Essentials of Economics (MindTap Course List)

8th Edition

ISBN: 9781337091992

Author: N. Gregory Mankiw

Publisher: Cengage Learning

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Would you expect capital deepening to result in diminished1etmns? Why or why not? Would you expect improvements in technology to result in diminished returns? Why or why not?

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(Long Run)
The country of Prosperous has:
Production function: Y = 2 K1/2 (AN)1/2, where Y=output;K=capital; A=technology; and N=labor
Saving rate (s): 20% per year
Depreciation rate (d): 10% per year
Labor growth rate (n): 2% per year
Rate of technological change (g): 8% per year
a. Transform the production function into the relation between output per effective worker (Y/AN) and capital per effective worker (K/AN). Does the function exhibit diminishing return?

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(Long Run)
The country of Prosperous has:
Production function: Y = 2 K1/2 (AN)1/2, where Y=output;K=capital; A=technology; and N=labor
Saving rate (s): 20% per year
Depreciation rate (d): 10% per year
Labor growth rate (n): 2% per year
Rate of technological change (g): 8% per year
d. If the country of Prosperous aims to achieve the optimal level of steady state consumption, what would you advise the government of the Prosperous to do regarding the country saving rate? Explain!

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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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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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(Long Run)
The country of Prosperous has:
Production function: Y = 2 K1/2 (AN)1/2, where Y=output;K=capital; A=technology; and N=labor
Saving rate (s): 20% per year
Depreciation rate (d): 10% per year
Labor growth rate (n): 2% per year
Rate of technological change (g): 8% per year
b. Calculate:
The steady state level of capital accumulation per effective worker
The steady state level of output, consumption and investment per effective worker
Graphically illustrate the above steady state condition.

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2. An economy has a production function:Yt = 3(squaredKt)(squaredLt).
The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress.
(a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1.
(c) Find the long-run growth rate of output per worker.
Now the economy has the following production function:Yt = 3Kt
but savings rate, depreciation rate, and population remain the same.
(d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt
(e) Find the equation for the evolution of capital per worker in terms of ktand kt+1.
(f) Find the long-run growth rate of output per worker.
(g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…

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(Long Run)
The country of Prosperous has:
Production function: Y = 2K1/2 (AN)1/2 ; where Y=output;K=capital; A=technology; and N=labor
Saving rate (s): 20% per year
Depreciation rate (d): 10% per year
Labor growth rate (n): 2% per year
Rate of technological change (g): 8% per year
c. Calculate the growth rate of the following variables when the economy achieves its steady-state:
Output per effective worker (Y/AN)
Output per worker (Y/N)
Output (Y)

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Parameters
Equations
s =0,20
marginal propensity to save
Y=WKr.L1-r
Production Function
u=0,02
Population growth rate
K.=s.f(k)−aK
Capital Accumulation
b=0,04
Technological growth rate
L./L= ?
Population Growth
a=0,05
Depreciation rate
W./W=b
Technological Progress
S=s.f(k)
Savings
a.
Find steady-state level of capital per effective labor: k*
b.
Draw a graph and show output function, actual investment and breakeven investment lines.
c.
Assume that in this economy, people start spending more and therefore marginal propensity to save decline permanently. What will happen to variables in the model (steady-state level capital per effective labor; output growth etc.).
d.
Instead of reduction in saving assume this time that we face lower fertility rate in the country. What will happen to variables in…

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Suppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.

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The current population of the United States is 327.2 million with 2.2% of the population is engaged in R&D at an efficiency rate of 1/375 per million persons per year. If R&D is the only source of total-factor productivity growth what is the growth rate of total factor productivity in the United States?

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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.

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