Impact of Market Imperfection on the Efficiency of PES Program

Wenting Chen1

Department of Economics

Norwegian University of Technology and Science

14 June 2009

Primary draft

Abstract:

1 Introduction

Payment for environmental service (PES) has been widely applied to renewable natural

resource conservation. Mayrand and Paquin (2008) provide a good overview on current PES

schemes. According to them, the basic principle for PES is that those in an upstream position

to provide environment services should be compensated for their provision and those

downstream who benefit from the service should pay for it. (Other definition for PES could

be found e.g. in Engel, et. al. (2008)). The rationale for PES program is that the program

creates a market for environmental services where there is originally no market albeit there is

demand for the service. The market PES program generates is aimed to internalize

environment externality. Existing PES programs mainly cover four types of environmental

services, namely, water services, carbon sequestration, biodiversity conservation and

landscape beauty. Although most PES programs are still in the pilot stage, it has been adopted

in both developing and developed countries. For instance, water resource protection in

Ecuador, Costa Rica, France and Australia, and Sloping Land Conservation Program (SLCP)

in China. Detailed comparative analysis of PES programs between developed and developing

countries can be found in Sunder, et. al (2008).

Off-farm labour market failure or inaccessibility is fairly normal phenomena in developing

country. For example, child labour or family labour with low access to the labour market or

1 Email:wenting@svt.ntnu.no

1

facing discrimination. An extreme case of market failure is simply non-existence of a market

which might be due to a fully enforced legal prohibition on certain transactions. (Sadoulet and

de Janvry, 1995). Correlation between PES program and off-farm labour supply has attracted

attention in PES literature lately. One stand of the literature tries to explore the impact of PES

programs on off-farm labour participation. For example, by studying the medium term effects

of Green for Grain (Chinese PES) program, Uchida (2007) finds a positive effect of the

program on off-farm labour participation. Similar result is also found by Bennett et.al (2008a)

on analyzing the impact of restructuring forest sector in China. They notice that households

became less dependent on the state forest bureaus and have been able to diversity their income

opportunities.

While the other line of study focuses on how off-farm labour market accessibility on the

effect of PES program or environmental service provision. Fewer studies are available

according to our knowledge. One study is done by Bennett et.al (2008b) who finds that

households with less exposure to off-farm labour markets fare better in managing their

planted trees in China, which will lead to higher ecosystem service provision. Another study

is carried out by Mullan (2008) who studies empirically how market failure, including credit

market, land market and labour market imperfection, affects participation decision of

landowners. She found that labour market imperfection does matter. When constrained by

accessibility to labour market, those with high land-labour ratio are more willing to participate

in environmental programmes that release labour. When the PES program requires additional

labour investment, the opposite relationship holds.

However, according to our knowledge, on one hand, no study available until now which

provides a theoretical foundation for the impact of labour market imperfection on PES

program efficiency especially when upstream providers are both consumer and producer of

the environmental service. Demand for environmental service (e- good) such as better water

quality by uptstream providers depends on the abundance of the e-good and whether it is used

as an input of existing agricultural activity. When e-good is scarce and is used in the

production of existing agricultural activity, consumption of environmental service maybe less

elastic than that when e-good is abundant.

On the other hand, little attention has been paid on possible impact from relative labour-land

ratio of environmental good compare to that of existing agricultural activities. That is,

2

whether environmental service production is more labour intensive or not compare to existing

farming activities such as crop cultivation may affect the marginal impact of PES.

The main contribution of the paper is to provide an analytical framework for how labour

market accessibility affects the impact of PES program on production efficiency and

environmental service provision by taking account the relative labour intensity in

environmental service production and other agricultural activities, as well as the consumption

elasticity between the e-good and agricultural goods. Following the similar category defined

in Zilberman et al.(2008), the study focuses on two types of environmental service production,

the service that is produced by changing existing agricultural activities (working land program

in Zilberman et al. ,2008) and the one that is produced as a by-product of a new private good,

such as forest (land retirement program in Zilberman et al., 2008).

In the paper, following questions are answered

How does labour market accessibility affect the optimal environmental service

provision after introducing PES program?

How does labour market accessibility affect the marginal impact of PES payment on

environmental service provision?

Will the impact of labour market imperfection be different for the two ways of

environmental good production?

Our analytical results show that accessibility of off-farm labour market does not affect the

production efficiency of environmental service. Off-farm labour market accessibility does

impose different requirement for positive marginal impact of PES payment on environmental

service provision. The impact depends on both labour-land ratio between e-good and

agricultural good production, the consumption elasticity of the e-good and off-farm wage rate

when labour market is accessible. The impact is similar for both ways of environmental good

production.

The results also provide policy implication such as doing necessary pilot survey to estimate

relative labour intensity between environmental service production and existing agricultural

goods production. PES program will be more effective in the area with high off-farm wage if

higher off-farm wage leads to larger marginal impact of PES on optimal e-good provision. w

3

If the opposite condition holds, adopting PES program in poorer areas with low off-farm wage

will be more efficient given budget constraint.

The structure of the paper is as follows. Section 2 provides basic assumptions and settings of

the models. Section 3 explores the impact of labour market accessibility on production

efficiency and marginal impact of PES payment on environmental service provision when

environmental service is produced by changing existing agricultural activities. Section 4

studies the labour market accessibility when environmental service is a by-product of a new

private good. Section 5 provides the numerical simulation (not covered by this version)

2. General description of model

Different from most PES literature (e.g. Zilberman et.al, 2008; Alix-Garcia et.al, 2008) , we

assume that upstream landowners2 are both producer and consumer of the environmental

service, . The environmental service provided by changing existing agricultural activity

includes, for example, improvement in biodiversity and high water quality. There are many

ways to manage and increase biodiversity on a farm, both above ground and in the soil.

Activities such as mix planting more than one type of crop (e.g. planting the disease-

susceptible rice varieties with resistant varieties in Chinese experiment had 89% greater yield

and 94% lower incidence of rice blast/a fungus for the former rice type compared to

monoculture) in order to increase the genetic diversity of a particular crop, crop rotation

which could alter the environment both above and below ground so as to avoid building up

populations of organisms that feed on that plant and sanitation which involves removing and

destroying the overwintering or breeding sites of the pest as well as preventing new pests

from establishing on the farm (Dufour, 2001). Pest control also result in less pesticide use and

hence better groundwater quality. Rainfall and temperature recording and leaf counts are one

of the monitoring methods used to control pests (Dufour, 2001). Environmental service

produced by a new product such as reforestration usually mean water quality improvement,

stable climate and reduction of sedimentation of rivers. Preventing soil erosion and restoring

erosion and desertification is the main environmental service Chinese PES programs intend to

achieve (Zhu et.al., 2004)

e

2 We will not directly include the landless in our model. Welfare impact on the landless will be discussed in section 5.

4

Each landowner is assumed to consume two products: crop ( ) and environmental service

( )

Cc

ec

U c

3 . Since the study does not intend to study the impact of transaction cost of PES program

and externality between upstream landowners but only the externality of environmental

service between upstream landowners and downstream users, one representative landowner is

adopted in the model. Constant elasticity (=1) of substitution between crop and

environmental service is conjectured. Utility function of the landowner is defined as

( , ) ln (1 ) lnC e C ec c c .

Each landowner produces two goods: and . Both land ( ) and labour ( ) ( ) are

necessary input for the two goods

Cq eq iA iT ,i c e

4 .Cobb-Douglas production function has been long applied

in efficiency study for crop production.(e.g.Case studies in different developing countries in

Part II in Singh et.al. 1986). In the same vein, the production function of crop and

environmental service are assumed to be Cobb-Douglas type5. For simplicity we presume

constant return of scale in production. Our presumption is supported by some case study. For

example, household study in China does show that crop productions operates more or less

under constant returns to scale with sum of elasticity value for land, labour and fertilizer

varying from 0.928 to 0.999.( Wu et.al. , 2005) . Crop production function is specified as

1( , )C C C Cf A T A T and 1e( , )e e eg A T TA for environmental service production.

Coefficient and describe the technology used in crop and environmental service

production respectively. and indicate the elasticity of land in crop and environmental

service production.

We also assume that there are two types of landowners according to the land-labour ratio

( /A T ), the small landowner and the large landowner. A and T refers to the total land and

labour endowment for the landowner. The representative landowner belongs to one of the

types. Under our assumption, small landowner not only has less total land and labour

3 Our model skips the consumption of leisure for simplicity. 4 For simplicity, we do not include the use of other inputs such as water, fertilizer, herbicide or pesticide or machinery which is covered by study such as Zhang (1999). Since use of chemical fertilizer, herbicide and pesticide could be reduced by adopting biointensive integrated pest management (IPM) such as crop rotation, heat or steam sterilization of soil, cold storage, regular monitoring and rainfall and temperature records checking (Dufour, 2001). All the listed management are labour intensive so that the reduction in these input factors could be included in the increase in labour use. 5

5

endowment, but also has low land-labour ratio. Vice verse, the large landowner would have

both more total land and labour endowment and high land-labour ratio.

The landowner allocates his total labour endowment (T ) among production of the two goods,

crop and environmental service, and off-farm activities ( ), OT C eT T T TO . When 0OT ,

there is off-farm labour market is not accessible. Off-farm labour market failure is more

common in developing counties than in developed countries. For PES program in particular, a

lot of upstream environmental service providers are located in watersheds or marginal areas

(Engel, et. al., 2008), where gender discrimination, child labour use within household, poor

infrastructure, or the restriction on mobility between rural and urban area could all possibly

contribute to malfunctioning of or inaccessibility to off-farm labour market. Therefore, our

paper might be more relevant to developing countries. When 0OT , the landowner could

trade his labour in the off-farm labour market. indicates a small landowner who sells

labour hour to off-farm activities.

0OT

0OT implies a large landowner who purchases extra

labour from off-farm labour market.

For trading in the off-farm labour market actually happen after the labour market is accessible,

we impose another assumption on real wage rate, where the real wage rate is higher than the

labour productivity of small landowner and lower than the labour productivity of large

landowner when labour market is not accessible.

Similarly, landowner allocates total land endowment ( A ) between crop and environmental

service production, i.e. C eA A A . Crop market is assumed to be perfect competitive. This is

a more realistic assumption especially when the crop is traded in the international or national

market. landowner faces a fixed crop price, Cp .

For downstream, there are environmental service users who purchase the environmental

service.

N

3. When environmental service is produced by changing agricultural activities

In the section, we will examine the case where environmental service that is produced by

changing agricultural activities. The shortage of environmental service provision is usually

6

due to the positive externality of the service between upstream producer and down stream

users. PES literature view environmental service as a kind of quasi-public good which implies

that the use of the environmental service is excludable and this makes price charge feasible,

but the consumption of the service is nonrivalry, that is the consumption by one person will

not reduce the consumption of the others. For example, water quality improvement in the

river basin is available for both upstream farmers and downstream water users, while the latter

could be charged for the improved quality in the form of water tariff. Landscape

enhancement is another example, for which ecotourism is the main source of payment from

downstream users, whom mainly are from other areas or big cities. Due to the special

characteristic, nonrivalry, of quasi-public goods, consumption and production of the

environmental service cannot be separated. The amount of environmental service consumed

by the upstream landowner equals the amount he produces ( ec qe ). The utility function of

the landowner could then be rewritten as ( , ) ln ) lnC e eU c q c q(1C . In the following

subsections, the impact of off-farm labour accessibility on both production efficiency and the

marginal impact of PES payment on the optimal service provision will be discussed.

3.1 Without labour market

3.1.1 Ex-ante PES program

Before PES program is introduced, landowner can not trade environmental service in the

market. Consumption pattern of a quasi-public good will be of no difference as that of a

private non-tradable good, namely the landowner consumes all the environmental service he

produces.

When off-farm labour market is not accessible, 0OT . The landowner simply sallocates total

labour endowment between crop and environmental service production, C eT T T .

Budget constraint requires that total expenditure of the landowner should not exceed the total

income at a given period, C C C Cp c p q B , where B is wealth held by the landowner6 and

could be either positive or negative7. Wealth B catches landowner’s expenditure on other

goods. The objective of the landowner is to maximize his by consuming crop and

environmental service given his budget, land, labour and production constraints.

6 Here the landowner is assumed to use up all the wealth after the period. 7 A positive stands for saving and a negative stands for a loan. B B

7

1

1

( , ) ln (1 ) ln

. . (3.1)

( , ) (3.2)

( , ) (3.3)

(3.4)

(3.5)

C e C e

C C C C

C C C C C

e e e e e

C e

C e

Max U c q c q

s t p c p q B

q f A T A T

q g A T A T

A A A

T T T

(3.1), (3.4) and (3.5) may be written as /C Cc q B pC (3.1’), C eA A A (3.4’) and

CT T T e (3.5’). Insert (3.2) into (3.4’), (3.3) into (3.5’), we get

1( , ) ( ) ( )C C C e eq f A T A A T T . The simplified objective function therefore reads

1 1

{ , }( , ) ln[ ( ) ( ) / ] (1 ) ln

e eC e e e C e e

A TMax U c q A A T T B p A T (3.6)

First order condition with respect to and yields eA eT

1 1 (1eT

)( ) ( ) 0

eA eC e

U A A Tc A

, and (3.7)

(1 )(e

C ec T

1 )(1 )( ) ( ) 0

eT eU A A TT (3.8)

(3.7) (or (3.8)) implies the increase in marginal utility when crop consumption raises by

increasing one unit input of land( or labour) is equal to decrease in marginal utility when

environmental consumption reduces due to one unit less land (or labour) available for

environmental production.

Dividing (3.7) by (3.8), we get the efficiency condition for environmental service production,

(3.9)1 1

e

e e

T T T

A A A

e

8, which states the technical rate of substitution between labour

and land are the same for crop and environmental service production in equilibrium.

By inserting into (3.7), optimal land and labour used in environmental

production satisfy the equations

( )e eT A *eA *

eT

8

e

e

C

C

A

T

A

T

, where

e

e

C

C

AA

TT

A

T

1and

e

e

e

e

A

T

A

T

1

8

** 1 * * 11

( ) [ (1 )] [ (1 )( ) ](1 )

ee e

C

ABA A T A A A

p e

9and

* *(1 )/ [ ( / 1) 1]

(1 )e eT T A A

.

or * * 1 *

* 1 * 1

( ) ( ) /

( ) ( ) (1e e C e

e e

A A T T B p A

A A T T

)

(3.10)

Optimal output of environmental service reads * * *1e e eq A T .

From the above equations, whether the small landowner or the large landowner produces

more environmental service depends on the parameter values. We will discuss this more in

section 5.

3.1.2 Ex-post PES program

After introducing PES program, the landowners could sell environmental service to

downstream users, e.g. municipality citizens in the case of water quality improvement and

ecotrouists for landscape enhancement. The budget constraint for the landowner (3.1)

becomes

N

C C e e C C e ep c p q p q Np q B . Other constraints keep unchanged. The simplified

objective function yields

1 1

{ , }( , ) ln[ ( ) ( ) ( 1) / / ] (1 ) ln

e eC e e e e e e C C e e

A T

1Max U c q A A T T N A T p p B p A T

First order conditions with respect to and are put as follows: eA eT

1 1 1 1 (1 )( ) ( ) ( 1)

e

eA e e e e

C C e

PU A A T T N A T

c P

0A

(3.11) , and

(1 )(1 )(1 )( ) ( ) ( 1) (1 ) 0

e

eT e e e e

C C e

PU A A T T N A T

c P

T

(3.12)

The same efficiency condition as (3.9) can be derived from above two conditions. Therefore,

introducing PES payment will not distort landowner’s production decision. The allocation of

the inputs does not seem to depend on market size of the environmental service , neither

on payment

N

ep .

9 The equation may indicate the existence of multi equilibra. However, the result depends on the parameter .

9

The optimal land ( ) and labour use ( ) in environmental service production will satisfy *eA *

eT

1

* **

* *

1

** *

11 1[(1 ) ( ) ]

1( )

1

1( 1) (1 )

1( )

1

e ee

e e

e

C ee e

A A A TA A A A

p BN T

p AA A A

0Cp

(3.13)

and * *(1 )/ [ ( / 1) 1]

(1 )e eT T A A

Or. * * 1 * *1 *

* 1 * 1 * 1 *1

( ) ( ) ( 1) / /

( ) ( ) ( 1) (1e e e e e C C e

e e e e

A A T T N A T p p B p A

A A T T N A T

)

(3.14)

Apparently, after introducing PES program, optimal land ( ) and labour ( ) input depends

on PES payment

*eA *

eT

ep . In order to obtain the impact of ep on and , we implicitly

differentiate (3.11) and (3.12) with respect to

*eA *

eT

ep . The result shows

*1 1 1

*2 2 2

/

/e e

e e

a b cA P

a b cT P

(3.15)

where

1 1 2 1 11

11

12

( ) ( ) ( ) (1 ) /( ) ( 1) /

(1 )( ) ( ) ( (1 ) ( ) ( 1) (1 ) /

( ) ( ) ( (1 ) (1 )(1 )( )

e e e e e e e

e e e e e e e C

e e e e

a A A T T A A A N A T P P

b A A T T A A A N A T P P

a A A T T T T T

C

1 1

22

(1 )( 1) /

(1 )( ) ( ) (1 ) /( ) (1 ) ( 1) /

e e e C

e e e e e e e C

N A T P

b A A T T T T T N A T P P

11 ( 1) /e e Cc N A T P

P

Pand 12 (1 )( 1) /e e Cc N A T

From crammer’s rule, * /eA P and follows * /eT P

*1 2 2 1/ ( ) /eA P c b c b and , where *

1 2 2 1/ ( ) /eT P a c a c 1 2 2 1a b a b . Since the

existence of maxima ensures a positive determinant (Proof see appendix), the sign of

and depend on the sign of the numerators. * /e eA P * /e eT P

10

11 2 2 1

2

( 1) [ (1 )( ) ( ) /( ) (1 ) /( )

(1 ) ( 1) ( 1) / ] 0

e e e e e e e e

e e e e C

c b c b N A T A A T T T T T A A A

N A T T P P

and 1 1 1

1 2 2 1 ( 1) ( ) ( )

1 (1 ) (1 ) /( ) /(( )

e e e e

e e e e

a c a c N A T A A T T

A A A T T T

0

0

as long as . Therefore, and 1eT * / 0e eA P * /e eT P . As predicted and consistent with

most of the literature, increase in PES payment will increase provision of environmental good.

The result is not surprising when the price of environmental service ep increases from zero to

a positive level, more inputs, labour and land, will be allocated to environmental service.

In addition, since can be written as a function *eA A andT from (3.13), namely *( , )eA A T .

Implicit differentiation of with respect to *eA A and T yields

*

2 1 * *

2 / 1/(1 )1

1/ 1/(1 (1 ) [ (1 )] [ (1 )( ) ] /e

e e C

A

) B T A A A P

A

and

* 2 2 * * 1

1 * *

(1 ) [ (1 )] [ (1 )( ) ] /

1/ 1/(1 ) (1 )[ (1 )] [ (1 )( ) ] (1 ) /e e e C

e e

A B T A A A P

T B T A A A

CP

As total land ( A ) and labour (T ) endowment for large landowner are both higher than those

for small landowner, arg* *l e small

e eA A

A A

and arg* *l e small

e eA A

T T

which indicates that

the marginal increase in total land or labour endowment has larger impact on optimal land

input for environmental goods for small landowner than large landowner. The same holds for

optimal labour input. However, it is difficult to see from analytical result that whether large or

small farm increase environmental production more.

Therefore, we reach Result 1:

Result 1: When environmental service is a quasi- public good and there is no off-farm labour

market, introducing PES program will increase provision of environmental service in

optimum .

11

3.2 With labour market

When the off-farm labour market is accessible, landowners could trade their labour hour in

the off-farm labour market. 10 Labour used in off-farm activity is now non zero, i.e. .

Budget constraint now becomes,

0OT

C C C C Op c p q wT B (3.16), where is the fixed wage

rate in the off-farm labour market. Off-farm activity means additional income when

and a cost when . Landowner’s maximization problem is similar to that without

labour market except budget constraint is replaced by (3.16) and labour constraint by (3.17)

w

0OT 0OT

C eT T T T O .

The reduced form objective function now reads

1 1

{ , , }( , ) ln[ ( ) ( ) / / ] (1 ) ln

e e OC e e e O O C C e e

A T TMax U c q A A T T T wT p B p A T

First order condition with respect to , and yields eA eT OT

1 1)eT(1

T)

( ) ( 0eA e O

C e

U A A Tc A

, and (3.18)

(1 )(O

C ec T

1 )(1 )( ) ( 0

eT e eU A A T )T T (3.19)

[ (1 )( ) ( ) ]OT e e O

C C

wU A A T T T

c p 0

(3.20)

In (3.20), marginal productivity of off-farm labour (the first term) equals real marginal

wage (

OT

C

w

p). (3.19) could be written as (3.19’) e

e

C

q

C C

U

p U e

T

wq e11. is the marginal

productivity of labour used in environmental good production.

eTq

e

C

q

C

U

U states how much

consumption of environmental good need to be increased so as to keep the utility unchanged

with one unit decrease in consumption of crop. When environmental good is not tradable, the

substitution rate between the two goods can be regarded as a shadow price for environmental

consumption. Thus (3.19)’ implies marginal cost of the labour used in environmental good

C e CC

10 We assume that off-farm labour hour is perfect substitutable with on-farm labour hour. 11 As and , (3.16) is equivalent to

C C e eC T q TU q U q /CTq w P e

e

C

q eT

C C

Uwq

P U .

12

production (C

w

p) equals its marginal benefit ( e

e

C

q eT

C

Uq

U). Our analytical result is consistent to

the result in Singh et. al (1986).

Dividing (3.18) by (3.19), we obtain the efficiency condition

e

e

e

Oe

A

T

AA

TTT

11 (3.21)

(3.21) shows that with perfect off-farm labour market, technical substitution rate between

labour and land is the same for crop and environmental services, which is the same in the case

of without off-farm labour market. This indicates that accessibility to off-farm labour market

has no impact on the production efficiency decision.

Optimal provision of environmental service is determined by the above first order conditions.

Optimal labour and land use in environmental service production are

1

* (1 ) (1 ) Ce O

pT T T A

w

and

1

* (1 ) (1 )( ) C

e O

pA T T

w

A

respectively.

Whether landowner will produce more environmental service compare to that when off-farm

labour market is not accessible depends on not only the relative labour intensity of

environmental service production, but also the off-farm wage rate. This is consistent with

Mullan (2008)’s finding though direct comparison is ambiguous. However, given the

accessibility of off-farm labour market and its wage rate as well as the total land and labour

endowment, the landowner who has high labour-land ratio and more likely to sell labour in

the off-farm labour market tends to produce more environmental service when crop

production is relatively more labour intensive (i.e. ). The intuition is that the shadow

price of labour (when off-farm labour market is not accessible) to the landowner who sells

labour will has lower labour-land ratio, hence is more efficient in producing environmental

goods. Vice verse holds for .

Meanwhile, the marginal impact of wage rate is also contingent upon whether crop or

environmental good production is more labour intensive. As exact impact is difficult to

determine by analytical result, we leave this to simulation part.

13

3.2.2 Ex-post PES program

The excludability of the quasi-public good makes it feasible to introduce PES program,

charging a fee on downstream users for consuming the environmental service. After

introducing PES program, the landowners could trade environmental service in the market,

his budget constraint hence is (3.22) C C e e C C e e Op c p q p q Np q wT B . Simplified

objective function of the landowner becomes

1 1) ( ) ( 1) /e e e e C{ , , }

( , ) ln[ ( / / ] (1 ) lne e O

C e e O C C e eA T TMax U c q A A T p B p AT T N A T p p w T

First order condition with respect to and yields eA eT OT

(3.23) 1 1 1 1 (1 )( ) ( ) ( 1) /

eA e e O e e e CC e

U A A T T T N A T p pc A

0

(3.24)

(1 )(1 )(1 )( ) ( ) ( 1) (1 ) / 0

eT e e O e e e CC e

U A A T T T N A T p pc T

(3.25) [ (1 )( ) ( ) ] 0OT e e O

C C

wU A A T T T

c p

The same efficiency condition as (3.17) can be derived. Hence we conclude that introducing

PES program does not distort the production decision of the landowner.

Optimal land ( *eA ), labour use ( )in environmental service production and off farm labour

use ( ) satisfy the above first order conditions.

*eT

*eT

Marginal impact of PES payment could be obtained from the implicit differentiation of (3.23),

(3.24) and (3.25) with respect to , namely eP

*1 1 1 1

*2 2 2 2

*3 3 3

/

/

0/

e e

e e

O

A PA B C D

A B C DT P

A B C T P

(3.26)

14

where

2 1 11

1

1

11

( ) ( ) /(1 ) /( ) /( ) ( 1)

( (1 ) ( ) /( ) ( 1) (1 ) /

( (1 ) ( ) /( ) (1 ) /

( 1) /

e O e e e C e e e C

e e e C e e e C

e e e C

e e

A T T T w A A A A A P N A T P P

B w A A A A A P N A T P P

C A A A A A w P

D N A T

/

1 12

22

2

2

( ) ( (1 ) (1 )(1 ) /(1 )( ) (1 )( 1) /

(1 )( ) /( ) (1 ) ( 1) /

(1 )(1 )( / ) /( )

C

e O e e C e e e

e O e e O C e e e C

e O C e e O C

P

A w T T T T A A P N A T P

B w T T T T T T T P N A T P P

C w T T T w P T T T T P

D

CP

1

3 3 3

(1 )( 1) /

/( ) ; /( )

e e C

e C e O C

N A T P

A w A A P B C w T T T P

From crammer’s rule, * /eA P and follows * /eT P

*1 3 2 2 3 2 1 3 1 3/ ( ) ( )eA P D C B C B D B C C B

/ and

*3 1 2 2 1 3 1 2 2 1/ ( ) (eT P A D C D C C A D A D ) / , where

1 1

3 2 2

3 3

A B C

A B C

A B C

1

2

3

. The existence

of maxima indicates a negative determinant 3 (Proof see appendix). the sign of * /e eA P ,

and will be the opposite to the sign of the numerators.

Since

* /e eT P * /O eT P

1 3 2 2 3 2 1 3 1 3( ) ( )D C B C B D B C C B

21

3( )( 1) 1e O e e

C

wT T T N A T

P 2 /( )e O Cw T T T P , as

long as (3.27) 1

* / 0e eA P

2 0 1 )(1 )(or ( 0 ) is satisfied. That is, increase in

PES payment will have a positive impact on optimum land used in e-good production as long

as elasticity of land input in environmental good production ( ) is small enough and

elasticity for crop consumption ( )is large enough.

Similarly, we obtain

3 1 2 2 1 3 1 2 2 1( ) (A D C D C C A D A D )

1 2

3( 1) {(1 ) (1 )(1 3 ) /(1 )

[1/( ) 1/( )] (1 )(1 ) /( )}

e e

e C

e e O e eC

A T wN

A A P

wT T T T A A T T T

P

O

, which is negative as

long as (3.28) (1 )(1 3 ) 0 . Therefore, * /e eT P 0 , namely, higher PES

15

payment will increase optimal labour used in environmental production when (3.28) is

fulfilled.

Condition (3.27) and (3.28) imply that the impact of PES payment on optimal land ( )

and labour( ) provision depends on consumption elasticity of crop (

eP *eA

*eT ) and environmental

good (1 ), output elasticity of land in environmental service production ( ) and relative

labour intensity (labour-land ratio) of environmental and crop production.

When crop consumption is more elastic than environmental service consumption

(1 ),

o Only if real off-farm wage ( / Cw P ) is low and crop production is more labour

intensive than environmental service production ( e C

e C

T T

A A ), will increase PES

payment lead to more environmental service provision.

o If real off-farm wage ( / Cw P ) is high enough and crop production is less

labour intensive ( e C

e C

T T ), reduction in environmental service provision

when increasing PES payment is possible.

A A

A more normal situation is when environmental service consumption more elastic than

crop consumption (1 ),

(i) As long as output elasticity of land in environmental service production is

small enough, ( 11

) and not too small ( 1 3

), will higher

PES payment increases the environmental service provision.

(ii) If output elasticity of land in environmental service production is so high

that 11

, together with high real off-farm wage ( / Cw P ) or if

output elasticity of land in environmental service production ( ) is very

small (1 3

) or when crop production is less labour intensive than

16

e CT T ) , higher PES payment might

lead to lower environmental service provision.

e CA A

When real off-farm wage ( / Cw P ) is low, the marginal impact of PES

payment on optimal land use is ambiguous, that is or

0

* / 0e eA P

* /e eA P . This leaves the total impact of increase PES payment on

environmental service production undetermined.

The following table gives a summary for the impact of PES payment on optimal

environmental service provision when environmental service consumption is more elastic

than crop consumption (1 ), Therefore, our study suggest that a pilot survey might

be necessary to estimate relative labour intensity in production of environmental service

and other agricultural goods, the consumption elasticity of the two good as well as the off-

farm labour wage when the labour market is accessible.

Table 1 (i) (ii) (ii.1) (iii)

1

1

and

1 3

11

and

1 3

, and

high / Cw P

11

and

1 3

, and

low / Cw P

If condition in

(i) and (ii) is

not satisfied.

* /e eA P + - -/+ +

* /e eT P + - - -/+

Impact of

on eP eq

+ - -/+ -/+

However the impact of on optimal off farm labour use is ambiguous in our analytical

result.

eP *OT

Since off-farm labour market is accessible in the case, its wage rate will affect the marginal

impact of PES payment on both optimal land ( ) and labour ( ) use in environmental

w

*eA *

eT

17

service production. Analytical result (see appendix) show that the impact of could be

either positive or negative depending on value of the parameters. If higher off-farm wage

leads to larger marginal impact of PES on

w

w *eA and , PES program will be more effective

in the area with high off-farm wage. If higher off-farm wage reduces the marginal impact

of PES on and , adopting PES program in poorer areas with low off-farm wage will be

more efficient given budget constraint.

*eT

w

*eA *

eT

Result 2 provides a short summary for above analysis.

Result 2: When environmental service is produced by changing existing agricultural activities

and off-farm labour market is accessible, production efficiency condition of the two goods

still holds. Meanwhile, introducing PES program may or may not increase the provision of

the environmental service depending on factors such as consumption elasticity of crop and

environmental good, output elasticity of land in environmental service production and

relative labour intensity (labour-land ratio) of environmental and crop production. Marginal

impact of PES program on off-farm labour use is ambiguous.

Comparing Result 1 and Result 2, though it is difficult to make decisive conclusion on the

impact of off-farm labour market accessibility on optimal environmental service provision

analytically, off-farm labour accessibility does affect the marginal impact of PES . A brief

summary is given in Result 3.

Result 3: When environmental service is produced by changing existing agricultural activities,

off-farm labour market accessibility does not affect the efficiency of the environmental service

production. Different conditions are required for positive marginal impact of PES payment on

environmental service provision when the off-farm labour market is accessible and when it is

not. When off-farm labour market is accessible, additional requirement form off-farm labour

wage is imposed.

18

4. When environmental service is a by-product of a new private good

In the section, we will study the situation when environmental service is a by-product of a

mew private good. The under supply of the private good ex-ante PES program is usually

attributed to its low profitability. A typical example is the reforestation program in different

developing countries, such as China (e.g Uchida et.al, 2007; Bennet et.al. 2008b; Bennet,

2008), Mexico (Munoz-Poma et.al, 2008) and Costa Rica (e.g. Pagiola, 2008). Under the

program, upstream landowner not only benefit from PES payment , but also obtains profit

from timber production, though at much lower harvesting frequency , or forest product such

as pulp and paper, as well as trading the non-timber forest product (NTFP). Bennet et.al (2008)

found amount to 20%-32.2% local households’ income increase could be mainly due to

increase in NTFPs income. NTFP varies from country to country depending on local climate

condition and consumption structure. A range of herbs, fungi, fruits and vegetables could be

either collected naturally in local forests or be cultivated on plots adjacent to or within forests

in Chinese case. (Bennet et. al., 2008b). The main environmental by-products for

reforestation, normally, is the improvement of water quality and reduction of sedimentation of

rivers nearby. For example, “The Green for Grain” program in China is aimed to prevent soil

erosion and restore erosion and “Shelterbelt Development Program” designed to combat

erosion and desertification. (Zhu et.al , 2004)

As in section 3, we still assume that upstream landowners are both consumer and producer of

the environmental service. However, provision of environmental service under this category is

a proportion ( ) of the private good output, k fq

(1C

(for example, the forest related product in the

case of reforestration) produced. Production of the private good is also assumed to use only

labour and land input. For simplicity, in our study, landowner does not consume the private

good but sell it to the market. Since the environmental service is still a quasi-public good,

which indicating non separation between consumption and production, the utility function of

the landowner now reads ( , ) ln ) lnC e eU c c c c . c qe e kq f . fq follows Cobb-

Douglas function (4.1) 1f f fq A T , where fA and fT is the land and labour used in

producing the private good. is the parameter catching the technology used. is the output

elasticity of land. The landowner allocates total labour and land endowment between crop (C )

and the private good production ( f ), that is (4.2) C fAA A and (4.3) C T fT T . In the

sections below, we will explore whether off-farm labour market accessibility affects the

19

efficiency of the environmental service provision and how does it influence the impact of PES

program on environmental service provision.

4.1 Without labour market

4.1.1 Ex-ante PES program versus ex-post PES program

Since the landowner will not produce the private good before introducing PES, the landowner

will not provide environmental service. All land ( A ) and labour (T ) are used in crop

production.

After introducing PES program, the landowner allocates part of his land and labour to the

private good (e.g. forest) production. The budget constraint becomes (4.4)

C C C C f f e fp c p q p q p kq B . Other constraints follow (3.2), (4.1), (4.2) and (4.3) . The

simplified maximization problem of the landowner becomes

1 1 1

,

1

( , ) ln ( ) ( ) / /

(1 ) ln /

f f

C e f f f f f f f e C CA T

f f e C

Max U c c A A T T p A T Nk A T p p B p

k A T p p

The first order conditions with respect to , and become eA eT ec

1 1 1 1 (1 )( ) ( ) ( 1) /

fA f f O f e f f CC f

U A A T T T p N kp A T pc A

0

(4.5)

(1 )( ) ( ) ( 1) (1 ) /

(1 )(1 )0

fT f f f eC

f

U A A T T p N kp A Tc

T

f f Cp

(4.6)

Where 1 1 1( ) ( ) / /C f f f f f f f e C Cc A A T T p A T Nk A T p p B p

Apparently, the efficiency condition similar to (3.9) holds, that is (3.9’)

1 1f f

f f

T T T

A A A

, which implies the technical rate of substitution between labour and

land are the same for crop and the private good (forest) production in equilibrium. Optimal

provision of environmental service satisfies condition (4.5) and (4.6). It depends on the

degree of its link to the private good ( k ), the market price for the private good ( fp ), PES

payment ( ep ). Similar to section 3.1.2, higher PES payment ( ep ) will increase environmental

20

service related private good production, hence environmental service as long as labour used in

the good production satisfies . The impact from other factors such as and 1fT k fp are left

for section 5.

Hence, we get the Result 5:

Result 5: When there is no labour market, PES program will increase the provision of

environmental service when the service is a by-product of a new private good. The higher the

environmental payment, the more is the environmental service provision.

4.2 With labour market

4.2.1 Ex-ante PES program versus ex-post PES program

Before PES program, in the sub model, there is still no environmental service provision from

upstream landowner. All land ( A ) will be used in crop production. Part of labour endowment

(T ) will be used in crop production, part is trade in the off-farm labour market.

After PES is introduced, the budget constraint for the landowner reads (4.4’)

C C C C f f e f Op c p q p q p kq wT B . The land constraint is (4.3’) C fT T T OT . Other

constraints are the same as (3.2), (4.1) and (4.2). The simplified maximization problem

becomes

, ,

1 1 1

1

( , )

ln ( ) ( ) / / /

(1 ) ln /

f f O

C eA T T

f f O f f f f f e C C

f f e C

Max U c c

A A T T T p A T Nk A T p p w p p

k A T p p

OT C B

First order conditions with respect to , and yield eA eT OT

1 1 )( ) ( ) ( 1) / 0

fA f f O f e f CC f

U A A T T T p N kp A 1 1f T (1

pc A

(4.5’)

(1 )( ) ( ) ( 1) (1 ) /

(1 )(1 )0

fT f f O f e f CC

f

U A A T T T p N kp pc

T

fA T

(4.6)

0)())(1(

COee

CT p

wTTTAA

cU

O

(4.7’)

21

Where 1 1 1( ) ( ) / /C f f O f f f f f e Cc A A T T T p A T Nk A T p p B Cp

By combining first order conditions, crop and private good (forest) production is still

efficiency, namely 1 1

f O f

f f

T T T T

A A A

.

Result of implicit differentiation of fA , fT and with respect to OT ep in the three first order

conditions are similar to those in section 3.2.2 except the environmental good production

function is replaced by the production function for environmental service related private good.

So are the results in Table 1. We provide a short summary on the marginal impact of PES

payment on environmental related private production, henceforth the environmental service

provision.

When crop consumption is more elastic than environmental service consumption

(1 ), Only when real off-farm wage ( / Cw P ) is low and crop production is

more labour intensive than environmental related private good (forest) production, will

higher PES payment increase environmental service provision. If crop production is

less labour intensive, increase PES payment might reduce the environmental service

provision.

A more normal situation, when environmental service consumption is more elastic

than crop consumption (1 ), only if output elasticity of land in environmental

related private good (forest) production satisfy 11

and 1 3

, swill

higher PES payment increases the environmental service provision. Increase PES

payment might have negative impact on environmental service provision either when

output elasticity of land in environmental service production is very high such that

11

and real off-farm wage ( / Cw P ) is high, or when output elasticity of land

in environmental service production ( ) is very small 1 3

and crop production

is less labour intensive than environmental related private good (forest) production

22

( f C

f C

T T

A A ). When real off-farm wage ( / Cw P ) is low, the marginal impact of PES

payment on optimal land use is also ambiguous.

Result 6 outlines a short summary for the above discussion:

Result 6: Labour market accessibility will not affect the impact of PES program on

production decision when environmental service is a by-product of a new private good (e.g.

reforestation).. Introducing PES program will increase environmental service provision when

environmental service. Marginal impact of PES payment on environmental service provision

depends on different factors such as real off-farm wage, consumption elasticity, and relative

labour-land ratio in production.

5. Numerical simulation

Not completed

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