Question

Consider the Basic growth model from your text and lecture as defined below: Production function: GDP = f(At, Kt, Lt); where capital (K) and labor (L) are substitutes and technology (A) aids production

Demographic Behavior: Lt+1= Lt(1+n) = Nt+1; where n is the population growth rate, N is the total population and there is no unemployment

Capital and Savings/Investment Dynamics: Kt+1 = It + Kt(1-δ); It = St = s*Y; where δ is the depreciation rate of capital, s is the savings rate and investment is I.

Technology Change: At+1= At(1+λ); where λ is the constant growth rate of technology Suppose output would be Y*1 in the next period if nothing changed.

Part 2: Consider the savings/investment functions

c) What is the effect of an increase in the savings rate s on GDP growth?

d) How does the savings rate affect growth (what is the mechanism, 1-2 sentences)?

Now suppose that a country has a very low GDP, such that GDP per capita can purchase exactly enough food to exactly satisfy a minimum consumption constraint (meaning all households must consume at least that much).

e) What is the savings rate of this country?

f) What level of capital will this country achieve in the long run?

Answer #1

c) there will be no effect on GDP in period t because increase in savings would increase GDP of period t+1.

d) now, we think about the mechanism of growth by savings then first consider St which increases due to increase in s . Higher St means higher It. Higher It implies higher capital in t+1 period and higher output.

e) If GDP of a country is low then it's saving rate would be
less than s^{*}.

d) In future country would try to increase it's saving and hence
capital that much where it achieves the optimal output
y^{*.}

Consider the Basic growth model from your text and
lecture as defined below:
Production function: GDP = f(At, Kt, Lt); where capital (K) and
labor (L) are substitutes and technology (A) aids production
Demographic Behavior: Lt+1= Lt(1+n) = Nt+1; where n is the
population growth rate, N is the total population and there is no
unemployment
Capital and Savings/Investment Dynamics: Kt+1 = It + Kt(1-δ); It
= St = s*Y; where δ is the depreciation rate of capital, s is...

Consider the Solow growth model. The production function is
given by Y = K^αN^1−α, with α = 1/3. There are two countries: X and
Y. Country X has depreciation rate δ = 0.05, population growth n =
0.03, and savings rate s = 0.24. Country X starts with initial
capital per worker k0 = 1
Country Y has depreciation rate δ = 0.08, population growth n =
0.02, and savings rate s = 0.3. Country Y starts with capital per...

Suppose that output (Y ) in an economy is given by the following
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Suppose that the population remains constant. Solve for the
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= 1. For k0 = 0.5 and k0 = 1.5, as initial capital per capita, ll
the values of per capita capital, output, the MPK, savings,
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3- Growth Model
Suppose that the output (Y) in the economy is given by
the following aggregate production function.
Yt = Kt +Nt
where the Kt is capital and Nt is population.
Furthermore assume that the capital depreciate at the rate of ẟ and
That saving constant and proportion s of income you may assume that
ẟ>s
1-suppose that the population remains constant . solve
for the steady state level of capital per worker
2- now suppose that the population...

Assume that an economy is described by the Solow growth model as
below:
Production Function: y=50K^0.4 (LE)^0.6
Depreciation rate: S
Population growth rate: n
Technological growth rate:g
Savings rate: s
a. What is the per effective worker production function?
b. Show that the per effective worker production function
derived in part a above exhibits diminishing marginal returns in
capital per effective worker
C.Solve for the steady state output per effective worker as a
function of s,n,g, and S
d. A...

Consider how unemployment would affect the Solow growth model.
Suppose that output is produced according to the production
function Y = Kα [(1 – u)L]1-α where K is
capital, L is the labor force, and u is the natural rate of
unemployment. The national saving rate is s, the labor force grows
at rate n, and capital depreciates at rate δ.
a. Write a condition that describes the golden rule
steady state of this economy.
b. Express the golden rule...

Consider Solow’s growth model with the following production
function:
Y = AKaL1-a
What is the steady state level of per capita income and capital
if A = 50, savings rate is 0.08, the depreciation rate is 0.02 and
the population growth rate is 0.02? a is 0.50.
Work:
Steady state level of per capita
income: _________
Stead state level of per capita
capital: _________
If the savings rate increases to 0.10, what will be the new
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Suppose Canada’s aggregate production function is given by the
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Y = K^1/3 *(AN)^2/3
Variables are deﬁned as they were in class. Suppose the savings
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0.05), the population growth rate is 2% (gN = 0.02), and the growth
rate of technology is 4% (gA = 0.04).
a) Solve for the equilibrium level of capital per eﬀective worker (
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2. Consider a numerical example using the Solow growth model:
The production technology is Y=F(K,N)=K0.5N0.5 and people consume
after saving a proportion of income, C=(1-s)Y. The capital per
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