Page 1

ECONOMICS OF UPLAND RESOURCE DEPLETION SHIFTING CULTIVATION IN THE PHI LIPPINES Morion S.delos

Angeles

WORKINGPAPER _ 88-02

February 1988

Philippine Institute for DevelopmentStudies

:


TABLE

OF CONTENTS. Page

List List

of

Tables

of

Figures

I.

Introduction

II;

A Normative Model of Optimum Use of Forest Lands for Agricultural Production: Resource Optimization Under Complete Markets .... . ........ , ............. ,..--

III.

IV.

........

_.,.... , .....

The Private Individual's Soil Resources: Resource Under Incomplete Markets

..... ...

Implied

Policy

VI.

Bibliography

VII.

Mathematical

Tools

........

ii

,.,.-

..................

.. ...... .. .... ..... .....

Annex

4

Use of Upland Optimization • ....... ...- ....

Some insights fromZthe Philippine Experience ....... ... ........... ......

V.

1

24

,

....

.............

29

33

35


LIST' ,OF TABLES

Page

Table

Table

•Table

1

2

3

:

:

:

Labor Use •Farming .

Examples Systems Allowable Density

in Hanunoo Swidden ........................

25

of Up!and Agricultural Evaluated in Terms of Population 28

ooeo_aomeoeoeo'eoomoe.oooo

Average Land Productivity Traditional Kaingin Farm Puting-Lupa, Mr; Makiling, 1978•1980 eooe.oooo_loooaooooomoo

In in

a

30


LIST,

OF FIGURES'

Pa_e

Figure

i:

Determination of Area for Agri a cultural Production by Various Decisionmakers ....................

15

18

Figure

2

:

Time

Figure

3

:

Shifting Lands

Figure

Figure

4

5

:

:

Paths

of

S,

O,

Agriculture

P,

in

and

u

........

Forest

.........................

.....

21

Theoretical Relationship Between Length of Fallow and Soil Productivity ....4.. ......... , ......

22

Relative intensity Graph of Various Subsistence Activities of the Batak in one Agricultural Year ... .......

27


ECONOMICSOF UPLAND RESOURCE DEPLETION: SHIFTING CULTIVATION IN THE PHILIPPINESI'/ by Morion S. delos Angeles2"J

I.

INTRODUCTION The

developed and

wood

prac%ice

two

principal

countries gathering o_

today for

sn1£tlng

Based mostly Res0urcelConservation Ph.D (Economics) 1986.

causes are

fuel

of land

(Eckholm

cultlvation"

deforestation clearing

_or

1976). has

in

on

agriculture

However,

largely

Chapter III of "Economic by Upland Farmers in the Thesis, University of the "

less

the

dominated

Analysis o£ Philippines," Philippines,

-2_:

Researchl Studies.

Fellow,

Philippine

Institute

for

Development


2

clearing is

an

of

of

forested

land

agricultural

fields

•means

of

agricultural

generally

than • crops,

with slash

In

system

rather

alternating

for

long

and

burn"

conduc£ed

by

fallow

short

(Pelzer,

such

system,

as

it

locally,

logging

activities.

inflicted

by

forests

note

fourteen

(M.C.Cruz, such

et

_e

agricultural with

a

The

effects

We

forested

land

represents cannot

be

in

of

investigate

clearing

by

usually

succeeded

i

the

the

the

•damage

loggers

on

Perhaps

of

Some

uplands in

land'use 30

the more

eountry's_

individuals

1980

systems

percent

of

the

understated.

the

investigation uplands

by

shifting

optimum

society's

relative

is

systematic

practiced

treatment

from

a

Cropping,

"kaingin"

the

it

1986).

provide

rotation

the

and

M)

systems

problem.

on

(14.0

to

formal

debate

million

therefore,

attempt

has

in

which

by

of

occupancy

al,

total,

practice

unresolved,

that

population,

national

and

agriculturists

remains

to

reached

by

upland

still

important

While

a

It

1968).

Philippines, termed

"by

.

periods•of

periods,

the

is

production

starting

cultivation

rate

viewpoint

of

of

and

use from

of the

•"Shifting cultivation", shifting field agriculture", "swidden farming•", "slash-and-burn farming" and "kaingin" are terms which• have been used by va_iQus •.authors to .... indicate, generally, similar agricultura% system.s and .are used interchangeably in this• paper.

The technologies development workinglpaper.

economics by

upland

projects

of

adoption

communities shall

be

of who

presented

soil are in

conserving

participants a

subsequent

of•


3

individual between

uplander's timber

slash

and

expiained on

production

burn

termS

access of

constraints

which

Sections completeness

of

a standard

2

use use

resulting

the

of

of

forest

Upland

agricultural

land Soil

of

rules

varying

and

degree

determinant

prices by

of

major In

are

the

as

ot

upland

resulting

stocks,

followed

of

valuation

resources.

zero

use.

effects

the

resource

production

decision

is

and

as "_ well

products/effects

future

model

bias,

resource

dissimilar

and

timepaths

varying

the

Specifically,

environmental,

_ of

discuss

is

economic

involved, upland

through

farming

discounting

to

for

choices

production

resource

the

specific

markets

use.

agricultural rates

are

traditional

swidden

externalities

land

external,

Here,

of

the

given

agricultural

exploitation,

valuation

resource

or

farming.

. in

open

viewpoint,

the from of

addition,

the

scarcity

rent,

discussed

under

different

resource-

users.

section

3_ubsequently

hypothesizes

the

likely

, [

behavior

of

conditions insights country. policy

forest of

on

use

under

accessibilityand shifting

This tools

land

in

is

Section

tenure,

cultivation

followed 4.

specific

by

in a

and

varlous

discussion

Philippine presents

parts of

the

some

of

the

implied


4

rX;

A NORMATIVE MODEL• OF OPTIMUM USE OF .FOREST _,AI_P_, • -FOR AGRICULTURAL PRODUCTION : RESOUR<;E,OPTIMIZATION' UNDER COMPLETE MARKETS

Consider

the

agricultural basic Howe

following

production

natural ,(i979,

on

resource

Ch.

forest

=

where

Q(t)

=

L(t)

=

composite

S(t)

=

stock resources

=

time.

function

""

[ L(,t)

calls

"stock

"(a)

an

S(t)i

a natural

)

reduction

as in

adopts

the

as

presented

by

of

as

future

use

p'91),

and

to

a

•and

the to

he

proceeds;

what

to

as:

derived

and

limit

he

defines

_( for the

finite

soil

production

reflect

which

costs

depletion due

land

an argument'to commodity

in"forest

input;

forested therein; and

extraction

(resource)

pla_ted

labor-capital

(ibid, of

, t]

crops

resource

effegts"

increase

co_odity

which

model,

. S(t)

agricultural, land;

includes for

depicting

5):

Q(t)

Howe

land

exploitation

(i)

t

relationshiips

(b)

the

a

total

i

quantity

of

inserted).

the An

effective

in

situ

example

logging

costs

resource',

of

such

for

(ibid,

stock

cutting

p.72;

effects smaller

italics

include sized

higher

trees.

i

We model forests

differ for

the

andsoil

in use

our of

treatment upland

resources.

of

S(t)

resources Under

as _ We

which

theshifting

adapt

include

the both

agriculture


k

system, as

the

_ollows.

the

flow

services

cleared

provides

production. burning

trees,

biomass;

vegetation

that

content

which

clearing

in

an

after

still

is

the

also

addition

burning

agricultural

enhanced

•. by

by

slightly

organic

(Sanchez,

•,

fores£

accompanied

of

the

felled

contains

are

increase•of

are

for _

resources

is,

uplahds•proceeds

forests

-fertility

the.soil

results

nitrogen

area,

•the

forested

standing

enough

••When of

burnt

•from

Immediately•af•ter

resulting

litter,

of

the

burned

•matter

1976),

and-

Thus,

an •

...

immediate

• (i.e.,

(_Q/_S(t)) better

> 0;

.sites

•example; land)

same

structure

topsoil

which

heavy

in

more

diffi_ul£

forest

the

burnt

uplands

stock

no

to

measures

'•

less,

.

forest "extract" the

forest ••

described current

the by use

be

to

the

Howe a

therefore for pasture

from

nutrient.s are

no

feasible

it

longer

as given

the

(usually becomes

products provided

r , due

of

rainfall Thus,

earlier

howeve

erosion

" agricultural

vegetation

from by

the

avaiiabie,,

• -•v•

or , .

subsequent

negative

of

not

for

or

compared

taken,

l_tter,

cropping z

manner,

are

ire

and,

are

may

10ngerprotected

because of

results

(e.g•_-, •grassland,

pr0d_ction

tropics)by

land

forested

production,

deterioratioh., is

effect

slope.

agriculturai

soil

stock

are

agricultural,

soilconservation

continued tO

which

non-forested•

the

Unless

•positive

uplands for

with

of

current)

stock a

cost

Inthis

.

_ffects

hold.

experienced

resource

cycle.

stock.

These in

the

effects future

due

are to


6 2 We

expect (_O/_L(t))

> 0,

and

(2

2

Q/_L

(t))

< 0

from

i

the

usual

returns)

behavior

(2)

agricultural of

(2)

production

(law

of

diminishing

•.

Equation•

price

of

p(t)

=

D

the

value

inverse

of

,

demand

given

function_

p(t_

as

the

for

composite

products:

next

•include

an

crops/c0mmodities such

The

is

[ Q(t)

, t]

relationship use

of

•shows•• sooial

agricultural

environmental

. benefits,

products,:

services

of

as

untilled

which

well

as

forest

the land,

s(t): Q(t) (3)

SB(t)

Here, the

we area

=

_

D[q(t),

integrate

over

under

demand

the

Q(t)

t]

to

d n

+

E_S(t)]

indicate

cur.ve,

that

we

are

•and•estimating

valuing

consumers'

surplus.

The by

a

soil

environmental

stock

of

erosion

ecological present

study

as

>

lands 0.

the

and largely

off-site

lead

E[S(t)]

may•pertain

well•as

focuses

among

forest

(dE/dS)

forests

diversity,

concern _f

services

to

more

to

others the on forest

which the

such

provision soil

erosion

servicesl.

environmentali

are

provided

minimization as

of

windbreaks,

of

oxygen. as

The

the

primary

Larger

stocks

services,

thus


7

Subsequently, agricultural costs _bss area•. in

crops

such of

we

as

the

to

costs

soil

as

opportunity •

production involves

cost

of

labor-capital,•

due

to

a•reduced

those

harvest

imposed from

of • raising

direct and

forest on

the

agricultural

crops

due

problem

the

social

cost

of

for

• discount

rate

and

the • labor-capital

agricultural

_

input,

•production

as the

on

forest

becomes:

Max. L(t)

_[

subject

to

:

Equation control

I 0

-rt D( n,t)d_

+ E

(4.1)

S(t)

=

(4.2)

S(t)

>

(4),

problem the

state net

•production

cost,

iperiod,

product,

• (4.1)••

where

maxlmizing

time

land

forests,

[S(t)]

- wL(t)]

e

dt

Q(T)

dT,

t

s(t)

the

future,

secondary

Q(t) (4)

of

fertility.

_

optimization land

foregone

the

landswhich

include

difficulty

Setting unit

forest

• services

the

decreasing

•investigate

opportunity

Indirect

increasing

the

on

environmental

particular,•

and

now

benefits,

wL(t),

from

•under

environmental

the

services

{

decision (4)

_ or

equation

complete

a

describes

••Equation

social

Thus,

is

-

0.

and• (4.2)

L(t)

variable.

•S(0)

(3)

future

optimal

variable says

that

subtracting

• markets, and

an

over the

we

and are

current a perpetual

agricultural

effects

of

using


8

part

of

forested

Considered.• are

Presumably,

based

on

of

forested

of

upland

Equation rate

the

S(O)

(4.2)•

of

is

agricultural

while

change

crop

occurs

pro_iuction"

when

t_e

are

decisions

all made

concerns.

(•4.1) land;

for

•this

societal

Equation

land,

uplands

an

accounting

constant

a

production

denotes• is

the

of

S(t)

the

equation (>0)

on

initial

the • stock

reiflects

the

effect

reduction

of

forest

forested

land.

stock•bf

non-negative ,• is

the

for

conditioh

of

S(t).

The

•inc°rp°rate

the

therefore:

•e

(5)

s(t) For

-a . Q(t)

purposes

constraint equation

:

of

• equation rt by

_e

manageability, (5)

dt

into•

or

we

(4 )

and

equiva_entiy,

mulitiply rlt e _ ,

:

to

whole

form

the

the

rake

i

current of

the

net

value social

Hamiltonian benefits

function

at

instant

which'

depicts

%:•

Q(t) (6)

H

=

_

D(_,

t) -

dq

+

wL(t)

E -

[S(tl)] a

. u!(t) Q(t) .• •

Here,

u(t)

is • equal first

of

sacrifices

the

to l.e

two•

benefit cost

is

,

terms

rates;

current

Lagrange

corresponding

of the

labor-capital imposed

value

on

to

(6)show third

the term

constraint

direct

pertains

• inputs,

while

future

periods.

multiplier,

the

add tol

which (5).

•The

environmental the

opportunity

last••term

represents


9

Differentiating

7)

H

_H _L(t)

= .

D

with

respect

[Q(t),

t]

. •

to

_(t) _L(t)

dS(t) dQ(t)

-a.

L(t)

+

.•

gives

us:

dE[S(t)] dS(t)

_•Q(t) _L(t)

-

w

u(t) _O(t) _L(t)

Obtaining

(_H/_L(t))

'=

••

Condition

on

(8),• p(t)

price,

=

-

O, we•derive•the

•••

cost/

dE

and

following

basic

5/

ren£:-

[S(t)]

, dS(t)

dS(t)

+

w

_O]q7

_Q(t) 3L(t)

+ a

That

••is,

products three

the

derived

since

loss dS/dQ

marginal

from

components.

marginal

. u(t)

foreBt

The

of

social land

firs_

<• O.

The

two

at

term

environmental

value any

on

of time

the

must

right

Services.

other

agricultural

covers

This

components

include

are

the

is

positive.

the

marginal m

_production cost up

cost

(or

second

scarcityrent)

which

wiped

(the

are

•out

(third

agricultural society•.'s

not

on

replenished term).

_roduction

and

the

and_

on-site

from•

mlrgina!

resources

marginal forest

therefore

inter_temporal

the

being

because•secondary•forests The

• commodities viewpoint,

term),

cost

land}

includes

Of

user used are

producing

according

to

environmental,•

costs.

5/ matical

-- The •appendix derivations.

presents

the

details

of

the

mathe-


I0

Once no

the

longer

pays

agricultural better

hand • side for

of

society

eq.

obtaining

_sour_es

as

exceeds the

lands.

additional

_such

(8)

toproduce

commodity•on•forest

off

other

right

lowlands

Hence,

or

it

unit

of

society

is

next

agricultural

the

p(t),

products the

from

international

market.

The

movement

may

be seen

(9)

Basic

from•the

+

From

in

of

2

[p(t),

(9)

size

benefits

> 0,

is

of

u(t)]

i_n_n _itu

+

[p(t)

and

•resources

Here is

enjoyed

u(_)] > 0,

we

carried

by

dE dS (t)

- a

(dE/dS)

positive.

f0restland

are

on

8Q(t) _S(t)

(8),

(_Q/_S)

equation

rents

now

:

a.

equation

that

optimum

scarcity following:

condition

u(t)

given

of

=

> 0

then

can,see

u(tl

;

thus,

(u(t)/u(t)) that

forward, [

society

r.

whenthe three

(left-hand

types

side

of

f,

(9):

(a)

increase

production value

of

italics

costs

in

of

additional

its

value;

(b) •

..agrgc_.ZCura z enylronmental

inserted).

The

sum

reduction I

commodities; services

9f

of

these

future

and

(Howe

ben4fits

(c)

the

1979,

p.93;

should

yield

i

the

u(t),

socially

the

required

of

return

r

on

the

value,

of

scarcityrent.

Hence, the

rate

optimal

the rate

first of

basic

producing

condition agricultural

(eq.

8),

crops

tells on

us

forest


11

land of

While

basic

forest

III.

2

(eq. 9)

shows

the

optimai

stock

lands.

THE PRIVATE INDIVIDUAL'S USE OF UPLAND SOIL RESOURCES" RESOURCE OPTIMIZATION UNDER INCOMPLETE MARKETS After

having

discuss

land

of private

tenure;

those

case

Private

A

potential

ignore of

his

would

without

With

for

tackle

with

secure

rights

Secure

agriculÂŁural

environmental

;

Land

in

and

the

objective

function,

with

Tenure

a

products services

The

would

provided

Corresponding the

perfectly likely by

Q(t) [ /

Maxlmize

formulation

omission

of

E

[S(t)],

D (_,

t) d_

wL(t)]

-rt e

-a

Q(t)

-

o t

subject

to:

(i0.i)

(i0.2)

(ii)

corresponding

p(t)

the

in:

L_t)

The

now

"We

those

cultivator

resources.

(i0)

:

we

Cultivators.

upland

off-site

rules,

criteria.

users

in situ

result

decision

property

Resource-User

setting

the

resource

shifting

The

Competitive

stock

of

societal

decision-making

cases

special

3.1

derived

individual

three

of

condition

=

basic

conditions

w Qi't)

L(t)

+

a "

S(t)

S(t)

>

would

be:

. u(t)

0

.

dt


12

I%

(12) "

'_(t)

+

[_(t)

Equation

(ii)

- a.

implies

agricultural

crops

raised

the

cost

p(t)

social

because

off'site

the

value

the

factor

the

same

both more

of

demand

area

society

would

for

equations

incomplete

through larger

the

forested swidden areas

tend

to

be

than

tha6

as

are

of

not

deforested

(8)

that

is,

(8)

_by

eq.

would

ailarger

in

area

that

given for

u

iconditions,

o_

the

whenl

the

agricultural included

produce

rent

is, i golving

by

, f0rested

the

situ

basic

given

faced

environmental to

than

Therefore,

against

Hence,

off-site

lower

products

difference

< u.

of

eguation

individual

second

p(t)

Ignored;

> 0.

That

uplands

farming

are

result,

the a

Q

because

a

be

in i

convert

faster.

for

implies

Converting

would use,

respectively, > 0

less

an

As

rise

would

agricultural

or

consider.

two

(12)

for

cost"

earlier

(dS/dQ)]

agriculture

u

(dE/dS)

is

.r . .u(t)

"private

costs

.

crops,

(12)woul_

and

(ii)

=

uplands

_ecisi0n-makers,

equation the

the

indicated

curve

agricultural

upland

in

in

the

eDvironmental

equation

of

Q(t) S(t)

that

[-- (dE(S)/dS)

types

_(t)] .

in and (9)

magnitude market

is

effects

of

croplands

in the

and

scarhity

decision'making

a_so

exchange, rent

rises

faster.

Furthermore? public individual

choice

private in

normally

terms uses

of a

the rate

time higher

preference than

what

differs

from

rate: a

an

public


13

planner

would

comparing

equations

(dE/dS)

3.2

apply,

> 0, we

The

Individual

(9)

and

the

resources the

_or

a

right s

effects

U(t)

=

0.

would

be:

(13)

p

In

this

=

Land

area

be

u.

from may rights.

use

more

a decreasing

of

soil

responsive stock

of

soil

rights.

land

are

decreasing

forests)

case,

corresponding

the

u and

property

would

r&s, that

production

secure

public

mind

land-use

exclusive,

of

the

Tenure

changing

tovarying

effects

use

in

between

Secure

withoutâ&#x20AC;˘pr0perty

to

(of

has

for

bearing

gap

of

thus

agricultural

upland

future

th'an one

When, stock

who

given

on-site,

resources

Without

according

cultivator

and

wider

to

differ

Solving

(12),

effects

production

An/upland

> r."

evena

User

to

additionally

to

r

obtain

Reaction timber

or

may

not

secure,

be

excluded,

basic

the or

conditions

w

_(t) 8L(t) (.14)

u(t)

â&#x20AC;˘=

r.

u(t),

or

u(t)

=

u(t)

The

price

thatthe

tilled, to

his

public, valuation

production,

That reflected

as

is, by

cultivator (erstwhile) Of

depicted

the

attaches forest

effort by

eq.

that

to

his.produc

land

is

went

into

equivalent

e only

agr'icultural

(13).

assuming the time preference r, for purposes of. asimpler

rate is properly exposition.


14

Public farming; cost

land

a

"smaller

rises

at

u(t)/u(t)

.in

the

following

with

the

the

>

used

stock

a

at

of

faster

a

faster

forests

rate.

equations

(9),

differences-being >

(12)

and

(u/u)

>

0,

for-swidden

,.results

accounted

[_Q(t)/_S(t).]

rate

Thafi

relationships:

terms

a.u(t)

is. hence

and-

is,

solving

. (14) (u/u)

>

forby

[dE[S(t)

.user for

would

yield

(u/u)

> _ 0,

exclusion

of

/dS(t)]

>

'0,

and

rights

for

tilling

the

forests

0.

Indeed,

with

the

absence

of

property 1

"I "

the are

Uplands, even

the

upland

depleted

at

a

resources faster

'

whichinclude

rate

because

the

stock

effects

[

are

excluded

tenure

indecision-making.

leads

comparing

_to

an

even

equations

marginal

user

faster

rate.--

arrived

at

Moreover, higher

(14)

cost

and

rises

byvarious

discount

(12),

and

because

Figure

of

the

forest

of

rate.

_

land

.i .shows

users

insecurity

> r,

_s

Thus,

the

faster

depleted

results

Of

landâ&#x20AC;˘

at

.a

decisions

Theforest

area

1

used

for

agricultural

production

by

socilety

(aQ) -

than by

that the

largest

In we

shall

aQ.

is

thereby

U/U

determined

by

individual area

the

aQ

special

!/

Scarcity_rent

.'=

_

â&#x20AC;˘

<aQ

case more

furthermore resulting

individuals

withoutproperty

(i.e.,

discuss

private

of_the fully

faster being

rights

less

A

and

who.

â&#x20AC;˘

aQ),

and

uses-

the

< aQ).

cultivated in

(aQ

is

Shifting

in

section

cultivator-, 2._

frequently depletio equal

n of

below,

by soil

to zeroS"

in

which the

Several

area

users,

_es0urces. fact,

implies


is

p(t )

_ .MC(t)

= (dE[S]

'dS)(dS(t)/dQ(t))

+-

w(aQ/_L):+ .a.u(t) -_C(t).

p(t )

%

i_( t )

\

= w(aQ/aL)+

a a

"_ t) = w(_0/as)..

• i

:

[_(t)

• I •l I I -

|

ap,

FIGURE.

I I . i. I. I

I I I

I

.

L

""

t • I • !

I [ I .I I

<_

D(t )

I. I •

-_ _a_4

_(t)

,- -.

I : ..DETERMINATIONOF AREAFOR ,.AGRICULTURALPRODUCTION .BYVARIOUS DECISION 'MAKERS

L

E G.E.N

D :

Decision-maker

Marginal Cost

Area

for Agricultural production

society

MC

aO

individual .with property rights

_

a_

individual,w/o property rights

MC

a_


16

3.3

Behavior

Given.• •paths

of

_•, •2,

these,

we

forest

production and

of

in

scarcity

focus

on

rent

in

products•

and

soil)

for

proceed

of

three

cases

factors_

for

hot5

time

to

determine

stock,

time

agricultural

discussed

above.

products,

assume

th@t

services,

We

abstracting•from

agricultural

and

the

agricultural•commodities

therefore

We

products

over

price

amenities.

resource,based

•_

resource

the

supply

demand

and

now

uplands,

resource

changes

may

(and

the

R

forest

for

relative

varying•

prices

will

hold.

We the

compare

market

is

decision

maker

resource

stock,

property (ii)

forest

soil

complete,

with

butwho

_rights

would

We

0.

attribute

a

produce

would

initially

at

lower

a higher

decrease

Further,

since

the

from

a

faster

social

and

[p(t)

individual's - a

discount

u(t)

and , he

of•the

> u(t)

in

als0

[-dE[S(t)]/dS(t)) sector

resource

commod{ty the

ra_e

rate, private•

< or user

r is

{

society;

and

price

resource

stock

is•

lower

than

i

discount

u(t)]

(8)•

rate.

F

the

from

equations

private

,

individual

effectsbecause

•agricultural Q

an

where

amenities

since

•the

level at

by

stock

> p(t),

Thus,

society,

off-site

obtain

p(t)

>

p(t),

the

by use

internalizes

exist.

(dS(t)/dQ(t))]

use

resource

•who disregards

the • relationship,

user

resource

excludes

equations

the

leiss than

initial that

for

°1

(dE/dS). (9)

> _•

and

H_n_e,

(12). •

the

terms

•scarcity

rent


17

thus

increases

resource

faster

stock,

-.After resource

more

a

for

individual

..has

.elapsed,

longer

time

stockswould

result,

in

,

extracting

who

uses.

the

rapidly.

. ,

in

the

the

however,

higher

lower

incremental

costs

.

resource'based

- product.

In

addition,

1 rents

rise

p(t)

at

> p(t)

In

case

or

rates,

Q(.t)<Q(t)

when

the

uplands,

,faster

of

the

u

(Figure

a resource

shifting

or

user

> u.

Eventually,

2).

who

cultivator,

has the

no

tenure

in

situation

is

the even

J

worse:

the

initially

decrease-rapidly increase

time,..

who.

has

Q

no

production.." >

lower

rapidly.

in

u

to

u.

,

higher

This

> Q

levels, means

and

tenure

disregards

Scarcity

rent

Thus.,

and that

.<.p

virtually

production...

agricultural

a

scarcity

during

because even.

'rent

would

earlier

point

resource

user

an the

the

wouldrise

affecting

during

production.would

stock,

ata

effects

higher

agricultural

latter-point

in

rate,

of or

commodity

time..,, p

> p

A

when

3.4

Q

< Q

The

Shifting

For public

..

Cultivator

upland..farmers forests,

several-

the

.cultivators

land

occupying .may be

in . a

inadequately

tilled

similar

many

secured

timesover

fashion,".thus

by

crowding

}'.

occurs, specially alternatives,

in

the

exploitation

under, in

condit_bns, the

economy

of

open

of"high (clark.

access

fishery

unemployment, 1973),.

and

resources, orlack high-man-land

of


18 FIGURE 2" ,..

TT_MEPATHS OF S, . . ,. ,

Q, p

AND u.

............

_

•" •

_._---'_"_-" -

,,

Social optimum ' ' "

I* I_%

-_'- -__

-- S

_"

•_

7-:

private

-- S

w/o property

,,,,i

, i

I,

rr

I

J

.

I

' I I

i

, "

I , ,

I

i

,

' ' .I I

- _!

. p

I

_,_,t

'_,"_ ,...,-" ' ---_"_ _ _'- _ "-"_

•b.

jL

• ,_

1_ _ .-_- I/

_

i

_._._"_-.. _,,.,,'"- , _ ' "

I I

L

/ s'"/" I,) J, _

,,' " ...-

I__.--° I ! I . I •

rW

,, ,-JJf

,

,

I I

p, U

I

i

tim_ pa,ths of agricultural prOduction and lstocks of forest lands i

...........

rights

.

I I

a.

optimum.

w/property private opt_It_,rights

__

I

II

J,, /

_

"

..

"

time •paths of agricultural and scarcity rent

•prOduct price


19

ratios.

In

stringent

time

seasonal

few

because

are are

uplands to

that

slash-and-burn

of

If

time

portion of

of

is

a

average

is

only

the

first

the

Fast rains

Mostshifting 1-3

cultivation more

come,

after too

a

which

farmer

the

is

is

highest.

till

invasion

of

shifting

the

has

agricultural follows yields.

field

weeds to

it

negative

subsequent the

is,

In figure

resources

lower

therefore

that

burning

for

soil

type

Indeed,

and

curves

in

relevant

_

declines.

top

and

feasible

technique,

section,

illustrate

product

laborious,

low

available

the

afÂŁerfelling

the

is

slash-and-burn

sloping

resulting

by

arenot

input I,

for

depletionof

imposed

kaingin-making.

lines

cultivators

years,

or

a

not

preparation

production

total

is

season),

productivity

Solid

the

labor

land

downward

is

where

availability

labor

curv6

harvest

with

of

hiring

variable

agricultural

curves

labor

planting

product the

conditions

preparation

surplus

only

agricultural

production. after

or

the

the

is

when

portions

low

and

farming,

total

the

occurred

used

a time-saving

agriculture

when

3,

adopt

land

effeCtive

during

induced

ÂŁropical

for

and

tools

incomes

tMe

under

constraint

patterns,

(e.g.,

in

addition,

for

makes

another

0nly

further field

is

desirable.

The effects

shifting by

cultivator

either

use

technology,

the

availability

developing or of

udjusting produce

Who

has

better, his from

tenure

stock

land-conserving,

consumption the

avoids

land,

soil-

pattern andor

to

seek

suit other


20•

•sources

of

during

livelihood.

the

fallow

replenish

system

by

• of

other

of

w. crul,

1982

for

the

e_amples

country's

•.

is

soil

is

Indeed, on

to from

under

a given

evolution

of by • a

!documented case

minority of

able

eMploitatiQn

been

practice

that

protected

Philippine•f•isheries'!

The

is

_he

resource

cultural

implies

feasible

usershas

• of

••up!an_s)

the

land

this

rules

for

Of

rights.

resource

choi.ce

which

piece

users;

determined

community

1984

the

property

•commonly

latter

period • during

itself,

•encroachment

The

(e.g.

and

Lynch,

groups

shifting

in

to

the

another

r

field

is

cost

thus

(and

natural

allowing

process

The upland

choice

of

Ithe rules

for

man'land

the

presented

opposite

(Figure by

Figure

3b).

Sanchez

a

technique

the

the•use

,stable" long

of

(1976,

p.

land of

area

land. of

periods

• such 384)

the land

among

the

availability••and

For

areas

shifting are

with

followed with the

diagrams

which

we

low •

a_riculture

areas

{

4.

the

preparing

eventualshorteningof Similar

through

of ; declining

characterizes

and

user

reiatiOnship

system

fallow

marginal

degrees

on

case

density,

[

as

a

higher

conservation

cultivators,

governing

where

population period

as

varioUs

upland

result,

3a);

in

ratios,

soil

burning

depending

population

avoiding

regeneration).

of

results

of

on-site

of

productivity,

may

a process

(Figure high fallow

• have

been

reproduce

here


21 FI-GURE

3 ;i SHL_r-'_EAG_CUL_mE

IN.I__3_T

J

......

Total

product ,

'

'

" _ .-f_

:

• • . ,,

-

/i"i /_i

I

J

/: j

"

i ,

-

I

I

-.-

!/ .

_._'_

+

"

/i

_i/ I

J

'

,.

"

a

_i

_ +

i .

!,,, i

i

.

r4 •

i

0

: . i

j/i.5 I

¢_ _!

,

I

_"%./- ;

. , Q_ Q_

IQi

I

]

i-

..t_

a.

T_' J

_.

, Jr

..

"

_,,,._ ,,%..,._

'

:, .... .. / • / i /

,

"

t 2

.

X-

_Q_

]

" ;

-!

"

'

t,3 ,.. t_

_,_

s_a.hleshifting agriculture replacing aforest managedfor timber production

II

I

.

,

.,

..

I I'II I

I

...+

Total _roduet

.....

-

'

'

' _

"

•-

•. /

/ . b.

/

F "

"t -, ..1__

_-_--"--_

..

E/

.,,...-/ _-; i.. +,.',-• / .+ ./. ./ ._t J ,,_i ...:/. ./ • /i<,,_-F,_ -..I/\L._["_ i .. / :_" V ol__2 • / " ,_' ,"JJ,._.l_q,', 1-_. /i;_), _"% " . "

-•

:--"

: :'

/i _:!

.

.

" • _"/.J"_ /1: i

.

"

'1,

. "

.

_

'

l

',! ""#

!.

i/i

t-

1

t

"

)

./1

"

21 _.,_

/'_.-' I";

-_'_, -

i i Q:

,

.

.

2 _3.t4

an unstable shifting cultivation syst_n

.. " Time

..


22

-- _ -

-

L--Y ._; CLIIlivallon

_

y_t_

,

_

. I

_

Maintenance

u°,,e_es_,V Retlenefal.ion

years ,.

o_o<._a,y _ F dlJ_w

---" •

I

!

y_dtt,

'],

1 1

,_

_,

I

i

• I

i

I

__n_nce years

!

1

I

I

1

O,',t,_a,,o,,,'=C<;'_7o-_ -_'--> ...... years

I

0

.5

FIGURE 4: Source:

_

year'.,--

\/.

--

I I0.

q

I

I

__v._. __ =

I

,....,141. .:.<.20_".. 25 _' 30' : Years

Theoretical failowand

t

I 35""

relationship betw__n soil productivity.

t

1 :

40 :'

.45

"

length of

Guiliemen, R. _956. Evolution de l'agriculture autochtone dans l_ savarun__sde i'Oubangui, Agron, Tropica]e (France) ll: 143-176; reproduced p. 384

in Sanchez

(197.,6),Figure

i0.17,


23

The the

F-labelled

forest

lands.

which

The

production. signify

•.

is

have

and

the

Q is

•_irst

of

to

tlme

t

forest

agricultural

•F

at

the

the

when

C0nducted by

from

curves

to•

output.

at

indicated

use

the

harvested.

•thus

production

pertain below

of

the

been

timber

traditional

located

values

is

• to

'Q'

production

by

timber, ,

are

3a • depicts

shall

signified

been

current

agricultural

refer

labelled

They

iower

trees

has

curves

Figure for

curves

forest

the

is

stand •

used

of

Production

of•crops,

the

of

expense

segment

Of

curve

future F

that 4

covered

du_ing

the

time

interval

(t

, t 1

The

dashed

portion

of

curve

Q

). 4

shows

production

of

2 biomass

by

the

cultivation

untilled

again

fallowed

in year

t

land

.

which

Figure

3a

is

used

there£ore

for

shows

a

2 shifting piece equal

of of and

equal.

land

gives

the

variagt of

in

such

a way

is used '•only

at

same

other

•of

yield, this

intervals

periods

and

piece

of

land

when

at

shorter

which

increasing

a

given

which

things

diagram

fallow

that

are

remaining depicts

yields

is

a not

here.

The agriculture, result

patterned

forest

A

lengthening shown

fields

in

same

which productivity

occurs

declines

in

subjected time the

to

shifting

intervals,

long-run.

The • determination of t •is the subject area of study/ and is treated as a •given here. may see Samuelson (1976) for this.

shall This

of The

is

another reader


24

depicted•in

• Figure

•3.1b

(t ' < t , t ' .< •2 2 3 production dedlines.

This

figure

effects

of

off-site

where

the

fallo_

periods

t

,. t. ' < t ) , ! and 3 " .4 '4 (Q ' <.Q. , Q ' < Q ' and 2 2 3 3

shows

both

depletion

user

.but

enviEonmental.

it

•effects

c0st.a:nd, -does •

of

decrease,

agricultural Q

'.< 4

Q "

on-site

not.

).. 4

Stock

present

slash-_nd-burn

the

farming_

[

Thus,

only

the

concerns

of:the

individuail

(timber

IV.

manager

and

theshifting

.SOME INS!GHTS We

now

points

we

FROM THE

.presen raised

cultivator)

evidence

gathered

We.

focus

not

always,

firit

t

some

• in

the

i,

data

and.

has of

several

discussion

on

.agricultural

the

hastens

severalyears.

use

except

compared

of

at

for

as

on

felling climax

alternative

j

are

usually,

labor,use, by

was

the

eleven

years.

and

3),

We

• ofdecay,

note

protection, This

forests

biomass

in

relative"to

activity

gathered

"Hanunuo

is

(woody which

.(old-@rowth)

• of

but

minorities.

labor-u6!ng,.

of•secondary the

by-.citing

kaingin-maki.ng.

interplanting,

more

•thick

the

Cultural

least

theconversion to

whichi

(stages:2

.. such

for.. the

trees,

data

climax•forests

and"harvesting,.are

for

Of

vargous

oh

swidden.farming

weeding,

intensive

systems

members

.cycle

activities,I

bamboo•type•),,

researchers

presents

•presented.

the

,

by

a

are

whichsupport,

preceding

"stable"

(.19.57)

that• felling other

on

which

Conklin

:Mi.ndoro,

by

evolved

Table

Burning

makers

PHILIP, PINE I_XIPERIENCE

by

decision

,.,,,

from which

is

true or more

forests. the could

felled take


'25

TABLE LABOR-USE

IN HANUO0

I SWIDDEN

of

FARMIN_

Ma_,.--day s Swid_e_ i_ Secor, d Growth

New

=

C lima Sta_es

i

Site

Act ivity

" Forest

Selecting

.8

•2

SlashirmD

•3

Fel i ir,g

4

5

•6

Piar, tino Maize Plargting Rice lr,terol ant inq. Repiar_t iTi'._ Fencing Protect i_g Guardir, c! First Weedir_o Secorld Weedino_ ThirJr_irw_0& Last

" Wee diri0

Harvestir__q Maize •H-arvestirt_ Rice Storir, o' Rice Cleahirtg Norr--ora in -Cuit i vat ior, arwd Harvestir_g ' • .

Total

SOURCE:

43. 8

18. _

i..2 .5 .21.9

5. • .2 _2. 5;

1.2 18.8 37.5 6 18.8 18.8 50.0 1_.5 . ;_5.0

Cor, klir,

(1957).

4 18.8 5.0

..

1.2 16._ 37.5 .6 : 18.8 9.4 _5.0 18.8 25". 0 31.2

.

5.0 .2 6.21.2 lb.2 3 t. 5 .3 18_ 8. 9.4 25.0 18.8 25.0 3!.2

-'i0.0 37.5 3.8 25.0

10.0 37'5 3.8 25.0

10.0 37.5 3.8 25.0

62.5

b2.5

6_.5

,

. -.

,

..

Bainboo

12.5:

, 358. I

371.9

,

Cor,klir,'s original figures whic_ we_'e cor_verted to rnar,-days.-usirig

pe_?..mar_-clay..

Woo c_y

.4

397.5

,

N.B. : hours

"

.8

Fire •breaking Burriirlg Rebu_r_i'rJ_o

--8

x

(

were exoresseo a facto_ of..8.,

:tr, mar,r_ari-hours


26

The

highly

seasonal

rainfed

uplands

•Palawan

•Island.

differing

some

collection labor

to

allowable

that

of is

the

practice

such

years,

system's

trusive"

with by

this

include in

numbers

Of

depicted where

the•

a

system.

a

small

seventy-five

a

that

very

terms

of

system,

agricultural is

!ow

as

notes

to

Rice's

potential

for

that

lowlanders

assumed

far

•Rice

at_:empt

predominantly

an•

(as

the

this

living

•in

80).

• pattern

Rice •,

•by

an in

to

in

people.

practiced

a system

has

on

••The first

l•iveli•hood it

similar

depends

systems

refers

As

with

2 presents

resulting

of

cultivation to

Table

density.

concerned),

p.

second

people

three

lengthy.

normally

(1981,

support

evaluate

source

large

shifting According

of

andlpa_ticipation

uplands

used.

upland,

quite

are

is

The

the

Batac

undertaken

other

population

the

major

supporting

clusters

the

of•livelihood

fishing,

to

"s ingle-crop-i•a use

system

for

from

activities

are

sources

of

being

(1981)

computations

(18)

capacity

system

labelled

be

food

products,

conditions

Rice

cycle

5,

crops

supplementary

non-farm

forest

the

agricultural

pasture

Figure

produce

the

producing

market.

•geoclimatic

maximum

of

by

Various

of

of

Indeed,

by

depicted

abilities•to

group,

the

is

• pattern

a

Ikalahans The

years.

Table

single of

crop

Nueva

agricultural

fraction (75)

in

compared The

2 • is is

Vizcaya cycle to

third

•that

Of

planted. typically

is

eighteen

the

previous

system,

which


27


28

TABLE EXAMPLES

OF

a

"

UPLAND AGRICULTURAL'SYSTEMS OF ALLOWABLE POPULATqON

.

EVALUATED DENSI?Y

IN

TERMS

_ca.di t i9r,a_

No r,-T_md i_tior,a i Systems:

Single Crop Intrusive

Single C_c',p Ind i _er,o_s

.

Usual period cultivation

m

2

,,

"

of

.

,

Ir,diqer, ous Ir,t er-Croppin9

.

,,

5 years

4

year:_

5 years

,L

b.

Subsequent use

_ 40 •yea_?_

pasture

-

-

i

c.

Required

faliow

.per:_orJ d_

Total agricultu_a% •cycle ( a+b+c)

e.

Utilizatior, (a/d)

f.

rate ..

"Sr_ years

14

yea_s

1 I yea_s

. " _" 75 Yea_s

18

yea_s

16

7%

•Cultivated larfd r,eecled pe_ _ami ly as observed

.

1.4

2.2.%

h_.

_1.0

'J

_. "

h.

A_i.cult ural neeclecl per : (c/e)

31%

h_.

0.7

ha.

2. 3

ha.

,25. 3

ha,

i

la_,d _?arhily 20

ha.

4.5

ha_.

Agricult ural ar,d • watershed lan_ • riemclecl

i.

years

Maximum

per

family

_9.5

ha.

al iowem

populatic, r, der,s_ty per 1000 -,bern'tares

SOUrCe:

420,: ha_

Rice

a. 4

(198[L')_ 'TaDle

2,

20_

fmrnD

p.

80.

. _-_ "_arn.

-, 3"9. 5] Tam,


29

•is

swidden

•therefore

farming • able

with

multiple

tosuppor

t a

iarger

system"is.usua!lyobservedof, Kalingas

of./Northern

An

the

.aspect..

of

.Tiboli

of

more

and

people.

is

This

Mindanao

and

the

by-Rice

which

.:is.

not

" '

usually

.tackled

terms,

.is..tl_e

by

other

researchers,

.at. least

watershedarea.implied

(item.

the

group

presented

W.

of

yields

Luzon.

important

systems

crops,•

h

of. Table

environmental

by

2). ' " This

service

the.

empirical

three,

implies

provided

in

.a

upland

recognition

byforests

in

the

uplands.

Table.. for

a

3

presents

grQup.

of

data."on

erstwhile

!owlanders :

porti0n-of yields...

a major Over

time

characterized View,.

and

degradation

as

minoritiesare

V.

.urgency

now

[

productivity cultivating

a

[

Luzon.

It

whose

shows

decreasing

conditi0n

has.

theenvironmental for

been

point

solving

.cultivation..Problems

the

.where"

"

of

upland

non-culturall

concerned.

derive

the

.decision

conditi0n.s.for has

rice

IMPLIED POLICY TOOLS •To

public

a watershed

.critical.from

.-implies and

watershedin for

upland

property

respectively,

various

maker,

we

opti_izationl.by .rights; as

and..the

follows:

pol•icy

tools

rewrite

the

society; ,squa£ter"

available set the

of

first

private on

forest

to

the basic

user

who

lands


30

TABLE AVERAGE FARM "_=¢ _"

"_" _ _ _'_"_'_-

LAND IN

_-- _---_ :_ _

::_. :_

PRODUCTIVITY

PUTING _,_-_-_-

LUPA_

_- _==

3

IN MT.

A TRADITIONAL MAKILING,i

_-_-_-_-_-_-_-_-

_=¢_

w_.D_._. _-',,_

1978-1980 =s _ -,i. _ .-,:._•

Producti_,r,. Per (ca_an)

Year

197e

26.74

1979

13.89

19_o _---__--.-_---_-__=,___

Source:

KAINGIN

_.68 _:______

Corpuz

Hectare

(1984),

___

Table

28,

p,88

_.,_

_

_ _. _==


31

(8)

p(t)

= w/[ •

(11)

^ (t)= p

(13)

p(t)

We

Q(t)/

= w/[

Q(t)/

the

restricts

access

encourage

the

.

L(t)]

+ a

. u(t)-(dE[S(t)]/dS(t)])

+

.

(dS(t)/dQ(t))•

W/[

note

marginal

Q(t)/

L(t)]

a

L(t)]

assignment to

the

Upland

user• cost,

of•

property

uplands

by

cultivator or•a

. u(t)

•rights,

which

users,

would

other

to

consider

(i.e.,

(3.11)

at

least

the

( 3.•!3).

versus

.'

Furthermore,

a comparison

between

Shows

that

•the additional•policytool

user

to

take

environmental

cost

equations

account would

charges. would

be

curves,

as

optimal

of

to

him

tax

.

in

indicated

agricultural

use

of of

•Figure of

the at

the

the

forest

land

such

off-site

a

rate

which

or

impose

•policy

relevant

i. '• These

(•3.11)

allow

[dS(t)/dO(t)],

rotation in

and

would

some

Application

result

(3.8)

that

[ - dE[S{t)]/dS(t)]

environmental discussed

into

effects

approximates

an

u(t)

tools marginal"

would

lead

to

fromthepublic

standpoint.

A

problem

feasibility

of

farmers

whose

policy

tool

subsidies

•may

arise,

imposing minimal

however,

environmental cash

income,

unimplementable.

It

may

be

soilconservation

a more at

effective

•least

in

the

if may

with

respect

charges

on

any,

would

even

incentive

be

to

SUbsistence make

argued, for

the

such that

encouraging

short-run.

9_/ versus

•See Baumol subsidies

and Oatas (1975) for a discussion as environmental policy tools.

of

taxes


32

•More of

•importantly,

•fields

••still

rotations, provide

when-

implies an

source

large

•area•of•

that

• For

of

end

up.landarea

subsistence.

major

the

of

there

are T

is

.those

livelihood,

land.to

result

a

stable

shifting

periods

under.fallow

during

.and

cannot

who

relyion

the

uplands

this.

implies

the

need

be.worked.out,

I/n£h

of

an

as

a

for area

a

at

a

' l

time•

for

a

•rotation

Moreover,

.w_thin

there

.an

• is

requirements,

given

year

to

.be

met,

through

food

that

like•.

That

detrimental

land-extensive, population

on

sources

is,. given

effects

the

is

'is cropped, when

.through

food •

surplus

a .large

tract

such

..hunting,

as

of

••, ••

the

has

years.

months)

.fishing,and

land

either working

other

n

whi_ch

(dry

(implying.again,or

.of

during

off, farmingseason need •

production land) •,

a

period

on

potential

severely

land-use•

technology

soil.conservation,.and for

limited.

a

supporting

Therefore,

is.

.a there

growing. is

a

case

F

for

developing

a more

•efficient,

erosive.type_of.technology the

for

-land-saving, producing

•less

soil-

non-timber

croPs•in

need•

securing

up•lands.

The r@ghts

dis•cuss•ion to•use

•encouragement Conserving. conserving

up•land • of.

" .The

alternative

Case

out

the

resources"for

for

uplandfarmers,

and..well,defined overemphasized.

t_us. points

.rights

agricultural

technologies

agro-forestry, control' for•such

for

.use.,

and

which

are

soil-

Subsidies

for

soil -•

of•upland use'cannot

resource therefore

use be


33

- BIB.LIOGRAPHY

Aguilar, _FI., Jr. "Social Forestry for upland Development Lessons from •Four Case Studies." Final Report submitted to the Bureau of Forest DeveloPment by the Institute of Philippine Culture, Ateneo de Manila University, Quezon City, 1982. •

Baumol,

w.

J.

Poiicy.

and

.

W. E.

:- Oates.

Englewogd_Cliffs,

New

. Th e Theory Jersey,

.

',,5

of _Env!ronment@l

Prentice_Hall,

1975.

Cadelina, R. V. •"•Food • Management Under Scarce Resources by Philippine Marginal Agriculturists: Techn01og_ical Pluralism Towards National Building." Philippine Economic Journal, 20 (1), 1981., _ •Clark,

.• C. W. 181:630_634,

Conklin, " H. Orqanization 1957. Corpuz,_ E. "A Modified Makiling." Philippines

"The Economics August 197_.

of

Overexploitation_"

"Hanunoo Agriculture. (_AO) Forestry Development

science,

Foo_i and Paper•No.

igriculture 12. Rome,

Comparative Economic Study of Traditlmnal Kaingin, Cropping Patterns and •Tree Farming in Mt. Unpublished, M. S. Thesis, University•of the at Los Banos/ Co!lege, Laguna, 1984.

Cr_uz,

M. /C. "Popuiation Pressure, Migration and Implications for Upland Development." Philippine for Development Studies • Working Paper 84-05.

Cruz,

W. D. "Technical and Institutional charge in Renewable Resource Development (withApplication for Traditional Fisheries," Unpublished_ Ph.D, Dissertation, .Univeristy of Wisconsin-Madison, 1982,

Delos

Angeles,• M. S. "Economic Analysis of Resource Conservation by Upland Parmersin the •Philippines." Ph.D. (Econ.) Thesis, School of Economics University of the Philippines, 1986.

Eckholm, E. P. Losing PrroS.pects/. New York: •

Howe,

C. W, • Policy.

.

•Ground•: Environmental Stress W.W. Norton & Co. 1976. .

.

.

Natural Resource Economics, Issues, John wiley and Sons, Inc., 19_9.

Markets: Institute

and

Food

v

Analysis,

and


34

Kamien,

M. I. and N. L. Schwartz.',Dynamic !Optimization: The Calculus of Variations and Optimal ControZ, in Economics and Management." Series Volume 4 in Dynamic Economics: Theory and Application, Edited by Maurice Wilkinson, North Holland,-198i. .

Pelzer, K. Asia," Rice,

J. "Man's Role The Journal of

in changing the Landscape of Asian Studies, 27 (2), 1968.

Southeast

D. "Upland Agricultural Development in ÂŁhe Philippines: An Analysis and a Report on the Kalahan PrOgrams." Adaptive Strateqies and Change in Philippine Swidd_n,based Societies. Edited b_H. Olofson, Forest Research Institute, College, Laguna,. 1981.

Samuelson, P.A. "Economics of Forestry Economic Inquiry_ 14 (4): 466-492, Sanchez, P..A" JohnWiley and Lynch,

O.J., Fuijisaka, Agriculture InstituÂŁe 1986.

Properties of Sons, 1976.

Soil

in an; Evolving December 1976. Management

in

Society."

the

Tropics.

Jr . "Philippine Law and Upland . Tenure, " in S., P. Sajise, and R. A. del Castillo, Man_____, .and the Tropical Forest_ WiDrock International for Agricultural Development. Bangkok, Thailand,


APPENDIX •MATHEMATICAL

ANNEX

Optimum Agr-icultur,al Useof Forest Lands: Soil Conserving Technology (Agrof0restry) Unknown

Given

the

agricultural function• and

(i)

following

firstthree

production, (2),

and

social

environmental

O(t)

function

(I),

benefits

services

•equations

from

from

agricultural agricultural

resource

•_Q _L (t)

_Q

,

_S (t)

_2Q

and

'

stocks:

p(t)

=

[O(t_,

(3)

SB(t)

= _0 (t) D[_(t),

Net

benefits

(4)

Max

from

_ /0 L(t)

s.t.

[

dQ

> 0

d2Q

%S _(t)

(2)

'--d_

< 0

t]

resource

t]d_

+ E

use

[S(t)],

is

maximized

IQ (t)O , 0 [_(t) t] dD + E

S(t)

S(0) - a • f0

dE dS > 0

as

[S(t) _- wL(t)]

follows:

e'rtdt

Q(T)dT

S(t) > O the

(5)

S(t)

products

dt

_2Q

_L 2(t)

D

,

first =

constraint ~a•.

Q(t)

of

equation

(4),

we

obtain:

the

demand.

= _ [L(t), s(t),t]

where

From

for


35

Using

(4 )

Hamilt0nian

(6)

_

may

be

=_N(t)D(_,t)

where

u(t)

equation

(7)

and

the

following

current

value

formed:

d_ + E IS(t)'

•is• the

(5),

(5 )

•and

current is

value

equal

DO(t)

_ = D[Q(t),tJ BL (t)

wL(t)]

_L (t)

_t"

multiplier rt

•to•l e

+

i U'_'Q

- a

_

associated

with

:.

dE[S (t)]

"

dS (t)

dS(t)

_Q(t)

"

dQ (t) •

8L (t)

_Q (t)

-w-a

. u(£)

Or, substituting

(2)

_ =

gives-

_ . _L(t)

p(t) -w

-

BL(t)

+

dE[S (t)I - dS(t)

a_. u(t)

dS(t) • dQ(t)

_O(t) •

_Q(t)

_Q (t) Setting obtain

_ _L(t)

dividing

by

_

we ) 0

:

(8)

ds

aL(t) = _(ti Thus,

and

0

we

have

(9)

p(.t) =

The

second

differentiating

basic

+

dE[S(t)]•• dS(t)

condition.

- cIE[S tt-_h]

_(t)

basic as

follows:

_ t,) S 0

1 as:

dS_ " •dO(t)

condition

dQ(t) (t,)- w - a

+

•_'w aL(t)

may

be

s_

•. u(t)

obtained

by


(I0)

u(t)

-- r

. u(t)

-

_H

._s (t) =

r.

[D [O(ti,

u(t)-

-a

•using

+

dE [S (t)] dS(t) 'r

•j _Q 8s(t)

. u(t) .

Again,

_Q 8S(t)

t]

(2)

and

rearranging:

'

J

(t) = r ..u(t) -

+

_Q _S(t)

p(t)

dS (t). dE[S(t)] I

= r . u(t)

Thus,

the

(ii)

u(t)

-

.. ' - •

•_

[p(t) - a . u(t)]

second

basic

_Q 3S(t)

a . u(t)

dE[s (t) ]

3S(-_

condition

-

dS(t)

is:

_Q +

For ' the

[p(t)-

private

omitted

as

conditions

a

, u(t)]

decision'maker's

an

argument

in

dE[S(t)] r.u(t)

-_SqE]-.+

dSqt)'

case (4) ,.

where

t_he

E[S(t)]

resulting

is basic

•would • be : w

(9)'

_

(ii)'

(t)=.

6(t)

Further, private

••

_Q(t) + a . _(t)

+

.pit) - a

when

the

individual

corresponding

b_sic

S(t) who

"W

_(t)

- 9

is excluded has

conditions

_L (t) (ii)"

• _(t)] _s(t):9

. _(t)

not

• Q(t) as

a co,stralnt

property as

follc_ws_

rig_tl

_

by have • ,

the

-

.• the

Economics of Upland Resource Depletion: Shifting Cultivation in the Philippines  

SHIFTING CULTIVATIONINTHE PHILIPPINES Morion S.delos Angeles February1988 PhilippineInstituteforDevelopmentStudies TABLE OF CONTENTS. V. Imp...

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