The Bennati-Drăgulescu-Yakovenko (BDY) game is an agent-based simple exchange game that models a basic economic system. The BDY game results in the agents’ wealth following a Boltzmann-Gibbs distribution. In other words, the result of the game is many “poor” agents and few “wealthy” agents. In this paper, we apply several tax and redistribution models to study their effect on the population’s wealth distribution by computing the resulting Gini coefficient of the system. We find that income taxes, both flat and progressive, that evenly redistributed taxed monies do little to change the Gini coefficient from the Boltzmann-Gibbs distribution. However, income taxes that are redistributed to the poorest agents can significantly lower the Gini coefficient, resulting in a more evenly distributed wealth distribution. Furthermore, we find that a very small wealth tax can lead to significant decreases in the Gini coefficient.

1.
T.
Piketty
,
Capital in the 21st Century
(
Harvard University Press
,
2014
).
2.
T.
Piketty
and
E.
Saez
,
Science
344
,
838
843
(
2014
).
3.
T.
Piketty
,
Am. Econ. Rev.
105
,
48
53
(
2015
).
4.
D.
Autor
,
Science
344
,
843
851
(
2014
).
5.
T.
Piketty
and
E.
Saez
,
Econometrica
81
,
1851
1886
(
2013
).
6.
E.
Farhi
and
I.
Werning
,
Q. J. Econ.
125
,
635
673
(
2010
).
7.
T.
Piketty
and
E.
Saez
,
Econometrica
81
,
1851
1886
(
2013
).
8.
N.
Irwin
, see https://www.nytimes.com/2019/02/18/upshot/warren-wealth-tax.html for “Elizabeth Warren Wants a Wealth Tax. How Would That Even Work?” (NYT, February 18, 2018).
9.
E.
Bennati
,
Int. Rev. Econ.
394
,
735
(
1988
).
10.
E.
Bennati
,
Rivista Internazionale di Scienze Economiche eCommerciali
394
,
735
(
1988
).
11.
A.
Dragŭlescu
and
V. M.
Yakovenko
,
Eur. Phys. J. B
17
,
723
(
2000
).
12.
V. M.
Yakovenko
and
J.
Barkely Rosser
, Jr.,
Rev. Mod. Phys.
81
,
1703
(
2009
).
13.
H. O. A.
Wold
and
P.
Whittle
,
Econometrica
25
(
4
),
591
595
(
1957
).
14.
S.
Guala
,
Interdiscip. Description Complex Syst.
7
(
1
),
1
7
(
2009
).
15.
J.
Li
,
B. M.
Boghosian
, and
C.
Li
,
Physica A
516
,
423
442
(
2019
).
16.
B. K.
Chakrabarti
,
A.
Chakraborti
,
S. R.
Chakravarty
, and
A.
Chatterjee
,
Econophysics of Income and Wealth Distributions
(
Cambridge University Press
,
Cambridge
,
2013
).
17.
E.
Scalas
,
U.
Garabaldi
, and
S.
Donadio
,
Eur. Phys. J. B
53
,
267
272
(
2006
).
18.
U.
Garibaldi
,
E.
Scalas
, and
P.
Viarengo
,
Eur. Phys. J. B
60
,
241
246
(
2007
).
19.
U.
Garibaldi
,
T.
Radivojeviè
, and
E.
Scalas
, in
Proceedings of Applications of Mathematics 2013
(
Institute of Mathematics, Academy of Sciences of the Czech Republic
,
Prague
,
2013
), pp.
77
87
.
20.
E.
Scalas
,
T.
Radivojević
, and
U.
Garibaldi
,
J. Econ. Interact. Coord.
10
,
79
89
(
2015
).
21.
D. V.
Schroeder
,
An Introduction to Thermal Physics
(
Pearson
,
New York
,
1999
).
22.
See https://dqydj.com/income-percentile-calculator/ for “Income Percentile Calculator for the United States in 2018,” July 12, 2018.
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