The welfare effects of erosion controls, banning pesticides, and limiting fertilizer application in the Corn Belt


Taylor, C.; Frohberg, K.

American Journal of Agricultural Economics 59(1): 25-36

1977


The partial welfare effects of alternative erosion control methods, banning insecticides, banning herbicides, and limiting nitrogen fertilizer in the Corn Belt are examined. The estimated welfare effects are partial since they reflect the change in consumers' plus producers' surplus arising from the production and consumption of corn, soybeans, wheat, oats, hay, and pasture but not the environmental benefits associated with pollution abatement or the administrative and enforcement cost of the policies. A large linear programming model of crop production in the Corn Belt was used to make the estimates.

The
Welfare
Effects
of
Erosion
Controls,
Banning
Pesticides,
and
Limiting
Fertilizer
Application
in
the
Corn
Belt
C.
Robert
Taylor
and
Klaus
K.
Frohberg
The
partial
welfare
effects
of
alternative
erosion
control
methods,
banning
insecticides,
banning
herbicides,
and
limiting
nitrogen
fertilizer
in
the
Corn
Belt
are
examined.
The
estimated
welfare
effects
are
partial
since
they
reflect
the
change
in
consumers'
plus
producers'
surplus
arising
from
the
production
and
consumption
of
corn,
soybeans,
wheat,
oats,
hay,
and
pasture
but
not
the
environmental
benefits
associated
with
pollution
abatement
or
the
administrative
and
enforcement
cost
of
the
policies.
A
large
►inear
programming
model
of
crop
production
in
the
Corn
Belt
was
used
to
make
the
estimates.
Key
words:
Corn
Belt,
erosion,
linear
programming,
models,
nitrogen
fertilizer,
pesticides,
pollution.
The
1972
Federal
Water
Pollution
Control
Act
mandates
the
development
and
imple-
mentation
of
controls
of
agricultural
non
-
point
sources
of
water
pollution
(U.S.
Con-
gress).
The
primary
responsibility
for
carry-
ing
out
this
mandate
rests
with
state
govern-
ments,
with
the
Environmental
Protection
Agency's
(EPA's)
role
being
one
of
seeing
that
this
is
done
in
a
satisfactory
manner.
The
EPA
currently
believes
that
in
many
cases
the
goals
of
the
act
can
be
carried
out
by
applying
practicable
best
management
practices,
including
conservation
practices
that
prevent
or
mitigate
entry
in
the
nation's
water
of
diffuse
-source
substances
that
tend
to
degrade
those
waters.
In
those
cases
where
applications
of
these
management
measures
are
inadequate
to
attain
or
maintain
water
quality,
the
EPA
intends
for
more
vigorous
C.
Robert
Taylor
is
an
assistant
professor
of
agricultural
economics,
Texas
A&M
University,
and
Klaus
K.
Frohberg
is
a
research
assistant
in
agricultural
economics,
University
of
Illinois.
Technical
Article
No.
12818
of
the
Texas
Agricultural
Exper-
iment
Station.
This
publication
was
supported
in
part
by
a
grant
from
the
Rockefeller
Foundation
to
the
University
of
Illinois
on
"Nitrogen
as
an
Environmental
Quality
Factor"
and
a
grant
from
the
Environmental
Protection
Agency
(No.
68-01-3584)
titled
"Economic
Evaluation
of
Implementation
Strategies
for
Control
of
Agricultural
Non
-Point
Sources
of
Water
Pollution."
With
the
usual
caveats,
thanks
are
due
to
C.
B.
Baker,
Steve
Sonka,
and
E.
R.
Swanson
for
their
critical
comments.
controls
to
be
implemented
(Pisano,
p.
11).
If
the
goal
of
the
act
that
"the
discharge
of
pollutants
into
the
navigable
waters
be
elim-
inated
by
1985"
is
strictly
interpreted,
the
more
vigorous
controls
seem
likely
for
many
agricultural
nonpoint
sources
(U.S.
Congress,
section
101.a).
This
article
presents
estimates
of
the
par-
tial
welfare
effects
of
the
following
public
policies
related
to
agricultural
pollution
in
the
Corn
Belt:
(a)
a
ban
on
the
use
of
herbicides;
(b)
a
ban
on
the
use
of
all
insec-
ticides;
(c)
nitrogen
fertilizer
restrictions
of
100
and
50
pounds
per
acre;
(d)
no
straight
row
cultivation;
(e)
gross
soil
loss
restrictions
of
two,
three,
four,
and
fi
ve
tons
per
acre;
(f)
terracing
subsidies
at
annualized
rates
of
$5,
$10,
$15,
$20,
and
$40
per
acre;
and
(g)
gross
soil
loss
taxes
of
$4, $2,
$1,
and
$0.50
per
ton.
The
pesticide
and
nitrogen
policies,
while
extreme,
are
plausible
under
a
strict
interpre-
tation
of
the
1985
water
quality
goals
that
are
set
out
in
the
amended
1972
Federal
Water
Pollution
Control
Act.
The
pesticide
regula-
tions
that
are
presently
under
consideration
by
the
EPA
and
states
will
not
significantly
affect
the
crops
considered
here
and
were
not
evaluated.
Illinois,
the
only
Corn
Belt
state
to
seriously
consider
limiting
fertilizer
use,
has
determined
that
nitrates
are
not
presently
a
problem
and
has
recommended
that
controls
26
February
1977
Amer.
J.
Agr.
Econ.
not
be
instituted
at
this
time.
But
since
some
water
supplies
to
the
state
exceed
the
contro-
versial
U.S.
Public
Health
Service
standard
for
nitrates,
this
issue
is
by
no
means
re-
solved.
The
magnitude
of
the
nitrate
problem
in
other
states
is
not
well
known.
Erosion
-
sedimentation
controls
are
much
more
likely
to
be
implemented
than
pesticide
bans
and
fertilizer
restrictions
and
therefore
constitute
the
practical
thrust
of
this
article.
While
the
primary
responsibility
for
non
-
point
source
management
rests
with
states,
the
federal
government
retains
the
authority
to
impose
more
stringent
requirements.
Fur-
thermore,
the
EPA
is
charged
with
encourag-
ing
uniform
state
laws
relating
to
the
preven-
tion,
reduction,
and
elimination
of
pollution
(U.S.
Congress,
section
103.a).
For
these
rea-
sons
and
also
because
of
the
large
number
of
conceivable
policies
that
differ
by
state
or
region,
this
analysis
focuses
on
regionwide
policies.
The
estimated
effects
are
partial
in
the
sense
that
they
reflect
the
change
in
consum-
ers'
and
producers'
surplus
arising
from
the
production
and
consumption
of
the
major
crops
but
not
the
environmental
benefits
associated
with
pollution
abatement
or
the
administrative
and
enforcement
cost
of
the
policies.
The
Model
The
model
used
for
this
analysis
is
a
linear
programming
model
of
the
production
and
marketing
of
corn,
soybeans,
wheat,
oats,
hay,
and
pasture
in
the
Corn
Belt.
The
pro-
duction
of
cotton
and
soybeans
in
this
area
accounts
for
about
70%
and
60%,
respective-
ly,
of
the
total
U.S.
production
of
these
commodities.
The
objective
function
of
the
model
is
consumers'
plus
producers'
surplus
in
the
corn
and
soybean
markets
minus
the
total
variable
costs
of
producing
a
specified
amount
of
small
grains,
hay,
and
pasture.
As
is
well
known,
the maximization
of
surplus
gives
a
competitive
equilibrium
solution
(Ta-
kayama
and
Judge).
The
demand
functions
for
corn
and
soy-
beans
are
incorporated
into
the
model
in
a
stepwise
fashion,
with
steps
in
24
,
increments.
The
demand
functions
used
in
the
model
are
(1)
Qc
=
5,613,712,245
763,775,100Pc
and
Q
S
=
1,469,981,594
130,224,637P
s,
where
QC
and
QS
are
the
bushels
of
corn
and
soybeans
demanded,
respectively,
and
Pc
and
Ps
are
the
per
bushel
prices.
At
the
mean,
the
elasticity
of
demand
for
corn
is
—0.50,
and
the
corresponding
fi
gure
for
soy-
beans
is
—0.64.
These
demand
functions
were
subjectively
specified
after
reviewing
recent
demand
analyses
(Houck,
Ryan,
and
Subot-
nik;
Vandenborre;
Brandow;
Rojko,
Urban,
and
Naive).
The
quantities
of
wheat,
oats,
hay,
and
pasture
demanded
were
treated
as
constants
in
the
model
because
these
are
relatively
minor
crops
in
the
area
and
also
because
the
inclusion
of
stepped
demand
functions
for
them
would
have
increased
the
size
of
the
model
to
the
point
where
the
cost
of
obtaining
a
solution
would
have
been
prohibitive.'
Fixing
the
quantities
demanded
of
the
minor
crops
causes
a
slight
over
or
under
(depending
on
the
policy)
estimation
of
the
change
in
surplus
resulting
from
the
policies.
2
The
land
base
for
the
area
modeled
was
divided
into
eleven
land
capability
units
(LCU's)
within
each
of
seventeen
geographi-
cal
regions
that
are
land
resource
areas
(LRA's)
defined
by
the
Soil
Conservation
Service
(SCS)
(USDA
1975).
Crop
produc-
tion
activities
in
the
model
differ
by
crop
rotation
(an
average
of
about
eleven
rota-
tions
for
each
LCU
within
each
LRA),
con-
servation
practices
(straight
row,
contouring,
and
terracing),
and
tillage
methods
(fall
plow,
spring
plow,
and
chisel
plow).
Rota-
tions
rather
than
just
single
crop
activities
are
Hay
and
pasture
account
for
about
27%
of
the
acreage
in
the
area.
In
the
benchmark
model
solution
as
well
as
in
actuality,
hay
and
pasture
are
primarily
produced
on
LCU's
that
are
unsuitable
or
marginally
suitable
for
row
crop
produc-
tion.
To
the
extent
that
wheat
and
oats
are
grown
to
diversify
production
and
reduce
risk,
the
inclusion
of
their
production
in
the
model
as
constraints
is
reasonable.
The
quantity
of
hay
and
pasture
that
had
to
be
produced
was
specified
by
LRA,
while
the
quantity
of
wheat
and
oats
demanded
was
specified
for
the
whole
Corn
Belt
area.
2
The
change
in
consumers'
surplus
(AC'S)
was
defined
to
be
ACS
=
ACS
;
,
where
ACS
;
is
the
change
in
consumers'
surplus
for
the
ith
crop,
with
CS,
_
(Pm
QRJ)1
2
,
where
i
is
corn
or
soy-
beans
and
CS
;
(P
8
,
PRI)Q
Bi,
where
i
is
wheat,
oats,
hay,
or
pasture,
P
5
,
is
price
for
crop
i
in
bench
run,
P
R;
is
price
in
model
run
for
the
policy
under
consideration,
Q
Bi
is
quantity
demand-
ed
for
crop
i
in
bench
run,
and
Q
R
i
is
quantity
demanded
in
model
run
for
the
policy
under
consideration.
Taylor
and
Frohberg
Effects
of
Erosion
Controls
27
included
in
the
model
to
reflect
the
influence
of
the
previous
crop
on
the
fertilizer
and
pesticide
requirements
of
the
current
crop.
A
simplified
matrix
representation
of
the
model
is
given
in
table
1.
The
fi
rst
column
of
this
matrix
represents
14,542
crop
production
activities.
The
vector
C
represents
the
per
acre
variable
production
costs
exclusive
of
labor
and
fertilizer,
while
the
vectors
Ye,
Ys,
Yw,
Y°,
and
Yh
give
the
yields
associated
with
each
activity.
Each
production
activity
takes
one
acre
of
land
from
the
appropriate
LRA
and
LCU
(see
row
11)
in
the
appropri-
ate
LRA
and
LCU.
The
vector
nsc
gives
the
carry-over
nitrogen
supplied
by
soybeans
to
corn
in
a
rotation.
The
vectors
nw,
no,
and
nh
give
the
nitrogen
required
for
wheat,
oats,
hay
or
pasture,
respectively.
For
a
given
land
type
and
conservation
practice,
a
single
pro-
duction
activity
is
set
up
for
hay
and
pasture.
This
production
can
either
be
transferred
to
pasture
(column
17)
or
baled
for
hay
(column
16).
The
second
set
of
columns
in
the
matrix
in
table
1
represent
two
steps
on
a
stepped
demand
function
for
soybeans.
These
steps
are
(2)
P
i
s
if
0
<
Qs
<
Qic
and
PI
if
Qis
where
P
i
s
is
price
of
soybeans
for
the
ith
step,
Qf
is
maximum
total
quantity
of
the
soy-
beans
that
will
be
purchased
at
the
ith
and
higher
prices
with
P
i
s
>
P.
Each
of
these
activities
draws
from
the
soybean
produc-
tion,
as
is
indicated
by
the
—1
coefficient
in
row
5.
The
soybean
demand
step
constraints
(rows
22
and
23)
reflect
the
inequality
shown
in
equation
(2)
above.
For
simplicity,
only
two
steps
are
indicated
in
the
matrix
in
table
1;
the
model
contains
seventy-five
such
steps.
The
fourth,
fi
fth,
and
sixth
set
of
columns
in
the
matrix
in
table
1
together
represent
steps
on
a
demand
function
for
corn
and,
for
each
respective
corn
-nitrogen
fertilizer
price
ratio,
represent
steps
on
a
fertilizer
response
function
for
corn;
that
is,
the
model
calcu-
lates
the
optimal
fertilization
rate
and
asso-
ciated
yield
for
each
market
price.
Before
considering
this
matrix
formula-
tion,
consider
the
special
class
of
response
functions
for
which
it
applies.
This
class,
used
by
Illinois
agronomists
to
tailor
fertiliz-
er
recommendations
to
individual
situations
(Illinois
Cooperative
Extension
Service),
is
one
for
which
the
optimal
per
acre
nitrogen
fertilization
rate
is
given
by
multiplying
the
maximum
yield
obtainable
(for
a
given
level
of
nonfertilizer
management)
times
a
factor
that
varies
with
the
price
ratio
but not
with
the
basic
soil
productivity
level.
The
fi
gures
used
as
a
basis
for
this
study
are
given
in
column
2,
table
2.
These
optimal
nitrogen
factors
imply
points
on
a
response
function.
The
points,
expressed
on
the
basis
of
percent-
age
of
maximum
yield,
are
shown
in
column
4,
table
2.
The
phosphorous
and
potassium
fertilizer
application
rates
are
assumed
to
be
equal
to
the
amounts
of
these
nutrients
re-
moved
in
the
grain.
This
should
approxi-
mately
maintain
the
P
and
K
levels
in
the
soil
(Illinois
Cooperative
Extension
Service).
The
steps
on
the
demand
function
consid-
ered
here
are
(3)
P
i
c
if
0
<
Q
c
<
Qf
and
Pf
if
Qf
5_
Qc
where
P
i
c
is
price
of
corn
for
the
ith
step
and
Qi
is
maximum
total
quantity
of
corn
that
will
be
purchased
at
the
ith
and
higher
prices
with
P
i
c
>
P.
To
follow
through
the
logic
of
the
matrix
formulation
for
incorporating
the
above
type
of
response
function
and
stepped
demand
functions
into
the
model,
fi
rst
suppose
that
the
supply
price
is
Pf
and
thus
that
it
is
profitable
to
produce
some
amount
of
the,
product.
With
a
positive
price
of
nitrogen
(1;,c),
the
maximum
per
acre
corn
yield,
given
by
the
vector
Ye
in
the
production
activities
set,
will
not
be
obtained
if
the
optimal
nitro-
gen
rate
is
applied.
Rather,
at
a
price
ratio
of
P
i
c/V
n
e,
only
K%
(from
table
2)
of
the
maxi-
mum
per
acre
yield
will
be
obtained.
This
is
reflected
in
the
model
by
the
fi
rst
sell
corn
activity,
taking
for
each
unit
sold
an
amount
(100/
Y
i
)
of
the
maximum
per
acre
yield
(row
2).
To
reflect
the
stepped
nature
of
the
de-
mand
function,
the
amount
of
the
product
that
can
be
sold
at
P
i
c
is
constrained
by
the
corn
demand
step
row
to
he
less
than
or
equal
to
Q.
The
optimal
nitrogen
level
is
at
a
price
ratio
of
P
1
71/,;c
in
n
1
pounds
per
unit
of
the
product
(from
column
3,
table
2).
The
total
nitrogen
requirement
will
thus
be
n
i
times
the
quantity
sold
at
Pf
.
The
cell
of
the
matrix
given
by
the
corn
nitrogen
needs
row
(row
16)
and
the
fi
rst
sell
corn
column
(col-
umn
14)
will
thus
give
the
total
quantity
of
nitrogen
required.
Table
1.
A
Matrix
Representation
of
the
Model
Transfer
n
Transfer,,
Crop
Corn
Production
Correct
Correct
Cons
from
from
Buy
n
Buy
n
Bu
Buy
n
Production
Sell
Correction
Corn
P,
K.
Soybeans
Hay
-Pasture
for
for
ft
for
Hay-
Bale
Row
Activities
Soybeans
Sell
Corn
Activity
Harvest
and
Labor
to
Corn
to
Corn
Corn
Wheat
O
Pasture
Buy
Buy
Buy
Hay
Description
(acres)
(w.)
(bu.)
for
Step
2
Costs
Requirements
(lbs.)
(lbs.)
(lbs.)
(lbs.)
(lh
(lbs.)
Labor
P
K
(tons)
Pasture
Constraint
Objective
function
—C
Base
corn
production
I
Yr
(sell)
Base
corn
production
2
(correct
harvest
costs)
Base
corn
production
3
(P.
K,
and
labor
correction)
r
Soybean
production
Y.
Wheat
production
Oats
production
Hay
-pasture
account
Hay
production
Pasture
production
Land
Terraceable
land
I
or
0
Labor
Potassium
fertilizer
Phosphorous
fertilizer
Corn
nitrogen
needs
rt
supplied
by
soybean
to
corn
nsc
n
supplied
by
hay
to
corn
nhc
Wheat
n
needs
nw
Oats
n
needs
1
2
0
Hay
-pasture
n
needs
rrh
Soybean
demand
step
Soybean
demand
step
2
Corn
demand
step
I
Corn
demand
step
2
Corn
transfer
2
P,'
P
t
.
—I
—I
HC
_
100
too
[
too
100
I
s
Y
2
Y
2
Y,
—I
—1
—1
—1
—I
1,
—I
—V
2
r
V.°
—V,
2
5
—1/
2
—V,,
—C
max
?0
—1
—1
—I
—1
—1
—I
—1
t
=0
=0
a
0
WD
a
OD
—I
m0
a
HP
aum
a
PP
s
L
5_
LAT
s0
L
s0
<0
s0
a
0
a0
s
0
<0
s0
5
-
Q1
-
Q1
'
s
(2[
`
G ` -
= 0
LL6I
eCinnaqd4
8Z
•uoag
'.18y
'Lalay
Taylor
and
Frohberg
Effects
of
Erosion
Controls
29
Table
2.
Economically
Optimal
Nitrogen
Rates
for
Corn
Optimal
Implied
Pounds
Yield
Corn
Optimal
n
of
n
as
a
Price
Factor
per
Bushel
Percentage
Divided
(lbs.
n
of of
the
by
per
bu.
of
Actual
Maximum
Nitrogen
maximum
Yield
Yield
Price
yield)
(n
i
(Y,)
co
1.3382
1.3382
100.00
40
1.2931
1.2937
99.95
30
1.2780
1.2792
99.91
25
1.2659
1.2677
99.86
20
L2479
1.2507
99.78
15
1.2178
1.2226
99.61
10
1.1575
1.1680
99.10
5
0.9766
1.0132
96.39
2
0.4341
0.5608
77.40
0
0
0
50.49
°
The
index
increases
as
one
goes
down
the
column
of
figures.
Supposing
that
the
maximum
quantity
that
can
be
sold
at
Pf
(Qf)
is
sold,
consider
selling
an
additional
quantity
at
the
next
highest
price
(Pf
).
Since
Pf
should
be
used
in
calcu-
lating
the
optimal
nitrogen
rate on
the
intra-
marginal
production
as
well
as
the
marginal
production,
the
per
acre
yield
and
nitrogen
rate
used
in
producing
the
quantity
sold
at
P
i
c
must
be
adjusted
if
any
production
is
sold
at
P.
In
the
model
this
adjustment
is
affect-
ed
by
the
addition
of
a
correction
activity
(column
6)
that
must
enter
the
basis
if
the
second
sell
corn
activity
enters.
Suppose
now
that
Pf
enters
the
solution
at
its
limit
of
(Q5
-
Qf).
The
constraint
on
row
26
will
force
the
correction
activity
given
by
column
6
to
enter
the
solution
at
a
level
of
Qf.
This
activity
does
not
incur
any
direct
cost;
how-
ever,
it
does
reduce
the
amount
of
the
maxi-
mum
production
that
can
be
sold
by
Qf
[(100/Y
2
)
-
(100/Y)].
Also,
it
corrects
the
optimal
amount
of
nitrogen
by
an
amount
equal
to
Qf
(n
2
-
n
1
).
If
both
Pf
and
P{
are
at
their
limits,
only
Y
2
%
of
the
maximum
possible
production
will
be
sold.
This
pro-
duction
will
require
n
2
pounds
of
nitrogen
per
unit
of
corn.
If
Pf
enters
the
solution
at
its
limit,
and
Pf
enters
at
a
level
less
than
its
limit,
the
model
will
give
a
linear
interpolation
for
yield
be-
tween
Y
i
and
Y2
and
a
linear
interpolation
for
the
nitrogen
level
between
n
1
and
n
2
pounds
per
unit
of
the
product.
There
are
seventy-eight
additional
steps
on
the
corn
demand
function
that
are
not
shown
in
table
1.
These
additional
steps
function
in
the
same
way
as
the second
step.
3
Since
some
harvest
costs
are
proportional
to
yield,
a
correct
corn
harvest
cost
activity
(column
7)
is
inserted
into
the
model
to
reduce
harvest
costs
by
an
amount
equal
to
the
per
bushel
harvest
costs
(HC)
times
the
difference
in
the
maximum
production
and
the
actual
production.
Similarly,
column
8
in
table
1
corrects
labor
requirements
that
are
proportional
to
yield
as
well
as
the
phospho-
rous
and
potassium
fertilization
rates
for
the
difference
in
the
maximum
production
and
the
actual
production.
Additional
activities
are
included
in
the
model
to:
(a)
subtract
from
corn
nitrogen
needs
the
amount
of
nitrogen
added
by
le-
gumes
in
rotation
with
corn;
(b)
purchase
the
required
amount
of
inorganic
nitrogen
ferti-
lizer
for
the
crops;
(c)
purchase
labor;
(d)
purchase
phosphorous;
(e)
purchase
potas-
sium;
and
(f)
allow
hay
to
be
baled
at
a
cost
of
$C
per
ton
or
to
substitute
for
pasture
with
the
baling
cost.
3
An
alternative
way
of
putting
response
functions
into
a
model
of
this
type
is
to
define
a
number
of
subactivities
for
different
fertilization
rates
(see
Taylor
I975b
and
Onishi).
Then
the
model
could
choose
a
linear
combination
of
the
various
rates
as
well
as
a
linear
combination
of
other
characteristics
of
the
production
activities.
The
disadvantage
of
this
formulation
is
that
it
substantially
increases
the
size
of
the
model,
while
the
advantage
is
that
one
is
not
restricted
to
using
a
single
response
function
for
a
crop
nor
restricted
to
the
special
type
of
function
illustrated
in
table
2.
To
include
subactivities
for
different
fertilization
rates
in
the
model
reported
here,
have
the
same
degree
of
accuracy,
and
include
rates
that
would
be
optimal
for
the
same
range
of
price
variation
would
require
eighty
produc-
tion
subactivities
(since
there
are
eighty
price
levels
and
eighty
steps
on
the
response
function)
for
each
activity
that
has
corn
in
the
crop
rotation.
This
would
increase
the
number
of
columns
in
the
model
from
14,821
to
846,357
and
decrease
the
number
of
rows
by
two
(rows
3
and
4
and
columns
6,
7,
8,
and
9
would
not
be
needed
because
these
changes
could
be
accounted
for
directly
in
the
coefficients
of
the
production
activities).
Consider
the
relative
cost
of
solving
the
two
formu-
lations.
The
model
in
table
1
was
solved
on
an
IBM
360-75
computer
using
an
IBM-MPSX
package
linked
to
a
budget
generator,
which
took
thirteen
minutes
to
generate
the
coeffi-
cients
on
tape
in
the
format
required
by
MPSX
and
twelve
minutes
to
convert
this
data
to
a
problem
fi
le,
which
is
the
internal
working
fi
le
for
MPSX.
To
optimize
from
scratch
takes
thirty-five
minutes
of
slow
core
(500K).
The
total
cost
was
about
$300
per
run.
Small
revisions
and
the
use
of
an
old
basis
as
a
starting
point
in
solving
the
model
were
less
costly.
Since
the
time
required
to
generate
the
data
and
convert
it
to
a
problem
fi
le
is,
for
this
problem,
about
proportional
to
the
number
of
columns,
the
model
with
the
eighty
subactivities
would
require
1,427
minutes
for
these
two
solution
steps
rather
than
twenty-five
minutes.
The
time
required
to
optimize
this
model
would
be
more
than
thirty-five
minutes,
but
how
much
more
cannot
be
calculated
a
priori.
Obviously,
the
model
with
eighty
subactivities
would
be
prohibitively
expensive.
Perhaps
a
less
expensive
computational
strategy
would
be
to
cut
down
on
the
range
of
rates
and,
if
the
solution
was
at
an
extreme,
generate
new
data
and
resolve
until
an
extreme
was
no
longer
encountered.
30
February
1977
Amer.
J.
Agr.
Econ.
The
basic
set
of
crop
budgets
used
for
the
study
was
obtained
by
updating
the
prices
and
input
levels
in
1970
budgets
that
were
prepared
by Worden
et
al.
for
the
USDA.
Since
a
different
regional
delineation
was
used,
budgets
for
LRA's
were
obtained
by
weighting
with
crop
acreages
the
budgets
for
the
USDA
regions.
These
updated
budgets
for
each
crop
and
LRA
were
then
modified
to
reflect
the
different
yield
levels
of
LCU's,
tillage
methods,
conservation
practices,
and
rotations.
Yield
adjustment
coefficients
for
LCU's
were
obtained
from
unpublished
USDA
data
(USDA
1975).
The
budgets
were
also
modified
to
reflect
nonyield
cost
differ-
ences
for
the
alternative
tillage
methods,
con-
servation
practices,
and
rotations.
These
lat-
ter
cost
adjustment
factors
were
obtained
from
many
sources,
including
farm
manage-
ment
manuals,
experiment
station
bulletins,
and
unpublished
data,
but
the
primary
source
was
the
Illinois
Cooperative
Exten-
sion
Service.
All
coefficients
are
for
1974
technology
and
price
relationships.
Specific
coefficients
will
be
furnished
upon
request.
The
land
acreage
base
for
the
model
was
obtained
from
the
1967
National
Conservation
Needs
Inventory
(USDA
1970).
The
land
con-
straint
in
the
model
for
a
LCU
within
a
LRA
was
the
total
of
1967
acreage
devoted
to
the
six
crops,
idle
land,
and
land
in
conservation
programs.
The
soil
loss
coefficients
in
the
model
were
based
on
the
universal
soil
loss
equation
(Wischmeier
and
Smith).
The
equa-
tion
is
(4)
A
=
RK(LS)CP,
where
R
is
rainfall
and
erosivity
index,
K
is
soil-erodibility
factor,
LS
is
a
topographic
factor
that
represents
the
combined
effects
of
slope,
length,
and
steepness,
C
is
a
cover
and
management
factor,
and
P
is
a
factor
for
conservation
practices.
Values
for
these
fac-
tors
were
obtained
from
Lee,
Wischmeier
and
Smith,
and
USDA
(1975).
For
contin-
uous
corn
under
a
spring
plow
system,
A
ranges
from
about
3
tons
to
over
340
tons.
Fall
plowing
increases
these
fi
gures
by
an
average
of
about
10%,
while
chisel
plowing
reduces
them
by
about
one-half.
Erosion
under
straight
row
cultivation
is
over
5
times
higher
than
erosion
on
a
terraced
fi
eld.
Model
Results
To
provide
a
base
from
which
to
measure
the
effects
of
a
policy,
the
model
was
solved
without
any
pollution
policy
imposed.
This
solution,
henceforth
called
the
benchmark
solution,
is
summarized
in
the
fi
rst
column,
table
3.
The
remainder
of
this
table
gives
the
model
results
for
the
policies
evaluated
in
this
study.
These
results
are
discussed
in
the
next
fi
ve
sections.
A
comparison
of
the
benchmark
acreages
with
actual
1969
acre-
ages
is
made
in
table
4
for
each
LRA.
Herbicide
Ban
The
impact
of
herbicide
ban
on
per
acre
crop
yields
was
based
on
data
from
a
six
-year
experiment
in
which
yields
with
and
without
herbicides
were
compared
(Slife).
Without
herbicides,
corn
yields
were
reduced
by
19%,
and
soybean
yields
were
reduced
by
22%.
In
line
with
Slife's
data,
it
was
assumed
that
without
herbicides
two
additional
cultiva-
tions
of
corn
and
soybeans
would
be
made.
As
indicated
in
table
3,
the
ban
reduced
consumers'
surplus
by
over
$3.5
billion
but
increased
producers'
surplus
(the
economic
rent
to
land)
by
about
$1.8
billion.
This
policy
also
reduced
the
fertilizer
load
in
the
environment
but
increased
by
13%
the
insec-
ticide
load
in
the
environment.
The
insecti-
cide
load
increased
largely
because
of
chang-
es
in
the
location
of
corn
production.
Labor
used
in
crop
production
increased
by
7%,
largely
because
of
the
additional
cultivations
of
corn
and
soybeans.
Insecticide
Ban
Estimates
of
the
effects
of
per
acre
crop
yields
of
banning
all
insecticides
are
shown
in
table
5
for
each
land
resource
area.
For
crops
and
crop
rotations
not
shown
in
this
table,
the
yield
effects
are
zero.
The
fi
gures
given
in
table
5
were
based
on
personal
communication
with
entomologists
familiar
with
the
Corn
Belt
(Kogan,
Kuhlman)
and
the
corn
rootworm
study
by
Taylor
(1975a).
These
estimates
apply
to
the
short
run.
It
is
not
clear
what
the
long
-run
effects
of
ban-
ning
all
insecticides
would
be.
On
one
hand,
the
elimination
of
insecticide
pressure
might
permit
the
insect
infestations
to
increase
over
the
levels
experienced
in
the
near
past.
But
on
the
other
hand,
the
continued
use
of
insecticides
might
result
in
an
insect
popula-
tion
that
is
resistant
to
the
insecticides
and
perhaps
even
more
damaging
than
current
strains
of
insects.
Table
3.
Estimated
Effects
of
the
Policies
Policy
Nitro-
gen
Re-
stric-
tion
Nitro-
gen
Re-
stric-
tion
No
Straight
Her-
Inset-
(100
(50
Row
Bench-
bicide
ticide
lbs./
lbs.)
Culti-
Effect
mark
Ban Ban
acre)
acre)
cation
SL
m
2
SL
s
3
SL
c
4
SL
m
5
$5/acre
$10/ac
$13/acre
820/acre
840/acre
84.07
$2.0/T
$1.0/i
00.5/T
Change
in
consumers'
surplus
(9
million)
0
-3,536
-632
-321
-3,325
12
-1.206
1
.007
-729
-433
0,3
-17
-27
-27
344
252
286
161
Change
in
producers'
surplus
($
minion)
0
1,799
531
21
2.036
-145
15
327
460
232
0.
1
194
333
942
-1,506
-959
-722
-418
Government
cost
1$
million)
excluding
adnunistrative
costs
0
0
0
0
0
11
0 0
0
0
6
I
381
576
1.233
-772
-515
-338
-212
Crop
price,
corn
(6)hu.)
2.46
3.04
2.60
2.56
3.08
2.46
2.80
2-62
7.54
2
52
2.46
2.
2.46 2.46 2.46
2.44
2.44
2.44
2.46
Soybeans
(6/ho.)
5.26
6.58
5.22
5,24
5.82
5.28
6.26
5-76
5.58
5.44
5.26
5.
5.28 5.28
5.28 5.56
5.44
5.34
5.30
Wheat
(8/hu.)
4.97
5.42
5.01
4.87
5.34
4.97
3.45
4.51
5,(34
4.93
4.97
4.!
4_99
4.99
4.99
4.57
4.74
4.79
4.82
Owls
($.13u.)
2.33
2_58
2.30
2.30
2.67
2.33
1.45
2.40
2.39
2.40
2.33
2-
2_34 2_34
2_34
2.19
2.28
2.26
2.28
Has
(5itonl
56.
15
62.53
57.75
56.07
63.73
55_97
55.33
58.07
58.36
57,
13
36.
14
56.03
56_21
56.2)
56.
19
51.01
52.67
53.21
54
15
Production:
corn
(mil.
burl
3.744
3,286
3.637
3.658
3.266
3.744
3,484
362
3,683
3,698
3.744
3,744 3,744
3.744
3.739
3.750
3.760
3,751
3,744
Soybeans
(mil.
1:941
785
607
791
790
714
785
655
72
743
767
785
785 785
785 785
746
763
777
782
Acres
terraced
(mil.)
0
11
0 0
0
0
23.63
9.
19
2.18
2.04
1.19
15.02
25.43
28.92
30.83
18.,53
7.74
1.
25
1.02
('Imseryation
tillage
(mil
.)
77.33
77.33
77.33
79.72
76.87
77.54
77_97
79.06
76.24
77.34
77.33
77.40
77.41 77.41
77.47
81.20
79.82
78.27
711.21
Gross
soil
loss
(mil.
tons
from
planted
acreage)
596
589
595
586
592
337
155
243
304
323
594
522
475
453
438
193
258
328
424
Gross
soil
less
Icons
acre
planted)
5.33
5.28
5.33
5.24
5_29
3.01
1
.21
2.07 2.74
2.88
5.26
4.12
3_46
3.21
3.07
1.49
2.
16
2.90
3-75
Insecticide
expenditures
index
100
1
13
0
95
I
II
100
89
103
93
93
100
HXI/
102
102
101
92
93
94 94
lierhir,ide
expenditures
index
1011
0
101
WI
11)2
99
89
91
97
100
100
100
99
99
99
10(1
99
101
100
.8
load
(bil
lbs
)
on
corn
acreage"
4.
19
3_81
3.52
3.19
2.20
4.
19
3.99
4.
10
4.15
4_
16
419
4_
19
4.19
4.
19
4.19
4.70
4.20
4.20
4.
19
Average
A'
load
(1173
(acre)
on
corn
acreage
100.58
85_89
85.22
75.83
48.73
100.69
102.13
101.
19
1.00.71
100.52
100,58
100.57 100.64
190.84
100.81
99,64
99.86
100.00
100.24
.
rota)
nit
nitrogen
from
organic
and
inorganic
sources.
3.taritio.ig
pun
JoieCvi
Effects
of
Erosion
Controls
32
February
1977
Amer.
J.
Agr.
Econ.
Table
4.
Planted
Acreages
of
Crops
1969
Actual
and
Benchmark
Solution
Region
Corn
and
Grain
Sorghum
Small
Grains
Soybeans
Hay
and
Pasture
Actual
Model
Actual
Model
Actual
Model
Actual
Model
1
,000
acres
Wisconsin
and
Minnesota
sandy
outwash
218
0
153
487
7
0
608
781
Southeastern
Wisconsin
drift
plain
1.677
789
781
1,810
191
789
1,981
1,930
Southwestern
Michigan
fruit
and
truck
belt
109
95
46
223
16
0
106
136
Southern
Michigan
drift
plain
1.428
2.844
610
523
607
645
1,184
1,225
Loess.
till,
and
sandy
prairies
5.259
5.718
3,689
2.611
1,151
2,039
3,803
4,145
Central
Iowa
and
Minnesota
till
prairies
4.976
4,993
1,132
1.460
3,644
4,308
2,084
2,276
Eastern
Iowa
and
Minnesota
till
prairies
1,630
1.356
465
415
789
1.356
984
1,021
Northern
Mississippi
Valley
loess
hills
1,440
1,980
660
22
133
0
2,511
2.644
Nebraska
and
Kansas
loess
-drift
hills
1,474
1,028
418
382
280
748
1.013
1.112
Iowa
and
Missouri
deep
loess
hills
3.189
2,001
530
328
1,406
2,001
2,205
2,613
Illinois
and
Iowa
deep
loess
and
drift
7,874
8,241
1,218
247
4,090
4,619 3,096
3,328
Iowa
and
Missouri
heavy
till
plain
1,207
890
253
0
897
611
2.927
3.270
Northern
Illinois
and
Indiana
heavy
till
plain
1,472
1,541
203
56
1,135
1.541
291
395
Indiana
and
Ohio
till
plain
4,480
4,591
1.687
4.283
3.475
2,272
2,434
2.329
Central
claypan
areas
870
1.421
384
302
983
657
956
907
Southern
Illinois
and
Indiana
thin
loess
and
till
plain
1.729
2,035
563
0
1.420
2.035
1.236
1,364
Central
Mississippi
Valley
wooded
slopes
2.015
2.249
627 339
1,269
1,238
2,506
2,340
All
41,047
41.700
13.419
13,488
21,493
24,859
29,925
31.816
For
the
insecticide
ban,
consumers'
surplus
decreased
by
$632
million,
while
producers'
surplus
increased
by
$531
million.
The
price
of
corn
increased
by
140,
but
the
price
of
soybeans
declined
by
4(C.
The
soybean
price
drop
or
the
production
increase
resulted
from
growing
more
corn
in
rotation
with
soybeans
to
avoid
large
insect
losses
to
corn.
Nitrogen
Restriction
For
the
nitrogen
policy,
it
was
assumed
that
the
per
acre
rate
would
be
reduced
from
a
mean
rate
of
about
140
pounds
(including
nitrogen
added
in
manure
and
by
legumes)
to
a
maximum
of
either
50
or
100
pounds.
It
was
further
assumed
that
a
restriction
would
apply
to
any
source
of
nitrates
including
those
added
by
legumes.
Since
the
precise
relationship
between
nitrogen
fertilizer
appli-
cations
and
nitrate
pollution
damages
has
not
been
established
(Aldrich),
there
is
pres-
ently
no
sound
basis
for
restricting
fertilizer
use
to
either
level.
The
50
and
100
pound
levels
were
chosen
to
cover
the
range
of
possible
restrictions.
Table
5.
Estimated
Average
Yield
Change
from
Banning
all
Insecticides
Region
Rotation
Corn
after
Corn
Corn
after
Soybeans
Corn
after
Small
Grains
Corn
after
Hay
or
Pasture
Wisconsin
and
Minnesota
sand
outwash;
southeastern
Wisconsin
drift
plain
Southwestern
Michigan
fruit
and
truck
belt;
southern
Michigan
drift
plain
Loess,
till,
and
sandy
prairies;
central
Iowa
and
Minnesota
till
prairies,
eastern
Iowa
and
Minnesota
till
prairies;
northern
Mississippi
Valley
loess
hills
Nebraska
and
Kansas
loess
-drift
hills
Iowa
and
Missouri
deep
loess
hills
Illinois
and
Iowa
deep
loess
and
drift
Iowa
and
Missouri
heavy
till
plain
Northern
Illinois
and
Indiana
heavy
till
plain
Indiana
and
Ohio
till
plain
Central
claypan
areas;
southern
Illinois
and
Indiana
thin
loess
and
till
plain;
Central
Mississippi
Valley
wooded
slopes
10
0
8
15
8
10
15
—12
8
5
2
0
0
2
—2
0
0
2
0
4
—8
5
—5
5
—3
5
5
—5
2
—2
10
—8
—8
10
—10
—6
—6
2
—5
Taylor
and
Frohberg
Effects
of
Erosion
Controls
33
The
100
pound
restriction
reduced
con-
sumers'
surplus
by
$231
million,
while
the
50
pound
restriction
reduced
it
by
$3,325
mil-
lion.
Producers'
surplus
increased
by
$21
million
with
the
100
pound
restriction
and
by
$2,036
million
with
the
lower
restriction.
Pro-
ducers'
surplus
increased
with
the
restriction
primarily
because
the
price
and
quantity
changes
to
a
large
extent
occurred
in
the
inelastic
portion
of
the
demand
curve
for
corn
and
soybeans.
Thus,
a
nitrogen
fertilizer
restriction,
which
would
clearly
be
to
the
disadvantage
of
an
individual
landowner
if
imposed
only
on
his
farm,
would
be
to
his
advantage
if
imposed
in
a
large
region.
Under
the
50
pound
restriction,
corn
acre-
age
increased
by
3.5
million
acres.
But
the
higher
acreage
did
not
compensate
for
the
reduction
in
per
acre
yield.
Hence,
the
quan-
tity
produced
went
down
by
478
million
bushels,
and
price
went
up
by
62¢
per
bushel.
Although
the
restriction
gave
soybeans
a
comparative
advantage
over
corn,
the
in-
creased
pressure
on
the
land
base
for
corn
production
increased
the
price
of
soybeans
by
564
per
bushel.
The
restriction
reduced
the
acreage
of
corn
grown
in
rotation
with
soybeans
or
small
grains;
hence,
insecticide
expenditures
increased
by
1R.
The
average
nitrogen
load
on
corn
acreage
decreased
from
a
benchmark
level
of
101
pounds
per
acre
to
76
pounds
per
acre
under
the
100
pound
restriction
and
to
49
pounds
per
acre
under
the
50
pound
restriction.
The
load
is
below
the
restriction
level
because
the
optimal
nitrogen
rate
on
some
of
the
poorer
land
is
below
the
restriction
level
and
the
average
is
pulled
down.
The
nitrogen
load
was
reported
in
terms
of
corn
acreage
be-
cause
the
other
crops
do
not
require
substan-
tial
addition
of
nitrogen
to
the
soil.
Unfortu-
nately,
the
impact
of
this
reduced
load
on
the
nitrate
content
of
water
supplies
is
an
unclear
issue
at
the
present
time
and
may
continue
to
be
so
in
the
near
future
because
of
the
complexity
of
the
nitrogen
cycle
(Aldrich).
Until
this
information
becomes
available,
it
will
not
be
possible
to
compute
the
social
value
of
damages
abated
by
nitrogen
restric-
tions.
The
administrative
and
enforcement
costs
associated
with
a
per
acre
restriction
would
indeed
be
very
high.
Strict
enforcement
would
obviously
be
unworkable
because
it
would
require
a
twenty-four
hour
check
on
all
fi
elds.
Perhaps
an
acceptable
degree
of
compliance
could
be
achieved
with
very
stiff
penalties
for
violators
combined
with
ran-
dom
on
-the
-spot
checks.
Other
nitrogen
pol-
icies
that
have
lower
enforcement
costs,
such
as
taxes
and
markets
for
pollution
rights,
have
been
suggested
for
this
problem
(Taylor
1975b);
however,
these
policies
would
not
be
expected
to
be
as
effective
in
controlling
the
intensity
of
use
as
a
restriction.
If
the
inten-
sity
of
use,
as
opposed
to
total
use,
is
the
major
factor
causing
unacceptable
nitrate
levels
in
water,
then
the
per
acre
restriction
may
be
the
best
alternative.
In
fact,
this
was
the
only
policy
mentioned
in
the
Illinois
Pollution
Control
Board's
proposed
plant
nutrient
regulations.
Erosion
Controls
The
estimated
effects
of
alternative
erosion
control
policies
are
shown
in
table
3.
Accept-
ing
Hai
berger's
applied
welfare
economics
postulate
that
producers'
and
consumers'
surpluses
should
be
added
to
arrive
at
the
net
social
cost
of
an
action,
we
fi
nd
the
relation-
ships
between
gross
soil
loss
and
net
social
cost
(excluding
administrative
costs
and
en-
vironmental
values)
that
are
shown
in
fi
gure
1.
As
expected,
the
socially
least
costly
meth-
od
of
achieving
a
specified
level
of
soil
loss
is
a
tax.
The
terracing
subsidies
are
substantial-
ly
more
costly
than
the
other
control
meth-
ods
considered;
however,
a
terracing
cost
sharing
policy
rather
than
the
policy
that
paid
the
same
per
acre
amount
(irrespective
of
actual
costs
of
terraces)
would
have
a
lower
social
cost.
A
per
acre
soil
loss
restriction
is
only
slightly
less
efficient
than
the
tax
policy
for
reducing
soil
loss
from
595
million
tons
to
about
400
million
tons.
For
achieving
a
soil
loss
level
of
about
337
million
tons,
a
ban
on
straight
row
cultivation
(i.e.,
require
contour-
ing
or
contouring
and
terracing)
is
only
slightly
more
costly
than
a
tax
policy
and
less
costly
than
a
per
acre
restriction.
In
table
3
there
are
substantial
equity
differences
between
the
types
of
erosion
con-
trol
policies.
Under
the
per
acre
restriction,
landowners
gain
and
consumers
lose,
while
the
opposite
holds
for
a
tax
policy.
To
achieve
a
soil
loss
level
of
about
330
million
tons
costs
$108
million
with
a
tax,
$201
million
with
a
per
acre
restriction,
and
$133
million
with
a
ban
on
straight
row
cultiva-
34
February
1977
Amer.
J.
Agr.
Econ.
1200
7,1
`
2
'
1000
PER-
ACRE
RESTRICTION
0
NO
STRAIGHT
ROW
CULTIVATION
0
800
I
-.
1/1
0
600
0
sm
400
SOIL
LOSS
TERRACE
SUBSIDY
TA
X
200
O
100
Figure
1.
policies
200
300
GROSS
SOIL
LOSS
400
500
600
(MILLION
TONS)
The
relationship
between
net
social
cost
and
gross
soil
loss
for
the
alternative
erosion
tion.
Landowners
lose
$722
million
annually
under
a
tax
policy,
gain
$232
million
under
a
per
acre
restriction,
and
lose
$145
million
with
a
ban
on
straight
row
cultivation.
The
direction
of
these
land
rent
effects
result
primarily
from
the
inelastic
demand
for
corn
and
soybeans.
To
achieve
a
soil
loss
of
330
million
tons,
consumers
lose
$33
million
un-
der
the
per
acre
restriction,
gain
$12
million
with
the
ban
on
straight
row
cultivation,
and
gain
$286
million
under
the
tax
policy.
The
consumer
gain
results
from
the
two
policies
primarily
because
of
relatively
lower
values
for
hay
and
pasture.
Another
equity
aspect
that
policy
makers
might
want
to
consider
is
the
relative
impact
of
the
control
methods
on
low
income
con-
sumers.
Because
a
terracing
subsidy
policy
does
not
significantly
affect
prices,
the
major
effect
on
consumers
will
be
through
in-
creased income
taxes.
Given
the
progressive
nature
of
the
U.S.
tax
structure,
this
policy
may
affect
low
income
consumers
much
less
than
a
policy
such
as
a
per
acre
restriction,
which
significantly
increases
food
prices
but
not
taxes.
The
soil
loss
tax
policy
might
benefit
low
income
consumers
the
most
be-
cause
it
would
lower
food
prices
as
well
as
lowering
taxes.
Concluding
Remarks
A
very
large
linear
programming
model
of
crop
production
in
the
Corn
Belt
was
pre-
sented.
This
model
incorporated
stepped
de-
mand
functions
for
corn
and
soybeans
and
therefore
gives
an
approximate
competitive
equilibrium
solution
for
these
markets.
One
advantage
of
this
model
over
other
norma-
Taylor
and
Frohberg
Effects
of
Erosion
Controls
35
tive
regional
models
of
crop
production
(see,
e.g.,
Taylor
1975b,
Mayer
and
Hargrove,
Heady
et
al.)
that
have
been
used
to
analyze
pollution
policies
is
that
it
gives
a
market
equilibrium
solution.
The
other
models
have
either
been
formulated
with
constant
prices
or
with
the
quantity
demanded
fi
xed.
A
sec-
ond
important
advantage
of
the
model
pre-
sented
here
is
that
it
gives
a
measure
of
the
change
in
social
welfare
resulting
from
a
policy,
namely,
the
change
in
consumers'
plus
producers'
surplus.
A
third
advantage
of
this
model
formula-
tion
is
that
it
incorporates
the
determination
of
optimal
fertilization
rates
for
corn
in
a
computationally
more
efficient
way
than
has
been
done
in
other
models.
The
increased
computational
efficiency
of
this
formulation
allows
much
more
detail
to
be
added
either
with
respect
to
the
number
of
fertilization
rates
allowed
or
with
respect
to
other
input
levels.
This
model
was
used
to
estimate
the
effects
of
various
controls
on
nonpoint
agricultural
sources
of
pollution.
Extreme
controls
of
banning
all
herbicides,
banning
all
insecti-
cides,
and
limiting
nitrogen
fertilizer
use
were
evaluated
to
illustrate
the
consequences
that
may
result
if
the
1985
goal
of
zero
pollution
is
strictly
interpreted.
These
runs
also
show
the
importance
of
these
chemical
inputs
to
agriculture
when
price
effects
and
regional
shifts
in
production
are
accounted
for.
Controls
on
gross
soil
erosion,
which
are
more
likely
to
be
implemented
than
severe
constraints
on
the
use
of
most
chemicals
in
agriculture,
were
also
evaluated.
As
expected,
a
soil
loss
tax
is
the
least
costly
method
for
achieving
soil
loss
reductions.
However,
a
per
acre
restriction,
perhaps
a
politically
more
viable
alternative,
was
found
to
be
only
slightly
more
costly
than
a
tax
for
achieving
up
to
a
50%
reduction
in
erosion.
The
terrace
subsidy
policy
considered
was
substantially
less
efficient
than
the
other
policies,
but
a
policy
that
paid
only
the
cost
of
the
terraces
rather
than
a
fl
at
rate
might
be
much
more
efficient.
Future
research
on
agricultural
nonpoint
sources
of
pollution
needs
to
concentrate
on
estimating
the
external
costs
of
pollution
and
the
administrative
and
enforcement
costs
of
pollution
controls.
After
this
information
is
obtained,
a
model
of
the
type
presented
here
could
be
modified
to
include
these
costs
and
give
the
socially
optimal
level
of
pollution.
Future
research
should
also
concentrate
on
fi
nding
the
optimal
mix
of
point
and
non
-
point
pollution.
[Received
March
1976;
revision
accepted
Septem-
ber
1976.1
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