Optimal levels of fertilization under risk: the potential for corn and wheat fertilization under alternative price policies in Argentina


Janvry, A.De

American Journal of Agricultural Economics 54(1): 1-10

1972


Because economic return from fertilization is stochastic, a precise assessment of the risk in fertilizer investment is critical, especially in less-developed countries. Using maize and wheat fertilizer response data from the Argentine Pampa, production conditions under which use of fertilizer would be economical are determined. Government protection of an obsolete fertilizer industry, high fertilizer prices, and inadequate tax concessions for users retard development of modern fertilizer technology. Despite current prices, fertilization would be possible on a majority of Argentinian farms. Lack of use is attributed to the unavailability to farmers of technical and economic information. Social gains from alternative fertilizer price policies are calculated.

Optimal
Levels
of
Fertilization
Under
Risk:
The
Potential
for
Corn
and
Wheat
Fertilization
Under
Alternative
Price
Policies
in
Argentina*
ALAIN
DE
JANVEY
Because
economic
return
from
fertilization
is
stochastic,
a
precise
assessment
of
the
risk
in
fertilizer
investment
is
critical,
especially
in
less-developed
countries.
Using
corn
and
wheat
fertilizer
response
data
from
the
Argentine
Pampa,
production
conditions
under
which
use
of
fertilizer
would
be
economical
are
determined.
Government
protection
of
an
obsolete
fertilizer
industry,
high
fertilizer
prices,
and
inadequate
tax
breaks
for
users
retard
development
of
modern
fertilizer
technology.
Despite
current
prices,
fertilization
would
be
possible
on
a
majority
of
Argentine
farms.
Lack
of
use
is
attributed
to
the
unavailability
to
farmers
of
tech-
nical
and
economic
information.
Social
gains
from
alternative
fertilizer
price
policies
are
calcu-
lated.
p
ARTICULARLY
in
nonirrigated
farming,
the
physical
outcome
of
fertilization
is
stochas-
tic
since
it
depends
upon
noncontrollable
climatic
events.
The
economic
return
from
fertilization
is,
hence,
itself
stochastic;
and
it
is
of
importance
to
assess
as
precisely
as
possible
the
level
of
risk
that
farmers
assume
when
they
invest
in
fertilizers.
This
is
especially
true
in
many
less-developed
countries
where
farmers
face
relatively
unfavorable
input-output
price
ratios,
thus
working
within
narrow
profit
mar-
gins.
These
farmers
in
addition
usually
do
not
have
the
financial
resources
to
bear
losses
in
bad
years,
since
fertilizers
are
purchased
on
short-
term
credits
without
insurance
schemes
that
would
allow
them
to
spread
over
successive
crops
the
risks
assumed
in
any
one
year.
Finally,
farmers
may
be
only
in
the
early
process
of
adopting
fertilizers
as
a
new
tech-
nology,
and
a
failure
to
assess
the
risk
they
have
to
assume
in
using
particular
fertilizer
doses
may
lead
to
serious
setbacks
in
the
spread
of
technological
changes.
This
is
es-
pecially
relevant
now
when
promoting
further
geographical
expansions
of
the
Green
Revolu-
tion
is
of
such
concern.
Added
to
these
considerations
is
the
fact
that
fertilizer
trials
are
scarce,
again
particularly
in
less-developed
countries;
and
it
is
useful
to
try
*
Giannini
Foundation
Paper
No.
329.
I
am
indebted
to
G.
Edward
Schuh,
Lehman
Fletcher,
Lowell
Hardin,
Darrell
Fienup,
and
the
members
of
the
Ford
Foundation
Proyecto
Pro
Economia
Agraria
in
Buenos
Aires
for
helpful
suggestions;
also
to
T.
W.
Schultz
for
bringing
the
problem
to
my
attention.
ALAIN
DE
JANVEY
is
assistant
professor
of
agricultural
economics
at
the
University
of
California,
Berkeley,
and
Ford
Foundation
project
specialist
in
Argentina.
to
extrapolate
the
experimental
results
avail-
able
to
other
climatic
and
production
condi-
tions.
This
can
be
done
partially
by
charac-
terizing
the
distribution
function
of
the
un-
controllable
factors
that
affect
yields.
In
this
paper
a
method
to
assess
the
risk
at-
tached
to
the
application
of
particular
fer-
tilizer
doses
is
proposed.
The
frequency
dis-
tribution
of
the
internal
rates
of
return
that
can
be
gotten
from
any
specific
investment
in
fertilizers
is
obtained.
Of
particular
interest
here
is
the
probability
that
farmers
must
recover
at
least
the
cost
of
using
fertilizers.
The
method
is
applied
to
Argentine
data
of
corn
and
wheat
fertilizer
response
in
the
humid
Pampa
under
nonirrigated
conditions.
It
is
used
to
assess
the
production
conditions
under
which
present
use
of
fertilizers
is
economical.
This
leads
to
a
partial
interpretation
of
the
causes
of
technological
stagnation
in
that
country.
It
also
permits
an
estimation
of
the
economic
returns
from
fertilization
if
relative
prices
were
lower
than
at
present.
In
doing
so,
a
rough
lower
estimate
of
the
social
returns
from
alternative
fertilizer
price
policies
can
be
obtained.
Strategy
Fertilizer
response
of
corn
and
wheat
is
de-
termined
by
a
set
of
controllable
and
non-
controllable
factors.
Other
than
fertilizer
doses
and
cultural
practices,
the
most
important
con-
trollable
factor
is
soil
fertility
which
is
de-
termined
in
part
by
recent
use
of
the
land.
Cereal-intensive
crop
rotations
will
generally
deplete
the
natural
fertility
of
the
land,
and
fertilizers
play
the
role
of
substitutes
for
that
lost
fertility.
The
lower
the
soil
fertility,
the
2
/
DE
JANVRY
Am.
J.
Agr.
Econ.
higher
fertilizer
response
is
expected
to
be.'
These
considerations
indicate
that,
in
studying
fertilizer
response
in
the
context
of
production
functions,
it
is
indispensable
not
only
to
char-
acterize
soil
fertility
as
a
determinant
of
yield
but
also
to
allow
for
interactions
between
fer-
tilizer
and
soil
fertility.
In
this
way
the
es-
timated
marginal
productivity
of
fertilizer
may
shift
downward
when
soil
fertility
increases,
even
though
soil
fertility
and
yield
have
a
positive
direct
relationship.
Soil
fertility
is
characterized
in
this
paper
by
its
content
of
organic
matter.'
Noncontrollable
factors
may
or
may
not
be
stochastic.
Among
the
nonstochastic
ones
are
the
natural
characteristics
of
the
soil,
for
ex-
ample,
its
permanent
wilting
point.
Stochastic
factors
are
weather
characteristics
such
as
hail,
frost,
rainfall,
and
temperature.
In
analyzing
experimental
data
of
the
type
here,
the
conse-
quences
of
the
two
first
events
appear
as
bi-
nomial
variables
since
some
trials
are
charac-
terized
as
having
failed
because
of
hail
or
frost;
and
their
results
are
not
reported,
presumably
because
yields
would
not
have
been
sufficient
to
cover
harvesting
costs.
Rainfall
and
tem-
perature
affect
yields
differently
depending
on
the
growth
stage
of
the
crop.
Rainfall
will
be
characterized
by
soil
humidity
or
by
quantity
of
rain
in
each
of
several
critical
periods
of
the
growth
of
corn
and
wheat—seeding
and
tassel-
ing
for
corn
and
seeding,
stooling,
and
tasseling
for
wheat.
Because
substitution
and/or
corn-
plementarity
possibilities
exist
between
periods
of
rain
in
different
critical
periods,
it
is
neces-
sary
to
determine
the
joint
probability
of
rain-
fall
events
in
the
various
critical
periods
that
permit
the
attainment
of
the
same
level
of
yield.
Specify
a
response
function
of
the
class
y
=
A
11
Xtii•(x)ee(x)
where
f
i
(X)
and
g(X)
are
polynomials
of
any
degree
in
the
arguments
of
the
vector
X
of
factors
of
production.
If
g(X)
=0
and
f
i
(X)
1
At
least
within
a
reasonable
range
of
depletion
where
the
structural
characteristics
of
the
soil
have
not
been
de-
stroyed.
2
Because
the
soil
never
freezes
in
the
Argentine
corn
belt,
decomposition
of
organic
matter
occurs
all
through
the
fall
and
winter
months.
Consequently,
a
high
percentage
of
the
organic
matter
in
the
land
is
in
assimilable
form
at
seeding.
For
this
reason,
organic
matter
offers
a
good
characteriza-
tion
of
soil
fertility.
=a.,
the
function
reduces
to
a
Cobb-Douglas;
if
g(X)
=
E
13
;
X,
and
f,(X)=a
i
,
it
reduces
to
a
transcendental
function
[6];
and
if
g(X)
=
0,
it
reduces
to
a
Cobb-Douglas
with
variable
elasticities
of
production
[1
1].
On
the
basis
of
the
above
considerations,
specialize
it
to
Y
=
A
IV
A.
(M)
F
f
F
()
.
eg(N
,F
,NF)MbaR
Xi
Y
ie
Sip
where
Y=
yield
N=
nitrogen
F
=
phosphorus
M=
organic
matter
content
of
the
land
R=
stochastic
index
character-
izing
weather
X
i
=
cultural
practices
followed
and
the
soil
conditions
D,=
geographical
or
varietal-
dummies
fN(M)
and
f
F
(M)
=
polynomials
in
M
which,
using
a
goodness-of-fit
cri-
terion,
were
found
to
be
generally
best
specified
as
quadratics
MAP
=
b1
b2M
2
,
/FOP
=
b
3
b4M
2
and
g(N,
F,
NF)
=
a
linear
function
in
N,
F,
and
NF;
since
the
estimated
parameters
of
this
function
turned
out
never
to
be
sig-
nificant,
it
is
dropped
in
the
following
development.
The
weather
index
R
is
of
the
form
R=[jW
k
flk
where
Wk
denotes
soil
moisture
or
rainfall
con-
ditions
in
the
kth
critical
period.
If
a
o
=
A
Mb
5
al
=
b
2
M
2
cr2
=
b3
b4M
2
the
function
reduces
to
a
Cobb-Douglas
with
variable
parameters
in
the
only
two
inputs
that
have
prices
and
about
which
an
economic
de-
cision
has
to
be
made
Y
=
otoRNaiF«,.
February
1972
FERTILIZATION
UNDER
RISK
/
3
1
For
a
maximum
in
the
profit
function
to
exist,
it
is
necessary
to
have
bi
+
(b2
b4)./1/
2
<
1.
Equating
the
marginal
productivities
to
price
ratios
for
N
and
F,
the
optimum
fertilizer
doses
N
o
and
F
o
are
given
by
1
log
N
o
=
[log
a
o
R
(a
z
1)
log
ai
1
at
az
PN
a
2
log
a
2
(a
2
1)
log
(1
+
P
F(x
>
X)
=
1
x7
-
'e
z
lodx
mr(y)
f0
x
where
x
is
millimeters
of
rainfall
in
one
month.
Thom's
approximation
of
the
maximum
likeli-
hood
estimator
of
-y,
which
is
given
by
the
solution
of
the
quadratic
equation,
is
used,
12Zy
2
-6y-1=0
where
Z
is
the
natural
logarithm
of
the
ratio
of
the
arithmetic
to
the
geometric
mean
of
x,
that
is,
PF
a
2
log
(1
r)
p
i,
1
log
F
o
=
[log
a
o
R
(a
i
1)
log
a2
1
at
az
1
Z
=
log
log
x
to
being
the
number
of
observations.
The
maxi-
mum
likelihood
estimator
of
#
is
then
[13,
p.
+
a1
log
a
(a
i
I)
log
(1
+
r)
P
3911
PN
a
l
log
(1
+
r)
Here,
P
is
the
product
price
while
P
N
and
PF
are
the
prices
of
nitrogen
and
phosphorus,
re-
spectively;
r
is
the
interest
rate
over
the
period
between
seeding
and
the
sale
of
the
product.
If
the
levels
of
N
and
F
are
set
equal
to
one
when
no
fertilizer
is
applied
and
the
yield
ob-
tained
from
the
economically
optimum
fer-
tilizer
doses
is
denoted
by
Y
o
,
the
percentage
internal
rate
of
return
on
the
fertilizer
invest-
ment
is
P(Y
a
o
R)
IRR
0
=[
11100.
(1
-I-
r)(PNY0
PFFo)
This
internal
rate
of
return
is
a
stochastic
variable
since
the
weather
index
R
is
stochastic.
Costs
will
be
covered
if
/RR
0
.0,
and
it
is
im-
portant
to
characterize
the
probability
that
this
occurs.
In
general,
it
is
necessary
to
char-
acterize
the
frequency
distribution
of
/RR
o
conditionally
upon
the
levels
of
N
and
F
and
for
given
prices,
M,
X,
and
D
so
that
farmers
may
decide
upon
the
levels
of
fertilizer
use
ac-
cording
to
their
aversion
for
risk.
In
the
studies
of
Barger
and
Thom
[1],
the
cumulative
frequency
distribution
of
rainfall,
within
intervals
of
one
or
several
weeks,
is
well
adjusted
by
the
incomplete
gamma
function.
Using
monthly
rainfall
reports,
the
incomplete
gamma
function
can
be
adjusted
=
7
/
1
.
Karl
Pearson's
table
of
the
incomplete
gamma
function
can
be
used
to
tabulate
the
function
[
9
]
u(p+o
v2
r(u,
1
p)
=
e
-
vdy
r(p
+
1)1
0
y
v
where
p
=
1,
y=
x/(3,
and
u
=
0071/2).
There
exists
a
one-to-one
correspondence
be-
tween
IRR
and
the
weather
index
R
for
given
P
N
/P,
P
F
/P,
r,
M,
X,
and
D
plus
either
the
profit
maximation
rule
or
given
levels
of
N
and
F.
And
since
log
R
k
log
Wk,
there
is
an
infinity
of
combinations
of
rainfall
patterns,
characterized
by
the
levels
of
W1,
W2,
,
WK,
that
permit
the
attainment
of
the
same
internal
rate
of
return.
3
For
given
levels
of
W,,
,
WK-
1
,
the
level
of
W
A
that
will
satisfy
a
given
iso-R
curve
of
level
R
o
(say)
is
3
This
method
tends
to
overestimate
the
probability
of
reaching
a
particular
yield
level
if
the
elasticity
of
substitu-
tion
between
rainfalls
in
different
periods
is
in
fact
less
than
one.
Wk
should
then
be
introduced
in
the
weather
index
with
a
functional
form
different
from
the
Cobb-Douglas.
In
particular,
if
there
is
more
complementarity
than
substi-
tutability
among
rainfalls
in
successive
periods,
interactions
among
them
with
positive
expected
signs
should
be
speci-
fied.
f
K
-11(W
1
,-
,W
K-1
IR
O
)
f(W1)f(W2)
CO
4
/
DE
JANVRY
Am.
J.
Agr.
Econ.
1
K-1
log
W
K
=
[log
Ro
E
okwd
OK
or
W
K
=
h(W
1,
"
,
W
K-1/
R0)•
Assuming
the
W's
to
be
independently
dis-
tributed
gamma
variables,
the
cumulative
density
function
of
R
will
be
obtained
by
in-
tegrating
over
the
variable
interval
of
integra-
tion
F(R
>
R
0
)
=
q
w
2
=0
f(W
K
)dW
i
dW
2
al
K
.
q
is
the
binomial
probability
that
the
crop
will
not
be
destroyed
by
cataclysmic
events
like
hail
or
frost.
Since
the
parameters
of
the
gamma
functions
are
nonintegers,
an
analytical
solu-
tion
to
this
integration
does
not
exist.
Nu-
merical
integration
is
needed.
Once
the
frequency
distribution
of
R
and,
hence,
of
yields
and
of
internal
rates
of
return
has
been
obtained,
it
is
used
to
find
the
optimal
fertilizer
doses
for
a
given
level
of
risk
aversion
and
for
given
prices,
r,
M,
D,
and
X
variable
levels.
Optimality
is
defined
as
the
maximiza-
tion
of
expected
profits.'
Risk
aversion
corre-
sponds
to
a
statement
about
a
probability
level
that
characterizes
the
chances
with
which
an
individual
wants
to
cover
at
least
the
cost
of
fertilizer
use
in
any
particular
year.
For
ex-
ample,
a
producer
may
want
to
be
100
a-percent
sure
not
to
lose
money
in
his
fertilizer
invest-
ment.
The
objective
function
is
then
to
maxi-
mize
expected
profits
once
the
priority
goal
Pr(IRR
o
>0)=
a
is
satisfied.
Unconstrained
maximization
of
expected
profits
is
not
an
acceptable
criterion
here
be-
cause
the
variance
of
profits
may
be
large
and,
hence,
the
probability
that
losses
be
incurred
high.
By
restricting
the
solution
to
satisfy
Pr(IRR
o
>0)
=
.95,
for
example,
fertilizer
use
is
forbidden
when
costs
may
not
be
covered
in
more
than
one
year
out
of
20.
The
constraint
determines
the
subset
of
the
space
(PN/P,
Pp/P,r,
M,
X,
D)
over
which
maximization
of
4
Defined
here
as
net
income
and
not
in
the
Knightian
sense
of
the
difference
between
ex
ante
and
ex
post
returns.
expected
profits
can
be
performed
as
risk
aver-
sion
requirements
are
met.
Hence,
this
is
a
case
of
lexicographic
preferences
where
the
priority
goal
is
to
cover
cost
with
probability
a
and
the
secondary
objective
is
the
maximization
of
ex-
pected
profits.
Of
particular
interest
is
the
combination
of
prices,
r,
M
,
D,
and
X
levels
that
lead
to
a
zero
internal
rate
of
return
for
a
given
level
of
risk
aversion.
Specifically,
there
is
interest
in
the
relation
Py
=
f[MI
Pr(IRR
0
P
0)
=
a,
-
r,
X,
Id
which
can
be
named
the
"fertilization
possibil-
ity
frontier."
It
describes
the
set
of
relative
nitrogen
prices
and
soil
fertility
combinations
for
which
fertilizer
costs
are
just
covered
at
the
specified
level
of
risk
aversion.
Profits
are
posi-
tive
below
this
curve
and
negative
above
it.
It
shifts
upward
with
lower
levels
of
risk
aver-
sion
and
with
increases
in
the
X's
and
D's
that
are
positively
related
to
yield.
In
doing
so,
the
area
with
a
potential
for
fertilizer
use
expands.
To
determine
the
fertilization
possibility
frontier,
the
value
R*
of
the
weather
index
is
found
to
be
such
that Pr(R>
R*)
=a.
R*
is
used
to
solve
for
No,
F
o
,
Yo,
and
/RR
o
.
The
locus
of
points
where
/RR
o
=
0
is
the
frontier
since
Pr(IRR>
IRR
o
)=
a.
Analysis
Well-controlled
experiments
on
fertilization
were
conducted
in
Argentina
for
the
first
time
on
wheat
in
1969-70
and
since
1967-68
on
corn.
Few
data
are
available,
and
it
is
important
to
assess
the
results
obtained
in
a
probabilistic
framework
in
order
to
evaluate
their
generality
and
to
extrapolate
them
to
other
climatic
con-
ditions.
Fertilizer
use
on
cereal
crops
is
almost
non-
existent
in
Argentina.
It
has
been
estimated
that
some
0.2
percent
of
the
acreage
seeded
in
corn
was
fertilized
in
1968.
Wheat
fertilization
is
slightly
more
frequent,
mainly
because
cer-
tain
areas
have
been
continuously
dedicated
to
that
crop
and
now
face
serious
drops
in
soil
fertility
and
erosion
problems.
Nevertheless,
in
the
area
where
fertilizers
are
most
widely
spread,
a
recent
survey
[12]
indicated
that
only
about
12
percent
of
the
area
planted
in
wheat
had
been
fertilized.
As
a
result,
Argen-
tine
yields
of
corn
and
wheat
which,
50
years
ago,
were
similar
to
the
ones
obtained
in
the
FERTILIZATION
UNDER
RISK
/
5
February
1972
United
States
are
now
only
about
half
as
high.
5
While
grain
prices
are
substantially
below
world
market
levels
at
the
farm
gate
in
Ar-
gentina
(in
part
because
of
the
secular
under-
valuation
of
the
exchange
rate
which
adds
an
export
tax
that
generally
oscillates
between
5
and
10
percent
according
to
the
parity
of
the
peso
to
the
dollar),
nitrogen
prices
are
about
three
times
higher
at
the
farm
level
in
Argen-
tina
than
in
the
United
States.
Imports
of
anhydrous
ammonia
in
large
quantities
are
generally
not
possible
because
of
lack
of
storage
facilities
and
a
tax
rate
of
70
percent.
Imports
of
urea
(which
is
the
main
form
under
which
nitrogen
is
presently
applied),
ammonium
sul-
fate,
and
compounds
were
totally
forbidden
as
of
December,
1970.
6
Phosphates,
on
the
con-
trary,
are
not
produced
in
Argentina
and
are
imported
tax
free.
Their
prices
at
the
farm
level
are
comparable
to
those
found
in
the
United
States.
Table
1
shows
the
absolute
and
relative
prices
of
nitrogen,
phosphorus,
corn,
and
wheat
in
Argentina
and
the
United
States
in
1969.
All
prices
are
at
the
farm
level.
It
shows
that,
while
the
relative
price
of
nitrogen
to
corn
is
2.0
in
the
United
States
(that
is,
the
United
States
farmer
needs
to
sell
2
tons
of
corn
to
buy
1
ton
of
nitrogen),
it
is
8.1
in
Argentina—four
times
higher.
It
is
particularly
interesting
to
note
that,
if
Argentine
farmers
could
buy
their
nitrogen
at
U.
S.
prices
while
still
selling
their
corn
at
Argentine
prices,
the
relative
price
would
drop
to
2.9.
For
wheat,
the
relative
price
would
drop
from
7.5
to
2.7.
By
contrast,
phos-
phorus
prices
are
similar
in
Argentina
and
the
United
States,
the
price
ratio
of
phosphorus
to
wheat
being
somewhat
higher
in
Argentina
(4.4
compared
to
3.9)
since
wheat
prices
are
lower.
The
data
used
to
fit
a
response
function
for
corn
were
obtained
by
the
Instituto
Nacional
de
Tecnologia
Agropecuaria
(INTA),
the
na-
tional
institute
of
agronomic
research,
on
ex-
perimental
plots
located
on
farms
in
the
area
of
Marcos
Juarez
and
supposedly
managed
ac-
Genetic
improvements
were
aimed
at
maintaining
yields
on
soils
of
secularly
declining
fertility.
By
contrast,
the
spectacular
increase
in
U.
S.
yields
results
from
the
in-
teraction
of
genetical
and
chemical
innovations.
Since
January
1,1971,
import
of
all
nitrogenous
fertil-
izers
has
been
forbidden,
officially
to
protect
the
national
industry
from
dumping
which
is
taking
place
on
the
world
market.
Table
1.
Prices
of
corn
(C),
wheat
(W),
nitrogen
(N),
and
phosphorus
(F)
in
the
United
States
and
Argentina,
1969
Corn
Wheat
United
States
Argentina
U.
S.
dollars
per
bushel
1.16
1.15
.806
.914
U.
S.
dollars
per
ton
N
from
ammonium
92
289
N
from
urea
182
255
F
from
superphosphate
(46
percent)
161
196
Phosphorus
from
18-46-0•
165
147
P
N
/Pc
with
N
from
ammonium
2.0
9.2
P
N
/Pc
with
N
from
urea
3.8
8.1
PN.us/Pc.An
t
.
with
N
from
ammonium
2.9
PN,17B/PC.Arg.
with
N
from
urea
5.7
PN/Pw
with
N
from
ammonium
2.2
8.6
P
N
/Pw
with
N
from
urea
4.3
7.5
PN.178/PW.Ari.
with
N
from
ammonium
2.7
PN.US/PW.Arg.
With
N
from
urea
5.4
P
F
/Pw
3.9
4.4
P
N
=
$92
per
ton
(U.
S.)
for
the
United
States
and
$255
per
ton
(U.
S.)
for
Argentina.
cording
to
current
practices.'
The
estimated
function
is
log
Y
=
15.031
+
.117
log
N
.010
M
2
log
N
(-5.19)
(3.00)
(-1.95)
+
2.116
log
M
1.379
log
PW
(4.27)
(-3.82)
+
3.463
log
HS
+
1.940
log
HF
(6.10)
(3.62)
+
.392
log
PD,
R
2
=
.77
(11.32)
where
Y=
corn
yield
in
tons
per
hectare
N
=
kilos
of
nitrogen
per
hectare
M=
percent
of
organic
matter
of
soil
PW
=
permanent
wilting
point
in
percent
of
water
HS=
percent
of
soil
humidity
at
seeding
HF=
percent
of
soil
humidity
at
tasseling
PD=
plant
density
at
harvest
in
thousands
per
hectare
7
A
detailed
account
of
the
experimental
data
is
given
in
de
Janvry
[3].
In
de
Janvry
and
Koenig
[4],
several
other
experiments
conducted
by
INTA
are
analyzed
with
the
same
methodology
and
provide
results
highly
consistent
with
the
ones
reported
here.
IRR
0
=
200
In
o
=
0
35
37 37
35
31
1
24
14
210
219
225
226
.221
203
159
-
-
39
42 42
40
35
27
16
_
-
220
229
235
236
231
214
170
45
48 48
46
40
31
18
230
240
246
248
243
227
183
54
57
57
54
47
36
21
243
253
259
262
257
241
198
65
69
69
65
56
43
2
_
257
267
274
277
274
258
216
83
88
88
82
71
54
32
_
275
285
293
296
293
279
238
20
,.................
114
119
'
119
".....-
111
96
--"4•
73
43
4
297
308
316
320
319
305N5
48
-
176
184
183
170
146
111
64
7
327
339
348
353
354
342
304
89
_
P
N
p
8
7
6
5
4
3
IRR
0
=
300
2
M
6
/
DE
JANVRY
Am.
J.
Agr.
Econ.
Table
2.
Corn
fertilization
possibility
frontier
with
95
percent
risk
aversions
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
The
data
that
appear
in
each
cell
are
the
optimum
nitrogen
doses
No
in
kg/ha;
the
internal
rate
of
return
correspond-
ing
to
No:
/RRo
in
percent.
and
data
in
parentheses
are
t
ratios.
The
distribution
function
of
soil
humidity
was
derived
from
the
one
of
rainfall
by
using
a
linear
relationship
between
the
two
and
esti-
mated
from
seven
years
of
numerous
measure-
ments
of
soil
moisture
in
corn
fields.
Table
2
gives
the
fertilization
possibility
frontier
for
a
level
of
risk
aversion
of
95
percent.
An
interest
rate
of
5
percent,
a
plant
density
of
60,000,
and
the
average
observed
permanent
wilting
point
level
of
13.8
percent
were
used.
The
fertilization
possibility
frontier
appears
to
be
relatively
in-
sensitive
to
price
and
corresponds
to
a
soil
fer-
tility
of
3.4
percent
of
organic
matter.
Accord-
ing
to
soil
scientists,
about
half
of
the
acreage
presently
planted
in
corn
would
fall
within
the
frontier
[8].
Since
this
land
corresponds
mainly
to
smaller
farms
that
have
crop-intensive
ro-
tation
patterns,
it
means
that,
at
this
level
of
risk
aversion,
about
75
percent
of
the
corn-
producing
farms
could
actually
make
use
of
fertilizers.
Expected
profits
are
maximized
within
the
fertilization
possibility
frontier.
Table
2
gives
the
optimum
levels
of
fertilizer
use,
N
o
,
and
the
corresponding
internal
rates
of
return,
IRR
o
,
for
various
combinations
of
relative
prices
and
soil
fertility.
It
shows
that
even
under
present
prices
of
8
to
1
fertilizers
could
be
used
with
profits
on
lands
with
up
to
3.2
percent
organic
matter
at
the
95
percent
risk
aversion
level.
If
fertilizer
prices
would
drop
to
the
world
market
level
of
3
to
1,
doses
three
times
higher
could
be
used
and
rates
of
return
50
percent
higher
obtained
on
lands
with
up
to
3.4
percent
organic
matter.'
Data
on
wheat
fertilizer
response
were
generated
in
1969-70
by
the
INTA-Cimmyt-
8
Because
of
extensive
dumping
of
nitrogen
on
the
world
market,
the
conservative
assumption
is
made
that
Argen-
tina
could
import
this
fertilizer
with
a
consequent
farm
level
price
equal
to
the
United
States
price.
February
1972
FERTILIZATION
UNDER
RISK
/
7
Table
3.
Fertilizer
response
functions
for
wheat,
1969/70
Variables"
Region
Intercept
Log
N
Log
F
Log
M
AV
Log
N
M
2
Log
F
Log
LS
Log
LM
Log
LF
11.2
II-North
-
.1862
.0333
-
.0113
.9431
-
.0051
.0018
.0594
-
.0847
-
.0299
(Marcos
.81
Juarez)
(-
.267)b
(1.267)
(-
.429)
(
3.012)
(-1.097)
(
.379)
(
.348)
(-6.095)
(-1.943)
II-South
.4949
.1515
.1059
.5531
-
.0221
-
.0147
.4987
.3825
-
.7283
.73
(Pergamino)
(
.772)
(3.251)
(
2.216)
(
1.100)
(-2.959)
(-1.910)
(
8.184)
(
7.361)
(-4.990)
III
2.6327
.0278
.0145
-1.6804
-
.0012
.0021
.0005
.94
(Entre
Rios)
(
9.662)
(1.100)
(
.575)
(-8.542)
(-
.826)
(
1.479)
(
.013)
IV
.1924
.0246
.0986
.3246
-
.0002
-
.0015
-
.1000
-
.0667
.1510
.86
(Balcarce)
(
1.438)
(2.255)
(
8.470)
(
7.963)
(-
.632)
(
4.836)
(-4.174)
(-1.265)
(
2.556)
V.-South
-
.3593
.0394
-
.0571
.7932
-
.0048
.0150
.87
(Bordenave)
(-1.296)
(1.103)
(-1.410)
(
2.597)
(-
.873)
(
2.420)
N
=nitrogen
in
kg/ha;
F
=phosphorus
in
kg/ha;
M
=percent
organic
matter;
LS
=min
rainfall
at
seeding;
LM
=mm
rainfall
at
stooling;
LF
=ram
rainfall
at
wksling
b
Data
in
parentheses
are
I
ratios.
Ford
Foundation
program
[7]
for
all
the
eco-
logical
regions
of
Argentina.
The
response
func-
tions
estimated
are
given
in
Table
3
for
regions
II-North
(Marcos
Juarez),
II-South
(Per-
gamino),
III
(Entre
Rios),
IV
(Balcarce),
and
V-South
(Bordenave).
Data
for
regions
I
(Santa
Fe)
and
V-North
(Cordoba)
were
not
available.
In
several
cases,
rainfall
had
adverse
effects
on
yields
because
of
the
consequent
develop-
ment
of
weeds
and
pests.
In
general,
the
lack
of
control
of
weeds
and
pests
in
the
experiments
led
to
a
severe
underestimation
of
fertilizer
response
since
intensity
of
the
attack
and
fer-
tilizer
response
increased
with
rainfall.'
Again,
incomplete
gamma
functions
were
adjusted
to
the
distributions
of
LS,
LF,
and
LM
and
inte-
grated
numerically
to
obtain
the
cumulative
frequency
distribution
of
the
weather
index
R.
Table
4
gives
the
fertilization
possibility
frontier
for
a
level
of
risk
aversion
of
95
percent
in
region
II-South.
Under
present
prices
and
according
to
the
data
analyzed,
which
obvi-
ously
need
to
be
complemented,
fertilizer
use
would
not
be
possible
in
region
II-North"
but
possible
on
lands
with
up
to
2.7
percent
organic
matter
in
region
II-South
and
on
the
whole
acreage
in
regions
III
and
IV.
The
same
table
also
gives
the
optimum
nitrogen
(N
0
)
and
phos-
phorus
(F0)
doses
and
the
corresponding
inter-
'
Control
was
exercised
several
times
ex
post,
that
is,
after
an
outbreak
of
weeds
or
pests
made
it
necessary,
and
not
ex
ante
as
either
a
systematic
practice
or
part
of
the
experi-
mental
design.
The
analysis
of
earlier
results
[4]
shows
significant
fertilizer
response
in
that
region,
too.
nal
rate
of
return
(IRR
0
)
for
various
combina-
tions
of
nitrogen
prices
and
soil
fertility
for
region
II-South.
They
are
calculated
similarly
for
the
other
regions.
A
relative
price
of
4
was
used
for
phosphorus.
In
region
II-South
the
fertilization
frontier
corresponds
to
a
soil
fertility
of
2.7
percent
which
is
lower
than
for
corn
at
the
same
level
of
risk
aversion.
But
wheat
is
typically
grown
on
more
exhausted
lands
than
corn,
either
be-
cause
it
follows
corn,
sorghum,
or
sunflower
in
the
crop
rotation
patterns
[5,
p.
107]
or
because
some
areas
have
been
permanently
sown
in
that
cereal.
It
is
estimated
that
half
of
the
present
wheat
acreage
in
that
region
would
fall
within
the
fertilization
possibility
frontier.
A
notable
aspect
of
the
results
obtained
is
that,
while
optimum
fertilizer
doses
and
their
corresponding
internal
rates
of
return
are
highly
sensitive
to
climatic
conditions,
the
steepness
of
the
/./M
o
function
where
it
intersects
the
(PN/P,
M)
space
implies
a
high
stability
of
the
location
of
the
fertilization
possibility
frontier.
For
this
reason,
the
frontier
will
expand
only
slightly
with
lower
levels
of
risk
aversion.
For
example,
with
a
risk
aversion
level
of
75
per-
cent,
the
corn
frontier
would
shift
from
3.3
to
3.4
percent
organic
matter
at
current
prices.
Implications
Under
the
present
fertilizer
price
policy,
a
double
tax
write-off
is
allowed
farmers
on
their
fertilizer
costs.
But
the
small
farmers
whose
lands
lie
within
the
fertilization
possibility
frontier
because
they
are
used
intensively
and
8
/
DE
JA
NVRY
Am.
J.
Agr.
Econ.
Table
4.
Optimum
level
of
wheat
fertilization
in
region
II—South
(Pergamino)a
N.
70
109
66
105
58
93
49
79
38
63
28
47
18
31
9
18
1
5
183
189
195
198
199
193
177
137
15
-
8o
113
75
106
66
95
55
803
63
31
47
20
32
10
18
1
5
186
193
198
202
203
198
183
1)43
18
-
911
115
88
109
77
96
64
81
5o
64
3
47
23
32
12
18
1
5
190
197
203
207
208
204
189
1149
21
-
112
118
92
98
105
,
111
76
82
59
65
A
43
4
-
27
32
14
18
1
194
201
/
207
212
214
211
196
157
25
-
138
122
12
I.
9
11..
113
101
94
84
73
66
52
49
33
32
16
18
1
5
199
1
206
213
218
221
218
205
166
29
-
/
18o
127
167
118
146
104
120
86
93
68
66
49
42
33
20
18
2
5
1
204
212
220
226
229
228
215
177
35
-
251
133
232
123
202
108
165
89
127
69
90
5o
57
33
28
18
2
5
211
220
228
235
240
239
228
11
91
42
-
403
142
371
131
320
113
259
93
198
72
139
52
87
34
42\
18
3
5
221
230
239
2148
254
256
246
210
52
-
X
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
1
2.8
IRRo
=
200
IRR
o
=
0
P
O
P
8
6
5
3
2
The
data
that
appear
in
each
cell
are
the
optimum
nitrogen
(No)
and
phosphorus
(F
0
)
in
kg/ha;
the
corresponding
internal
rate
of
return
(IRRo)
in
percent.
who
could
make
a
good
use
of
fertilizers
to
relax
their
land
constraint
typically
have
incomes
below
taxable
levels.
Large
farmers
who
do
pay
income
taxes
have
lands
above
the
fertilization
frontier
and,
hence,
do
not
need
fertilizers.
Ironically,
the
tax
write-off
approach
as
an
incentive
to
fertilizer
use
is
irrelevant
for
both
categories
of
farmers.
High
fertilizer
prices
are
maintained
through
import
tariffs
and
restrictions
that
protect
a
monopolistic
national
fertilizer
industry
which
is
technologically
obsolete
and
operates
below
full
capacity
because
of
inadequate
demand
at
prevailing
prices.
Establishment
and
protection
of
this
industry
are
typical
of
the
import
sub-
stitution
policies
in
which
Argentina
and
most
other
Latin
American
countries
engaged
after
World
War
II.
Also
typical
are
the
prevalence
of
industrial
over
agricultural
interests
in
eco-
nomic
policy
and
the
disregard
of
the
external
cost
of
industrial
protectionism
on
agricultural
productivity
growth.
An
alternative
policy
would
consist
of
capitalizing
on
the
extensive
dumping
of
nitrogen
on
the
world
market
to
permit
temporary
imports
that
would
lower
nitrogen
prices
at
the
farm
gate
to
levels
com-
parable
to
the
ones
observed
in
the
United
States."
Once
fertilizer
demand
was
suffi-
ciently
high,
a
modern
technology
fertilizer
industry
could
be
developed
in
Argentina.
Present
Argentine
nitrogen
consumption
is
30,705
tons
a
year.
Modern
centrifuge
compres-
sion
plants
producing
1,000
tons
a
day
have
II
A
study
of
Tennessee
Valley
Authority
[101
calculates
that
the
world
demand
for
fertilizers
in
1970
is
satisfied
with
79
percent
of
world-invested
capacity
and
that
large
production
surpluses
will
exist
at
least
until
1975
in
the
United
States,
Europe,
and
Japan.
February
1972
FERTILIZATION
UNDER
RISK
/
9
costs
40
percent
below
the
present
200
tons
a
day
plant.
From
the
previous
analysis,
the
present
potential
demand
for
nitrogen,
both
at
actual
and
world
price
levels,
can
be
estimated.
This
permits
an
assessment
of
the
possibility
of
operating
a
low-cost
fertilizer
industry
in
Argentina.
Assuming
that
soil
fertility
is
uniformly
dis-
tributed
between
3/
1
and
M
u
,"
where
M„
is
on
the
fertilization
possibility
frontier,
the
opti-
mum
consumption
of
nitrogen
in
each
crop
and
region
is
given
by
f:
r
P
N
Pp
N
0
'="-
4,
M,
X,
D;
P
P
Pr(IRR
>
0)
=
.95]
f(M)dM
where
S
is
the
total
area
actually
harvested
in
that
crop
that
lies
within
the
interval
of
inte-
gration.
Taking
M
1
=1.5
percent
for
wheat
and
2.0
for
corn,
the
optimum
total
yearly
nitrogen
consumption
is
calculated
to
be
97,694
tons
when
relative
prices
are
8
and
281,853
tons
when
they
drop
to
3.
Added
to
present
con-
sumption,
the
totals
are
128,399
tons
under
present
prices
and
312,558
tons
under
potential
prices.
Thus,
it
would
seem
possible
to
establish
a
modern
industry
in
Argentina
as
soon
as
fertilizer
use
is
adopted
by
farmers
within
the
production
possibility
frontier.
A
lower
bound
to
the
social
rates
of
return
can
be
estimated
by
following
this
alternative
fertilizer
price
policy.
The
net
return
per
hec-
tare
of
lowering
fertilizer
relative
prices
from
8
to
3
is
given
for
each
crop
and
region
by
.5f
m„
P[(AYo
3N
0
4P
0
)
(A
Y
o
'
8N
0
'
4
Fo')if(
M)dM
where
,AY
0
is
the
increment
in
yield
due
to
application
of
the
optimum
fertilizer
doses
N.
and
F
o
for
given
prices,
M,
X,
and
D.
Assuming
again
that
acreage
harvested
remains
the
same
as
in
1969,
the
total
net
return
from
lowering
la
The
assumption
of
a
uniform
distribution
may
be
in-
adequate
since
f(M)
should
closely
resemble
the
frequency
distribution
function
of
farm
sizes.
On
the
other
hand,
the
results
are
robust
to
the
assumption
because
of
the
flatness
of
the
fertilizer
response
function
within
the
fertilization
possibility
frontier.
The
levels
of
M,
used
in
the
subsequent
integrations
are
based
on
the
soil
fertility
levels
observed
in
the
trials.
fertilizer
prices
would
be
$23
million
(U.
S.)
per
year.
If
it
is
estimated
that
the
cost
of
shifting
to
this
new
fertilizer
price
policy
would
be
(1)
to
compensate
the
owners
of
the
existing
fer-
tilizer
industry
at
the
full
present
value
of
their
investment
which
is
$15
million
(U.
S.)
in
order
to
close
it
down
and
(2)
to
invest
$10
million
(U.
S.)
in
storage
facilities
in
the
Buenos
Aires
harbor
to
facilitate
bulk
imports,"
then
the
internal
rate
of
return
on
this
investment
would
be
92
percent
in
a
single
year.
With
an
8
percent
discount
rate
and
a
10-year
horizon
over
which
it
is
assumed,
conservatively,
the
price
ratio
of
3
to
1
will
be
maintained
(Argentina
can
be
considered
a
price
taker
on
the
world
market
for
cereals—it
presently
exports
56
percent
of
its
corn
and
43
percent
of
its
wheat
crops),
the
internal
rate
of
return
would
be
622
percent.
This
estimate
is
definitely
an
understatement
of
the
benefits
Argentina
could
derive
from
this
new
policy
since
(1)
it
is
anticipated
that
the
acreages
planted
in
corn
and
wheat
would
ex-
pand
as
fertilizer
prices
drop,
since
the
need
to
rotate
land
with
pastures
to
maintain
soil
fer-
tility
would
decrease
and
the
relative
profita-
bility
of
these
crops
increase;
(2)
fertilizers
would
also
be
used
on
other
crops
and
on
pas-
tures;
and
(3)
external
benefits
of
this
invest-
ment
on
labor
employment
by
agriculture
and,
in
general,
its
impact
on
the
rest
of
the
economy
through
generation
of
higher
agricultural
sur-
pluses
and
the
relaxation
of
the
foreign
ex-
change
constraint
to
industrialization
are
not
taken
into
consideration."
A
question
of
importance
is
why
fertilizers
are
nearly
unused
on
wheat
and
corn
today
when,
even
at
present
prices,
they
could
safely
yield
acceptably
high
rates
of
return
on
nearly
half
of
the
wheat
and
corn
acreages.
A
host
of
rationalizations
has
been
offered—speculation
on
land
values
leads
to
extensive
use
of
it,
rental
laws
and
laws
on
the
indemnification
of
tenants
discourage
investment,
lack
of
credit
and
in-
surance
schemes,
price
uncertainty,
inadequate
13
This
scheme
is
not
presented
as
a
recommended
strat-
egy
but
only
as
a
way
of
calculating
the
cost
of
lowering
fertilizer
prices.
14
Bee
de
Dagum
[21
calculates
an
export
multiplier
for
Argentina
of
3
to
3.5.
On
the
other
hand,
costs
of
fertilizer
use
are
underestimated
because
increases
in
labor
and
capi-
tal
costs
that
result
from
its
application
and
from
harvest-
ing
higher
yields
are
omitted.
Since
hidden
unemployment
and
overmechanization
apparently
exist
in
most
small
and
medium
farms
in
the
corn
and
wheat
belts,
underestimation
would
not
be
serious.
Am.
J.
Agr.
Econ.
10
/
DE
JANVRY
behavioral
attitudes
toward
maximization
of
profits,
and
technological
change.
Although
each
of
these
factors
may
have
some
relevance,
the
major
limiting
factor
is
the
real
unavail-
ability
of
the
fertilizer
technology
to
farmers
in
the
sense
that
technical
and
economic
information
on
its
use
are
almost
totally
nonexistent.
Ferti-
lizer
experiments
have
been
few
and
economic
analyses
not
at
all.
Worse,
the
lack
of
careful
assessment
of
risk,
control
of
soil
fertility,
and
other
determinants
of
fertilizer
response
has
vitiated
the
interpretation
of
available
data.
Since
many
experiments
have
been
located
on
large
farms
which
are
on
the
wrong
side
of
the
fertilization
possibility
frontier
because
the
land
is
used
extensively
and
since
land
fertility
has
not
previously
been
taken
into
account
in
the
analysis
of
the
results,
the
conclusion
has
been
reached
that
fertilizer
use
is
indeed
of
dubious
economic
worth
in
Argentina
and,
eventually,
an
"insult
to
the
land."
In
addition,
the
current
unfavorable
price
situation
severely
reduces
the
economic
returns
from
fertilization
and
consequently
leaves
little
error
margins
for
individual
farmers
to
determine
pragmatically
the
production
conditions
under
which
an
eco-
nomic
use
of
fertilizers
can
be
made.
More
re-
search
and
extension
are
needed
not
only
to
bring
out
the
potential
for
fertilizer
use,
both
under
present
and
alternative
price
policies,
but
also
to
shift
rightward
the
fertilization
possi-
bility
frontier.
It
is
the
urgent
task
of
genetic
and
agronomic
research
to
develop
more
ferti-
lizer
responsive
varieties
and
a
package
of
cultural
practices
to
go
along
with
them.
Even-
tually,
as
this
is
most
probably
the
case
in
the
United
States,
all
of
the
cereal
acreage
would
then
lie
within
the
fertilization
possibility
fron-
tier
both
because
of
genetic
and
agronomic
improvements
and
also
because
the
land
would
be
used
more
intensively
in
cereal
production.
Since
the
profit
function
is
relatively
flat
in
the
organic
matter
dimension,
concern
about
levels
of
soil
fertility
would
become
of
minor
impor-
tance.
The
analysis
of
cereal
fertilization
under
risk
has
led
to
an
understanding
of
the
irrationality
of
the
past
and
present
fertilizer
price
and
agri-
cultural
research
policies
of
Argentina.
As
a
consequence,
this
country
is
losing
its
inter-
national
comparative
advantages
which
have
been
resource
based
by
not
participating
in
the
Green
Revolution
when
it
could
in
fact
be
one
of
its
greatest
beneficiaries.
The
unfortunate
truth
seems
to
be
that
comparative
advantages
can
also
be
factors
of
stagnation
because
they
often
act
as
retardants
on
the
needs
for
techno-
logical
changes.
This
is
particularly
true
in
countries
with
weak
institutional
bases
and
for
the
innovations
whose
research
returns
cannot
be
captured
and
must
be
generated
by
the
pub-
lic
sector
like
modern
biochemical
packages.
References
[1]
BARGE;
GERALD
L.,
AND
H.
C.
S.
THOM,
"Evaluation
of
Drought
Hazard,"
Agron.
J.
41:519-526,
Nov.
1949.
[2]
BEE
DE
DAGUM,
EsTELA
M.,
"Le
Multiplicateur
Dynamique
d'Exportation:
un
Modele
pour
l'Argen-
tine,"
Economie
A
ppliquee
22:89-112,
1969.
[3]
DE
JANVRY,
A.,
"Estancamiento
Tecnologico
en
el
Sector
Agricola
Argentina:
el
Caso
de
la
FertilizaciOn
del
Matz,"
Economica
17:3-28,
1971.
[4]
,
AND
R.
KOENIG,
"Economia
de
la
FertilizaciOn
del
Matz
y
Trigo
en
Argentino,"
Instituto
Nacional
de
la
Tecnologia
Agropecuaria,
Castelar,
Argentina,
1971.
[5]
FIENOP,
DARRELL
F.,
RUSSELL
H.
BRANNON,
AND
FRANK
A.
FENDER,
The
Agricultural
Development
of
Argentina.
A
Policy
and
Development
Perspective,
New
York,
Frederick
A.
Praeger,
Inc.,
1969.
[6]
HALTER,
A.
N.,
H.
0.
CARTER,
AND
J.
G.
HOCKING,
"A
Note
on
the
Transcendental
Production
Func-
tion,"
J.
Farm
Econ.
39:966-974,
Nov.
1957.
[7]
INTA,
unpublished
data
available
at
the
Agricultural
Experiment
Station,
Marcos
Juarez,
Argentina.
[8]
"La
Productividad
del
Suelo
en
la
Region
de
Per-
gamino
en
Relacion
con
Factores
Ambientales,
Tecnologicos,
Economicos
y
Sociales,"
INTA,
Per-
gamino,
May
1964.
[9]
PEARSON,
KARL,
Tables
of
the
Incomplete
Gamma-
Function,
London,
His
Majesty's
Stationery
Office,
1922.
[10]
Tennessee
Valley
Authority,
"Estimated
World
Fertilizer
Production,"
1966.
[11]
ULVELING,
EDWIN
F.,
AND
LEHMAN
B.
FLETCHER,
"A
Cobb-Douglas
Production
Function
with
Variable
Returns
to
Scale,"
Am.
J.
Agr.
Econ.
52:322-326,
May
1970.
[12]
VERGELIN,
C.,
"Soil
and
Water
Conservation
in
the
Carcarana
Watershed:
An
Economic
Study,"
un-
published
Ph.D.
thesis,
University
of
Wisconsin,
1971.
[13]
WILKS,
SAMUEL
S.,
Mathematical
Statistics,
New
York,
John
Wiley
&
Sons,
Inc.,
1962.