person output. 2.

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