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  5. Marcroeconomic Analysis:Solow Swan model 1 (ECON4019)

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Solow-Swan model without technology
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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...

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  • August 13, 2024
  • 10
  • 2023/2024
  • Lecture notes
  • Professor richard dennis
  • All classes

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  • solow swanmodel without technology

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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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