Animals domestication and Animals domestication and agriculture agriculture as as outcomes of

Full text

Animals domestication and
Animals domestication and
agriculture
agriculture as
as outcomes of
outcomes of
collusion
collusion
Pedro
Pedro Cosme
Cosme Costa Vieira
Costa Vieira
Research – Work in Progress – nº164, January 2005


Faculdade de Economia do Porto - Rua Dr. Roberto Frias - 4200-464 - Porto -
Portugal Tel . (351) 225 571 100 - Fax. (351) 225 505 050 - http://www.fep.up.pt

1
ANIMALS DOMESTICATION AND AGRICULTURE AS OUTCOMES OF COLLUSION
Pedro Cosme Costa Vieira
Faculdade de Economia do Porto, s/n
4200-464 Porto, Portugal
pcosme@fep.up.pt
Abstract. Although it is know that there are circumstances where the competitive situation
does not promote social welfare maximization, collusion is usually associated with firms’
strategies that decrease welfare. In this paper, using the theoretical framework of the industrial
organization, I demonstrate in a model with two sectors that the economic revolution induced
by the animal domestication and the agriculture is an outcome from the strengthen in
collusion between human beings in the course of historical time and not vice-versa.
Keywords: Collusion, welfare progress, domestication and agriculture emergence.
JEL: O13, Q34, Q57
1. INTRODUCTION
In industrial organization, collusion is associated with firms’ strategies that decrease the
social welfare, being indispensable its persecution by public authorities, Posner (1975).
Nonetheless, it is conjectured since Schumpeter (1942) that the static efficiency that perfect
competition promotes decreases the dynamic efficiency because the imitation with no cost of
the new technical discoveries makes unprofitable to set substantial resources to R&D. And
R&D is very important because “80 percent of the change in labour productivity (…) can be
explained by ‘technical change’” by itself, Solow (1957). Being that, in general terms there is
a trade-off between the dynamic social welfare gain from firms’ collusion in R&D activities
(research joint ventures) and the static social welfare loss induced by anti-competitive firms’
behaviour. Sometimes it is acceptable a welfare lose in the short-term to improve the dynamic
efficiency of the society, (Brod & Shivakumar, 1999, Vonortas, 2000).
In historical terms, I conjecture that welfare improvements of high magnitude are associated
with collusion / cooperation (that is a more sympathetic word) increases between human
beings. That is because evolution of society to higher levels of integration and cooperation

2
that permits the decrease in defence expenditures, the labour division, investments in R&D
and the exploration of economies of scale are only possible if there is increases in the
collusion level between people.
My conjecture seems in accordance with data. Being that over time cooperation evolved,
Axelrod (1984), in a non-monotonous path, the existence of ups and downs, peace and war,
integration and disintegration, in the human society seems related to decrease in cooperation
and trust between human beings.
In this paper, using the theoretical framework of the industrial organization, I demonstrate
within a theoretical model with two sectors that the social revolution induced by the animal
domestication and the agriculture emergence only was possible with the deepening of
collusion between human beings. The collusion permits the emergence of private property
that turns possible that each human being captures the benefits of resources devoted to
agriculture and animals domestication.
In evolutionary terms, collusion between human beings deepens by the agglomeration of
more and more individuals in groups, structuring a heterogeneous society cemented with
variable intensity. Starting with the proximal family with strong ties, groups enlarged to clans,
tribes, and so on, less coupled. Groups that by chance (as Darwinism proposes) turn more
cooperative are, on average, more efficient that implies having a faster replicating rate. Being
so, in a limited resources environment, on a long-term trend the less cooperative human
groups becomes less numerous and the society as a whole evolves to a more cooperation
status quo. Being so, the competition decreasing is a dynamic evolution process that occurs
by the reduction in the number of groups.
Without loss, I use simpler algebraic assumptions. First, I assume that the society is
homogeneous and collusion deepens by the decrease in competition between each pair off
human beings. Second, I assume a long-term stable state (whatever that means in evolutionary
terms), building up a comparative static analysis where there is no more dynamic evolution.
Being so, the collusion level is exogenous to the model.
The model I present is more explicative than the Smith’s (1975) model where it is assumed
that agriculture is pre-existent to the decision of applying resources to it (plants have been
selected and domesticated in a previous step). Comparing to TV documentaries, I assume that
agriculture emergence is an evolutionary process that starts when humans destroy a single
plant that wild animals dislike it and endorse its counterpart.

3
2. THE MODEL
There is a market with two sectors interrelated. In the vegetation sector human beings are
producers using land and labour as inputs and animals are consumers. In the meat sector,
animals are producers and human beings are consumers (hunters).
For the sake of simplicity it is not explicitly considered in the model that human beings eat
vegetables. Nonetheless it may be understand each kg of meat as an equivalent weight of
vegetables.
Assumption 1 – There is a territory divided in B land parcels of dimension normalised to one.
Assumption 2 – The human being j lives on the land parcel j where the vegetation level is Vj
and there are Aj animals.
Assumption 3 – There is a parameter ξ ∈ [0, 1] that measures the degree of collusion
between human beings. When ξ = 0 there is no collusion and when ξ = 1 there is perfect
collusion. The parameter ξ quantifies the exclusiveness of each land parcel to the human
being that lives there.
Assumption 4 – Although ξ is endogenous to the human evolution dynamics, I assume a
static analyses where it is exogenous.
Assumption 5 – There is common knowledge (no private knowledge), being the collusion
level ξ perfectly enforced.
A) The vegetation sector
Assumption 6 – Human being produces vegetation using land and labour. Being that in each
time instant there is the quantity Vj of vegetation and human being works in developing
agriculture with intensity Laj, then the vegetation production is Gj > 0 that is convex
decreasing with Vj and concave increasing with Laj:
( )
VjjL
jL
kkjLVjGGj a
a
a
+
⋅








+
⋅+== 1
1
1
;10 (1)
Assumption 7 – Animals eat vegetation. In instant t, each one of the Aj animals eats
vegetation, being ξ the proportion of the effort devoted to eat vegetation in the land parcel j

4
plus the proportion (1 – ξ)/B of the effort devoted to eat vegetation in every land parcel. In
probabilistic terms, ξ measures the probability that in instant t the animal j is eating in the
land parcel j. Being so, the total (expected) number of animals feeding in the land parcel j is:
∑
=−⋅+⋅=B
iBAiAjjA1/)1(ξξ (2)
Assumption 8 – Each animal eating velocity Ej > 0 is concave increasing with the quantity of
existent vegetation (it eats more if there is more to eat) and convex decreasing with the
number of animals that feed in that land parcel (there is competition between animals for
vegetation):
( )
VjjA
Vj
kjAVjEEj +
⋅== 2
; (3)
The vegetation net growth velocity in the land parcel j is the difference between the
production Gj and the consumption Ej:
(
)
(
)
jAjAVjEjLVjGjVa⋅−= ;;
& (4)
Understood 1/Vj as a “shadow price”, expression (1) represents the supply function that is
increasing with price and expression (3) represents the demand function that is decreasing
with price. Expression (4) models the market surplus and encompasses a dynamic adjustment
“price” process.
When human being increases the agriculture intensity, there is a positive shift in the
vegetation supply function that will imply a positive effect in the meat sector. It is comparable
to a technological improvement in one sector that spreads out to all the economy.
B) The meat sector
Assumption 9 – The total vegetation an animal eats is the sum for all land parcels where it
may feed:
∑
=−⋅+⋅=B
iBiAViEjAVjEjE1/)1();();(ξξ (5)
Assumption 10 - Each animal reproduces at the velocity Nj that is concave increasing with
the vegetation that it eats. When an animal eats too little, it dyes of starvation, N(0) < 0:
( )
1
1
3+
−
⋅== jE
jE
kjENNj (6)

5
Assumption 11 – Human being j hunts animals in the land parcel j at velocity Hj > 0 that is
convex increasing with the quantity of animals there is, Aj, linear increasing with the time
devoted to hunt, Lh, and convex decreasing with the animals’ ferocity, Fj:
( )
FjAj
Aj
LkFjAjLHHj hh
+
⋅
+
⋅⋅== 1
1
1
;; 4 (7)
Assumption 12 – Human being j devotes Lhj work effort to hunting. He utilizes the
percentage ξ of the total hunting effort in the land parcel j and the unspent percentage (1–ξ) of
the total hunting effort in all land parcels (remember that ξ may well be interpreted as a
probability):
(
)
(
)
∑
=−⋅+⋅=B
i
hh FiAiBjLHFjAjjLHjH1;;/)1(;; ξξ (8)
The total number of animals from land parcel j that are hunted is:
(
)
(
)
∑
=−⋅+⋅=B
i
hh FjAjBiLHFjAjjLHHj 1;;/)1(;; ξξ (9)
As the hunting technology is linear in the effort devoted to hunting, assumption 10, being
jLh the total effort devoted to hunting in land parcel j by all human beings, it becomes:
(
)
(
)
∑
=−⋅+⋅=B
i
hh BFiAijLHFjAjjLHjH1/)1(;;;; ξξ (10)
(
)
FjAjjLHHj h;;= (11)
The net animals’ growth velocity in the land parcel j is the difference between the production
Nj⋅ Aj and the consumption Hj:
(
)
(
)
FjAjjLHAjjENjAh;;ξ⋅−⋅=
& (12)
Assumption 13 – Human beings may decrease the animals’ ferocity by using domesticating
with intensity Ldj, being this technology convex decreasing:
( )
jL
kjLFFj d
d
+
⋅== 1
1
5 (13)
This assumption results from accepting that domestication results from an ecological
evolution: some animals have a slightly higher ferocity level than others; when a high ferocity
level animal is hunted, on average the animal population evolves to a less ferocity level and
vice-versa. The extra effort used in hunting an animal that is fiercer than the average is the

6
domestication intensity. In evolutionary terms, this permits humans to set the animals level of
ferocity.
Understood 1/Aj as a “shadow price”, expression (6) represents a supply function that is
increasing with price and expression (7) represents a demand function that is decreasing with
price. Expression (12) models the market surplus and encompasses a dynamic adjustment
“price” process.
When human being increases the domestication intensity, there is a positive shift in the meat
demand function. It is equivalent to an increase in income.
Resuming, the model condenses that in each time instant human being j sets Lhj effort devoted
to hunting, Laj effort devoted to agriculture and Ldj effort devoted to animals’ domestication.
From this decision, it results a certain level of consumption jH that is dependent of the other
human beings decisions and the collusion level ξ between human beings:
),,(jLjLjLHjHdah
= (14)
C) Human utility function
Assumption 14 – The utility function is increasing with consumption jH. Although taking
into account consumption in all periods, in a stead state, the utility function is assumes to be:
(
)
jHkLLLUdah ⋅=6
,, (15)
Assumption 15 – The human beings maximize the utility subjected to the “technology” jH
and the total working effort Y:
( )
{ }





++=
=
=dah
dah
dah
LLL LLLY
LLLHjH
asLLLUMaxYvdah
),,(
..,),,(
,, (16)
Assumption 16 – The decision of human beings is assumed in a condition of Cournot-Nash
equilibrium: each human being sets the strategy that maximizes his utility assuming that all
other human beings do not respond to changes in his strategy.
Assumptions 2, 5, 8 and 9 formalise that the competition decreases when ξ increases, being
this perfectly enforced.

7
3. MAIN PROPERTY OF THE THEORY
As the emergence and development of agriculture and domestication is a long-term process, I
assume a long-term stable state (whatever that means in evolutionary terms), building up a
comparative static analysis where there is no more dynamic evolution. Being so, the collusion
level is exogenous to the model. In a steady state, the velocity of variation of the quantities of
vegetables and animals formalised in expressions 4 and 12 is zero.
Proposition – When collusion between human beings increases, there is an increase in the
effort devoted to agriculture and to the domestication of animals. This increase induces a
raise in the quantity of vegetation, in the number of animals, a welfare improvement and a
decrease in the animals’ ferocity.
Proof. First, I will compare the situation were human beings are perfectly colluded with the
situation where human beings are in perfect competition. Second I simulate the in between
evolution of the endogenous variables.
Perfect collusion (ξ = 1): Each human is monopolist in his land parcel.
Expressions (4) and (12) are a non-linear system with two variables, Vj and Aj that may be
simplified:
( )
( )



=⋅
⋅=
FALHAEN
AAVELVG
h;;
);(),( (17)
[
]
[ ]










⋅−−+⋅⋅−+−⋅=
⋅⋅+−+−−⋅=
⇔VkkCCCA
kCkACkACkV
)1()1(45.0
4)/()/(5.0
221
2
22
202
2
0202 (18)
With 1)1(;
1
1
;
1212
53
4
1100 +⋅−−=
++
+
⋅⋅=
+
⋅+= VkCC
Lk
L
L
k
k
C
L
L
kkCd
d
h
a
a (19)
Calibrated the constants, this non-linear equations system is easily computed by relaxation in
a datasheet. Computed Aj, one obtain easily jH by expression (10).
Perfect competition: Each human being is a tiny part of the total.
The action of a single human being does not improve the production of vegetation nor
decreases the ferocity of animals. Being so, it is obvious that human being will employ all his
effort hunting (Lh = Y, Ld = 0 and La = 0).

8
Calibration and simulation: I assume that k0 = 1, k1 = 9 (the agriculture improves the
production of vegetables at most 10 times), k2 = 2 (it scales the animals’ technology of eating
vegetable), k3 = 2 (it scales the technology of producing meat), k4 = 1 (it scales the technology
of hunting animals), k5 = 10 (it scales the ferocity of the animals), k6 = 332.8 (normalised
maximum utility to 100) and Y = 5 (it is the average number of hours per day that OCDE’s
workers devote to work).
Using a Microsoft-Excel 2002™ datasheet, in the situation of perfect competition where Lh =
5, Ld = 0 and La = 0, it results from expression (17) that the vegetation production level is G =
0.532, the meat production level is N = 0.126, the ferocity level is F = 10 and the welfare
level is v(5) = 41.82. Using the Solver tools, it results from the maximization of expression
(17) that in perfect collusion Lh = 2.930, Ld = 1.369 and La = 0.701 that implies a vegetation
production level G = 1.499, a meat production level N = 0.301, a ferocity level F = 4.221 and
a welfare level v(5) = 100.00.
This two extreme situations show the appearance of domestications and agriculture when
human beings pass from a situation of perfect competition to a situation of perfect collusion.
In the next figures I show that there is an monotonous increase in the working effort spent in
agriculture, La and domestication, Ld with the increase level of collusion (fig.1) and that it is
accompanied with an improvement in the welfare (fig.2). The model was implemented in
Microsoft - Visual Basic 6.0 ™.
2,5
3,0
3,5
4,0
4,5
5,0
00,2 0,4 0,6 0,8 1
Collusion level
L
a
L
d
L
h
Fig. 1 – Working effort employed in agriculture, domestication and hunting

9
40
50
60
70
80
90
100
110
00,2 0,4 0,6 0,8 1
Collusion level
Welfare level
Fig. 2 – Welfare evolution with the increase in collusion level
Both comparing the two extreme situations and observing the simulation represented in
figures 1 and 2, the increase in collusion between human beings promotes the appearance of
the agriculture and domestication of animals and is associated with an improvement in the
social welfare. QED
4. CONCLUSION
Collusion is normally associated with strategies that decrease the social welfare, being
indispensable its persecution by public authorities. Nonetheless, it is conjectured at least since
Schumpeter (1942) that the static efficiency that perfect competition promotes may decrease
the dynamic efficiency because the imitation with no cost of the new discoveries makes
unprofitable to affect substantial resources to R&D.
In this paper I demonstrate within a theoretical model that the animal domestication and the
agriculture may be the outcome of increases in collusion level between human beings. The
collusion permits the emergence of private property that turns possible that each human being
captures the benefits of resources that he devotes to the development of agriculture and
animals’ domestication. Being so, it is not the economic development that promotes the
evolution of the society to new levels of cooperation and pacification (increases in collusion)
but the contrary: the cooperation and pacification of the society permits the economic
development.

10
REFERENCES
Axelrod, Robert (1984), The Evolution of Cooperation. New York: Basic Books.
Brod, A., Shivakumar, R., 1999. Advantageous semi-collusion. Journal of Industrial
Economics, 47: 221-230.
Posner, Richard A. (1975), "The Social Costs of Monopoly and Regulation," Journal of
Political Economy 83 (Aug. 1975), pp. 807-827
Schumpeter, Joseph (1942), Socialism, Capitalism and Democracy, Harper & Brothers: New
York.
Smith, Vernon L. (1975), “The Primitive Hunter Culture, Pleistocene Extinction, and the Rise
of Agriculture”, Journal of Political Economy, 83, pp. 727-55.
Solow, Robert (1957), "Technical Change and the Aggregate Production Function", Review of
Economics and Statistics. 39, pp. 312-330.
Vonortas, Nicholas S. (2000), “Multimarket contact and inter-firm cooperation in R&D”,
Journal of Evolutionary Economics, 10, pp. 243 – 271.
APPENDIX
From equation system of expression (17) to expressions (18) and (19):
First equation
(
)
(
)
2
02
2
0202
002
2
2
002
2
2
2
2200
20
210
2
4)/()/(
0)/(
0)(
)1()(
1
1
1
;;
k
CkACkACk
V
CVACkVk
ACVCAkVAk
VAkVAkVCAC
VVAkVAC
A
VA
V
k
VL
L
kk
AAVELVG
a
a
a
⋅
⋅⋅+−+−−
=
=−⋅−+⋅
=⋅−⋅−⋅+⋅⋅
⋅⋅+⋅⋅=⋅+⋅
+⋅⋅⋅=+⋅
⋅
+
⋅=
+
⋅








+
⋅+
⋅=

11
Second equation
(
)
(
)
[ ] [ ]
[ ] [ ]
[ ] [ ]
2
)1()1(41)1(1)1(
0)1()1(1)1(
0)1()1()1(
)1()1()1(
1
1
)1(
)1(
1
1
1
1
)1(
)1(
1
1
11
1
;;
221
2
2121
22121
2
121
2
22
212
1
2
2
5
4
2
2
3
43
VkkCVkCVkC
A
VkkCAVkCA
ACVkCAAAVkVk
AVkCAAVk
A
C
AVk
AVk
Lk
L
A
Lk
AVk
AVk
k
FA
A
LkA
E
E
k
FALHAEN
d
d
h
h
h
⋅−−+⋅⋅−+⋅−−+−⋅−+−
=
=⋅−−+⋅+⋅+⋅−−+
=⋅+⋅+⋅+++⋅⋅−−⋅−−
+⋅+⋅=+⋅−⋅−
+
⋅=
+⋅+
−⋅−
++
+
⋅
+
⋅⋅=
+⋅+
−⋅−
⋅
+
⋅
+
⋅⋅=⋅
+
−
⋅
=⋅

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