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Fine arts in Solow model: a clarification
Jason (JenShan) Kao
YeungNan Shieh
Taiwan Institute of Economic Research
Department of Economics, San Jose State University
Abstract
This paper shows that the Saito version of Solow growth model contains an error. It corrects
this error. It further applies some builtin functions of Mathematica to the correct version of
Solow economic growth model and derives some interesting graphs from the Solow
convergent paths.
We thank M. Wen and especially an anonymous referee for valuable discussions and comments. Any errors are sole
responsibility of the authors.
Citation:
Kao, Jason (JenShan) and YeungNan Shieh, (2008) "Fine arts in Solow model: a clarification."
Economics
Bulletin,
Vol. 1, No. 2 pp. 120
Submitted:
January 11, 2008.
Accepted:
February 22, 2008.
URL:
http://economicsbulletin.vanderbilt.edu/2008/volume1/EB08A00002A.pdf
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View Full Document1. Introduction
Recently, in
Economics Bulletin
, Saito (2007) applies some builtin functions of
Mathematica to derive some interesting and important graphical illustrations of the
famous Solow full employment equilibrium growth model.
Saito’s graphical illustrations
are based on the following differential equation:
= (1 – s)f(k) – (n +
δ
)k
(6)
•
k
where
k = K/L
,
n
= labor force growth rate,
δ
= depreciation rate,
s
= saving rate, and the
dot indicates the rate of change over time. To utilize the algorithm for computing, Saito
assumes that
f(k) = k
α
for
α
є
(0, 1)
and evaluates whether 
k*  k
 is larger than
ε
or not.
If 
k*  k

>
ε
turns to “TRUE”, Saito proceeds to the next stage with capital accumulation
according to
k
j+1
= k
j
+
•
k
j
= k
j
+ (1 – s)f(k
j
) – (n +
δ
)k
j
(10)
where
k*
(capital stock per labor at steady state)
= [(1 s)/(n +
δ
)]
[1/(1
α
)]
,
k
j
= the capital
stock per labor at
j
th stage of computing for
j = 0, 1, 2, ….
, where
k
0
is the positive
initial capital stock per labor.
Once 
k*  k

>
ε
turns to “FALSE”, then the computing
stops.
However, equations (6) and (10) contain an error.
They are different from the
basic differential equation of Solow growth model.
Since the purpose of Saito (2007) is
to offer alternative analyzing tools in teaching economic growth theory, it is necessary to
provide a correct version of Solow growth model.
The purpose of this paper is to correct the error in equations (6) and (10).
Using the
correct version of Solow’s differential equation, this paper further applies Saito’s
numerical examples to obtain some different graphical illustrations based on Solow’s
convergent paths.
2.
Solow growth model
The Solow full employment equilibrium growth model considers an economy that
produces a single consumptioninvestment good. This economy can be described by the
following system of five equations, in which the government sector is ignored for the
sake of simplicity.
Y = C + I
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