Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
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Chapter 6, Problem 7AP
To determine
To know: The long run growth rates of physical capital, human capital and output of an economy.
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Consider an economy described by the production function: Y = F(K, L) = K^0,3L^0,7
A. What is the per-worker production function?
B. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.
An economy has the per-worker production function yt=f(kt)=4kt)0.4,
where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04.
Saving is St=0.5Yt,
where St is total national saving and Yt is total output.
The slope of the per worker production function is given by
f' (kt)=1.6kt-0.6 .
What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.
Suppose that the production function is Y = 10 ( K )^1/4 ( L )^3/4 and capital lasts for an average of 50 years . Assume that the rate of growth of population equals 0 and saving rate s = 0.128 .
a. Calculate the steady - state level of capital per worker , output per worker , consumption per worker , saving and investment per worker , and depreciation per worker
b. Suppose that initial level of capital per worker is 100 , explain the moving process to the steady state . c . Use relevant graph to demonstrate .
Plsss provide detailed answers, thank you
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