Marcroeconomic Analysis:Solow Swan model 1 (ECON4019)
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Solow-Swan model without technology
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Course
Marcroeconomic Analysis:Solow Swan model 1 (ECON4019)
Institution
University Of Glasgow
Book
Macroeconomics
The first part of lecture notes cover the role of endogenous growth models in understanding the development of various countries. The notes then go on to cover basic notation required to understand endogenous growth models. The final part of the lecture notes goes on describe the basic structure of...
Complete notes for Macroeconomics at UCL (Term 1 and Term 2)
Summary: Financial markets and institutions; Macroeconomics Institutions, Instability and the Financial System - Wendy Carlin & David Soskice
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Marcroeconomic Analysis:Solow Swan model 1 (ECON4019)
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Macroeconomic Analysis Revision Q
Continous KCt)
Discrete Kt
As Kapital is a stockrather than a How KC) refers to the amount
of Kapital available at point in timet
KE -refers to the amount of kapital at the & period
beginning -
For Flow variables like output , UC) refers to the quantity of goods produced
-
time E , While It
refers to the quantity of goods produced doing period
t
-
Measuring the change in output over time -
:
Aut =
Ut-UE-1 discrete
output is rising N r E. .
time - When EO
dt -
and falling when (H) O
de
#
=
AD-U(t-AE) continous time
At
At A
as
gets l the less time
closer to zero we have
Basic maths
14 Xz-* log(n)
= =
log(X) + log(z)
2U =
*
-
log(u) log(X) log(z)
= -
Z
*
3u =
y -
log(u)
=
xlogX
4 exp(aX)-log(4) =
xX
For derivatives we have the following -
U =
log(x)- discrete
aXX
n(t) log(x( -) - (+ ) max(t)
=
=
=
dt d(t)
, How calculate the growth rate of an economic variable : -
e.g output (4)
Take the derivative wrt time of the natural log of output
g(u(t)
at
=
=
Egy
>
-
Example :
-
Capital (K)
Find the growth rate of (
k(+) =
) capital labor ratio
Lt)
① Find natural logs
..
.( (t)) log(k(t))
log log(((t))
= -
② Take derivatives of each log variable Nr
.
.
time
g(k(t))
g(kH-GL
=
It at
This is equal to. .
I
-interpretation the
:- the growth rate of capital-per-worker
labor.
the growth rate of capitan
minus growth rate of
If the Capital-labor ratio is not changing overtime , then capital and
labor must be
graving at the same rate
Example 2 : -
Calculate the growth rate of output from the Cobb Douglas production In
x
*
!
-
4 = k
log(4(+)) xlog(((+)) + (1 x) log(L(t))
= - -
then
-
we take derivatives NrE time
log(u(t))
DEA
=
Og(k(t))
x
de
+ (1 x)
-
g(L(t))
It ]
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