A bioeconomic analysis of the potential of Indonesianagroforests as carbon sinks

Russell M. Wise a,*, Oscar J. Cacho b

aCSIRO Ecosystem Sciences, GPO Box 284, Bellenden Street, Crace, Canberra, ACT 2601, Australiab School of Business, Economics and Public Policy, University of New England, Armidale, NSW 2351, Australia

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1

a r t i c l e i n f o

Published on line 29 March 2011

Keywords:

Bio-economic meta-modelling

Indonesia

Agroforestry

Carbon credits

Dynamic programming

a b s t r a c t

Agroforests managed by smallholders have been shown to provide biodiversity, carbon-

storage and rural-livelihood services. Consequently, these systems are being promoted as

an effective way of rehabilitating millions of hectares of degraded, formerly forested land in

many tropical countries. Current conditions at the forest margins in these countries,

however, make it easier to clear unprotected forests than restore degraded lands through

agroforestry. The result is large-scale deforestation that causes substantial losses of biodi-

versity and stored soil and biomass carbon. Agroforests will only be an attractive activity if

they are financially viable and socially acceptable. In this study we investigate the financial

viability of agroforestry systems as carbon sinks when carbon-credit payments are avail-

able. A meta-modelling framework is adopted, comprising an econometric-production

model of a land parcel in Sumatra, Indonesia. The model is used within a dynamic-

programming algorithm to determine optimal management of the system in terms of three

decision variables: tree/crop area, tree-rotation length, and wood harvest. Results show the

influence of soil-carbon stocks and discount rates on optimal strategies and reveal inter-

esting implications for joint management of agriculture and carbon as well as for the

possible restoration of degraded land.

# 2010 Elsevier Ltd. All rights reserved.

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journal homepage: www.elsevier.com/locate/envsci

1. Introduction

Large-scale deforestation and land degradation cause sub-

stantial losses of stored soil and biomass carbon which

contribute to climate change (Sampson and Scholes, 2000;

Fearnside, 2001). Agroforestry systems1 can contribute to

climate mitigation by sequestering atmospheric carbon, while

helping to maintain productivity and meet local cultural

requirements (Smith and Scherr, 2003; Makundi and Sathaye,

2004). Albrecht and Kandji (2003), for example, estimate the

carbon sequestration potential of agroforests to be between 12

and 228 Mg ha�1 (with a median value of 95 Mg ha�1) with

* Corresponding author. Tel.: +61 2 6242 1621; fax: +61 2 6252 1705.E-mail addresses: Russell.Wise@csiro.au, rusty.wise@gmail.com (R

1 Agroforestry systems are agricultural lands where trees have beenanimals (Albrecht and Kandji, 2003).1462-9011/$ – see front matter # 2010 Elsevier Ltd. All rights reserveddoi:10.1016/j.envsci.2010.12.008

between 585 and 1215 million ha of the earth’s area suitable for

agroforestry. Oelbermann et al. (2004) emphasise that the

capacity to sequester carbon varies globally and estimate the

biomass-carbon sequestration potential of agroforestry to be

approximately 2.1 � 109 Mg C year�1 in tropical biomes and

1.9 � 109 Mg C year�1 in temperate biomes. However, much of

the land in the tropics is managed by semi-subsistence

farmers and shifting cultivators, so their willingness to

participate in carbon-sequestration projects may be an

important factor to consider when designing reforestation

programs (de Jong et al., 2000).

The economics of agroforestry systems in the presence of

incentives to sequester carbon has been studied by authors

.M. Wise).

introduced and judiciously managed together with crops and/or

.

b

E1

•

•

E2

Y2

Y1 = bundle of commodities produced

from land planted to trees

Y2 = bundle of commodities produced

from land planted to crops

Y1z

•

•w

Fig. 1 – Pareto efficient production possibilities of

landholders when (1) not receiving payments for positive

environmental externalities and (2) when positive

external effects are internalised through carbon-

sequestration payments.

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1452

such as de Jong et al. (2000, 2004), Shively et al. (2004), Cacho

et al. (2003, 2004), and Seeberg-Elverfeldt et al. (2008) among

others. The effects of management, technologies and risk on

tree-based systems have been studied through bioeconomic

modelling by Grist and Menz (1996), Nelson et al. (1998) and

Predo and Francisco (2008) among others. We contribute to

this literature by focusing on the financial viability of

smallholder agroforestry systems in the presence of carbon

payments, subject to constraints of soil and biomass carbon

dynamics over the long term. Two articles of the Kyoto

Protocol provide the policy context for the analysis presented

here: Article 3.3 (Land-use, Land-use Change and Forestry) and

Article 12 (the Clean Development Mechanism). These articles

are designed to give incentives to developed countries to

invest in greenhouse-gas mitigation activities in developing

countries to help meet their Kyoto emission limitations

(UNFCCC, 1997). Allowable activities include terrestrial carbon

sinks such as small-scale forestry and agroforestry.

The uptake of land-based activities involving carbon sinks

within the CDM has been low relative to energy efficiency

projects, representing less than 1% of registered Certified

Emission Reductions (CERs) by early 2009 (Kossoy and Ambrosi,

2010). Reasons for the low uptake of projects involving sinks

under the CDM include the complexity of rules for certification

(Henman and Hamburg, 2008), uncertainty about permanence

of the carbon sequestered, and concerns over accuracy of

monitoring (Capoor and Ambrosi, 2009). In the case of projects

that involve smallholders, other barriers include risk to food

security, high capital costs combined with lack of access to

credit, and missing or poorly defined property rights (Lipper and

Cavatassi, 2004). There is evidence, in cases where markets for

agricultural output, labour, credit, or land are absent, or where

the transaction costs are excessive, that households’ accom-

modate these constraints by linking their production and

consumption decisions to meet their multiple objectives of food

security, income and leisure (de Janvry et al., 1991; Holden, 1993;

Vosti et al., 2002).

While we acknowledge that the smallholders of our study

area may not be able to maximise profit due to production

constraints, financial viability is a necessary condition to

make a production system attractive, and profit is an

important component in the objective function of farmers

(Tomich et al., 1998: 59). Furthermore, investor-driven pro-

jects, such as those funded by the Biocarbon Fund (World

Bank, 2002) and the Global Environment Facility (GEF, 2000) are

subject to acceptability restrictions. These include secure land

tenure; local government and policy support; infrastructural

and technical support; linkages to input and output markets;

the enhancement of tree management skills; and transparent

and equitable relationships between project partners (Smith

and Scherr, 2003; Roshetko et al., 2007). Such projects would

provide the enabling conditions for smallholders to adopt

agroforestry based on profit motives and they give legitimacy

to our approach. Milder et al. (2010) provide examples of

carbon-sequestration projects that have been successful at

enhancing local livelihoods because they have been both

profitable and socially acceptable.

This study is conceptually based on a production possibility

frontier (PPF) representing the tradeoffs facing landholders

with fixed resources and technologies to produce bundles of

products from two land uses, trees (Y1) and crops (Y2) (Fig. 1).

The optimal combination of Y1 and Y2 is determined by the

price ratio p1/p2. If the present value of crop outputs exceeds

the present value of tree outputs, the optimal point is likely to

be located closer to the vertical axis (point E1) reflecting the

current situation in much of south-east Asia where slash-and-

burn practices and shifting cultivation are widespread (Wise

and Cacho, 2008). If the external environmental benefits

provided by trees are internalised through direct payments for

sequestered carbon the price ratio ( p1/p2) will increase and

landholders are more likely to plant a larger area of their land

to trees (point E2, Fig. 1).

This paper builds on the study of Wise and Cacho (2008), who

found that the planting decisions that maximise profit are

driven by soil quality. In degraded soils, it pays to plant trees to

improve soil quality when carbon payments exist. But as soil

quality improves, there is a point where it becomes optimal to

switch from trees to crops and to not participate in carbon

trading. In this study, we identify profit-maximising land-

management strategies for cases where nitrogen-fixing trees

provide an alternative to inorganic fertilisers. We assume that

soil fertility can only be improved through nitrogen-fixation of

plants and the addition of organic matter. This represents a

system that is sustainable and does not require purchased

fertiliser.

2. Study area: Jambi Province, Sumatra

The Jambi Province of southern Sumatra, Indonesia, provides

our case study. Jambi is situated in the humid tropics and is

largely covered by Sumatra’s broad ‘peneplain’ agro-ecological

zone. It is almost flat land, less than 100 m above sea level, and

is divided into a lowlands area (10%) made up of river levees

and floodplains with fertile alluvial soils; and an uplands area

(90%) with a gently undulating landscape (slopes of 5–17%)

(Tomich et al., 2001).

This region is one of the alternatives to slash-and-burn

(ASB) benchmark sites and represents the equatorial rain-

forests of south-east Asia where primary forests are being

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1 453

cleared. The internal forces driving these land conversions are

resettlement programs and the increasing population densities

resulting from the inflow of migrants,2 facilitated by road

construction and the lack of economic opportunity elsewhere

(Tomich et al., 2001; Palm et al., 2004). The indigenous slash-

and-burnpractice to clear forest, along with shiftingcultivation,

has been widely adopted in the region to meet the food

requirements of a growing population (Menz and Grist, 1999).

Soils are depleted of nutrients faster than they can be restored

during increasingly shorter fallow periods (Sampson and

Scholes, 2000). In Sumatra cleared land is often invaded by

Imperata grassland, which has limited uses for local people and

is of low value (Tomich et al., 1996). Drivers of deforestation in

Indonesia have been strengthened recently by international

demand for bio-energy derived from palm oil, rape, and

jatropha (Fargione et al., 2008). Ideally, new agroforestry and

bioenergy systems would be established in degraded lands, but

it is normally cheaper to clear new forest than to restore

Imperata land (Purnomosidhi et al., 2005). Carbon payments

could provide the finance required to cover the costs of clearing

degraded grasslands and replace them with agroforestry.

2.1. The agroforestry system

The upland land-use systems found in Indonesia are deter-

mined by the availability of standing water throughout the

growing season. Non-rice crops such as maize, grain legumes

and tuber crops are grown where standing water is not

available (Fagi, 1992). Hedgerow-intercropping systems are

often found on steeper slopes, where rice or maize is grown

alongside tree-covered terraces (Fagi, 1992). Other systems

include relay cropping of maize, soybean (Glycine max) and

velvet bean (Mucuna pruriens) (Sitompul et al., 1992).

Here we use a rain fed hedgerow-intercropping system of

Gliricidia sepium and maize as an alternative to the baseline of a

degraded area covered in Imperata grasses. The biomass-carbon

stock of Imperata grassland is approximately 4 Mg C ha�1 and the

soil-carbon stock of degraded areas can be as low as 10 Mg C ha�1

and averages about 61 Mg C ha�1 (Roshetko et al., 2002). And

since soil-carbon stocks in the region often exceed 100 Mg C ha�1

in homegardens and secondary forests, there is great potential to

adopt appropriate land-use practices to sequester carbon (Nair

et al., 2009). The system and the management regimes

investigated are presented in detail in Section 3.2. Gliricidia is

an attractive tree within an agroforestry system because it is

nitrogen-fixing, produces large quantities of biomass for mulch,

and grows rapidly to produce various commodities including

firewood, fodder and timber (Sanchez, 1995; Stewart, 1996).

3. Method

3.1. Economic model

We use a bioeconomic model based on that of Wise and Cacho

(2008). The model focuses on the production side only and

2 The range in population density in Sumatra in 2000 was be-tween 191 people km�2 in Lampung Province and 45 people km�2

in Jambi Province (BPS, 2000).

accounts for the effects of competitive and complementary

interactions between trees and crops on the quantities of

marketable outputs produced such as firewood and maize in

addition to the carbon sequestered in the soil and tree

biomass. Separating the production and consumption deci-

sions of smallholders in this way reflects the situation of an

investor-driven CDM project where smallholders have access

to input and output markets.

The analysis is based on a landholder participating in a

CDM project and receiving payments for carbon sequestration

services. Carbon payments are based on the production of

certified emission reductions (CERs), the medium of exchange

under the CDM. The present value of net revenues (NPV)

obtained from an area of land, A, over a project-investment

period of T years is:

NPVðT; k;xÞ ¼ ðA� kÞ �XT

t¼1

atðst; k;xtÞ � d�t þ k �XT

t¼1

htðst; k;xtÞ � d�t

þA �XT

t¼1

CERtðst; k; xtÞ � d�t � k � cE (1)

where St represents the state of the land in year t and may be

defined by a set of land-quality indicators such as soil depth,

soil-carbon content and soil fertility; x is a vector of manage-

mentdecisionssuchasthe timingandfrequencyofpruningand

harvesting, weeding and fertilising; k is the area of the farm

planted to trees, which remains constant throughout the T

years, andA–k is the area planted to crops. The cost of establish-

ing a hectare of trees is cE and d = (1 + r) for the discount rate r.

CERt, at and ht are the net revenues obtained from the sale of

carbon credits, crop yields and tree products, respectively.

The net revenues obtained from the area planted to a single

agricultural crop are:

at ¼ pa � yat ðst; k; xtÞ � ca

t (2)

where yat is crop yield, pa is the price of the crop and ca

t is the

per-hectare variable costs of preparing the land, sowing seeds

and harvesting.

The net revenues provided by trees are:

ht ¼ ph � yht ðst; k; xtÞ � ch

t (3)

where yht is the quantity of tree product harvested in year t, ph

is the price of tree product and cht is the variable costs of

harvesting.

The third term in Eq. (1) is the net monetary benefit

received for the sale of CERs, which depends on carbon

accumulation in tree biomass and soil relative to the baseline

(referred to as ‘eligible carbon’):

CERt ¼ pc � ðybct ðst; k; xtÞ þ ysc

t ðst; k; xtÞÞ � cmt (4)

where ybct is the eligible change in the stock of tree-biomass

carbon, ysct is the eligible change in soil-carbon stock, pc is the

price of CERs and cmt is the annual carbon-monitoring cost per

hectare.

Eq. (1) represents a single rotation and does not include the

opportunity cost of keeping trees in the ground. The Faustman

model is the standard approach for solving the infinite forestry

planning horizon, and it has been extended to include non-

timber benefits by authors such as Hartman (1976), Comolli

(1981), Bowes and Krutilla (1985), van Kooten et al. (1995) and

Gutrich and Howarth (2007). Such models require that the

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1454

length of each cycle (T), the management variables defined

within the vector x, and initial land quality for each cycle Snremain constant for all cycles n = 1, 2, . . .1. These assump-

tions do not hold when the quality of the land changes over

time, possibly resulting in optimal tree areas and rotation

lengths changing between cycles. Therefore, in this context, a

‘cycle’ is a non-fixed period of time between optimal decisions.

Thus our decision model is:

VnðSnÞ ¼ maxkn ;xn ;Tn

ðNPVnðSn; kn; xn;TnÞ þ Vnþ1ðSnþ1Þ � d�Tn Þ (5)

subject to:

Snþ1 ¼ Sn þXTn�1þTn

t¼Tn�1þ1

f tðst; k; xÞ (6)

where Sn is the quality of the land at the beginning of forestry

cycle n, ft( � ) is the annual change in the state variable, andNPV

is as defined in Eq. (1). The problem is solved by backward

induction until convergence in V(Sn) is achieved (Kennedy,

1986). This involves combining a dynamic programming algo-

rithm with the simulation model described below.

3.2. The biophysical simulation model

The biophysical model of the Gliridicia-maize system comprises

three quadratic equations that interactively mimic soil-carbon

changes, tree-biomassaccumulation and crop-yielddynamicsas

functions of management variables. The equations were

estimated statistically from the dataset of 6200 data points

created by Wise and Cacho (2008) using the SCUAF model. SCUAF

(Soil Changes Under Agriculture, Agroforestry, and Forestry) is a

process model designed to estimate the effects that changes in

soil properties (nutrients, carbon and soil depth) have on tree and

crop productivity in response to changes in management and

environmental conditions (Young et al., 1998a).3 The interaction

between crops and trees is accounted for annually through the

varying effects that plants have on soil fertility and structure.

The SCUAF model was calibrated to represent a ‘typical’ site

in a sub-humid climate, with acidic, medium-textured soils of

felsic parent material and imperfect drainage. The carbon and

nitrogen contents of the system ranged between 10 and

33 Mg C ha�1 and 1.0 and 3.3 Mg N ha�1, respectively—depend-

ing on previous land use and degree of degradation. These

values fall at the lower end of the expected range of 10–

120 Mg C ha�1 for soils under a range of land uses in Sumatra

(Roshetko et al., 2002). The lower values of this range represent a

run-down soil requiring regeneration. The biophysical param-

eter values used to calibrate SCUAF are reported in Wise et al.

(2007) and are not repeated here.

The management parameters varied in SCUAF to create the

original dataset were area planted to trees (k, ha), fertiliser-

application rate ( fr, kg), and tree pruning and harvesting

3 Some of the input parameters that define management in-clude: species type, tree and crop rotation length, firewood prun-ing and harvest intensities, organic and inorganic fertiliser use,and slash-and-burn practices. Input parameters that define thebiophysical conditions of a study site include: slope, parent mate-rial, soil type and organic matter decomposition rates.

regimes (hr, Mg). Total area (A) was set to one hectare so

0 � k � 1 (i.e. k also represents a fraction of the area of the

smallholding). Only 70% of the annual biomass increment was

removed, the remaining 30% contributed to tree biomass, which

increased monotonically throughout the rotation. The pruning

and harvesting options were expressed as percentages of the

annual tree biomass growth. Pruned biomass was returned to

the soil to decompose and replenish soil carbon and nutrients

whereas harvested biomass was removed for sale as firewood.

In the model, soil quality and total carbon stocks can be

modified bychanging the control variableskandhr, whereas the

variable fr was set at zero, representing the unavailability of

inorganic fertiliser. The equations for the state of the soil (st),

tree biomass (bt) and crop yield ðyat Þ, respectively are:

st ¼ b0 þ b1 � st�1 þ b2 � ðst�1Þ2 þ b3 � st�1 � ð1� kÞ þ b4 � st�1 � hr

þ b5 � ð1� kÞ þ b6 � ð1� kÞ2 þ b7 � ð1� kÞ � hrþ b8 � hr (7)

bt ¼ a0 þ a1 � bt�1 þ a2 � ðbt�1Þ2 þ a3 � bt�1 � st þ a4 � bt�1 � k

þ a5 � bt�1 � hrþ a6 � st þ a7 � ðstÞ2 þ a8 � st � kþ a9 � st � hr

þ a10 � kþ a11 � k2 þ a12 � hr (8)

yat ¼ d0 þ d1 � st þ d2 � ðstÞ2 þ d3 � st � bt þ d4 � bt þ d5 � ðbtÞ2 (9)

Greek letters in these equations are model coefficients

estimated through non-linear regression (Table 1). The

estimated R2 and t values reported purely indicate the fit of

the quadratic equations to the SCUAF output and are not an

indication of the sampling/measurement errors that is

required for statistical inference. The parameter values for

which no t values are indicated are those that were modified to

represent a system with stronger complementary tree-crop

interactions than those reported by Wise and Cacho (2008).

The statistical model, defined by Eqs. (7)–(9), was used to

generate values for Eqs. (2)–(4). The yields of soil carbon,

firewood and biomass carbon in these equations were

calculated by simple differencing:

ysct ¼ ðst � s0

t Þ � ðst�1 � s0t�1Þ

� �(10)

yht ¼ ðbt � bt�1Þ � hr (11)

ybct ¼ ðbt � b0

t Þ � ðbt�1 � b0t�1Þ

� �� h (12)

The resulting outputs were used to generate the matrices

required to solve the optimisation problem represented by

Eqs. (5) and (6). The values for the economic variables in the

model are listedalongwiththeirsources inTable2.Thepricesare

quoted in US dollars using the 2009 average exchange rate of

10,400 Indonesian Rupiah per US Dollar (www.x-rates.com). A

real discount rate of 15% was used to represent the rate of time

preference of rural landholders in Indonesia (Tomich et al., 2001).

4. Results and discussion

Optimal decision rules and associated state transitions were

determined by solving the DP model for two carbon prices

Table 1 – Base-case values of the b, a and d coefficients for the dependent variables of the quadratic equations defining thebiophysical numerical model.

Coefficient subscript Soil carbon (b) Tree biomass (a) Crop yield (d)

Coefficient t-Value Coefficient t-Value Coefficient t-Value

0 0.7790 (17.18) �0.8730 (�11.16) �0.3920

1 0.9684 (238.65) 0.9910 (628.36) 0.1737

2 0.0004 (4.28) �0.0048 (�161.99) �0.0031 (�11.31)

3 0.0062 (8.45) �0.0005 (�11.59) �0.0003 (�4.48)

4 0.00005 (5.25) 0.2522 (121.85) �0.0017

5 �0.6216 (�24.49) �0.0003 (�39.31) 0.0010 (23.21)

6 0.0804 (5.16) 0.0871 (11.55) – –

7 0.0077 �0.0021 (�12.33) – –

8 �0.0066 (�31.12) 0.0051 (2.88) – –

9 – – �0.00005 (�2.63) – –

10 – – 2.7750 (50.42) – –

11 – – �2.0200 (�40.82) – –

12 – – 0.0020 (4.84) – –

R2 0.99 0.70 0.99

The associated t-values are given as a measure of the significance of each coefficient (a 95% significance requires the t-value be �+2.08 or

��2.08).

Table 2 – Base-case parameter values for economic variables (2009 US$).

Description Value Units Source

Firewood price 6.0 $ Mg�1 a

Price of carbon 17.5 $ Mg�1 d

Price of maize 180.0 $ Mg�1 e

Discount rate 15 % b

Hedgerow-establishment cost 64.5 $ c

Variable costs for crop 210.0 $ ha�1 c

Price of labour 1.5 $ day�1 f

Maize-harvest labour 5 days Mg�1 c

Prune and harvest labour 3 days Mg�1 c

Labour for weeding 40 days ha�1 year�1 c

Carbon content of wood 50 % g

Sources: a: Wise and Cacho (2005); b: Tomich et al. (2001); c: Grist et al. (1999); d: Galinato et al. (2010); e: Katial-Zemany and Alam (2004); f: NWPC

(2005); g: Young et al. (1998b).

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1 455

representing a ‘with carbon credits’ scenario (US$17.5) and a

‘without carbon credits’ scenario (US$0). The sensitivity of

these optimal results to the discount rate was tested by

decreasing the base-case rate of discount from 15% to 5%.

4.1. Optimal decision rules

The optimal state-contingent decisions—tree area (k*), fire-

wood-harvest regime (hr*) and cycle length (T*) are plotted in

Fig. 2. The effects of changing the carbon price ( pc) on optimal

management are found by comparing the solid and dashed

curves within each graph. The effect of the discount rate is

found by comparing columns 1 and 2 (Fig. 2).

A significant finding is that planting only crops is the profit-

maximising strategy when soil quality (measured as soil-

carbon content) is relatively high (>22 Mg C ha�1, for the given

parameters values). As soil carbon decreases (to

<22 Mg C ha�1) it becomes optimal to plant part of the area

to trees (0 > k < 1). Combining trees with crops when soil

quality is relatively poor is optimal because of two reasons: the

opportunity cost of growing trees is low because crops are less

productive in degraded soils; and Gliricidia trees are able to

restore soil quality through nitrogen fixation and residue

additions. Optimal management strategies involving combi-

nations of trees and crops represent points along the

production possibility frontier between ‘w’ and ‘z’ in Fig. 1.

The actual optimal point depends on the prices of tree

products relative to the price of maize and on the discount rate

as discussed below.

Assuming a 15% discount rate (left panel in Fig. 2) and in the

absence of carbon payments (dotted lines), it is optimal to

convert a minimum of 10% of the area to trees when St is

between 15.5 and 17.5 Mg C ha�1 (Fig. 2A) for rotations of

between 7 and 9 years (Fig. 2C), and to return no pruned

biomass to the soil as residues (Fig. 2E). It is optimal to

undertake this minimal move towards trees because the soil is

still productive enough to produce acceptable maize yields.

However, at values of St less than 15.5 Mg C ha�1 it is optimal

to convert between 70 and 90% of the land to trees for rotations

of between 24 and 44 years, and to only harvest 20% of pruned

biomass. This larger commitment towards trees occurs

because the profitability of crops has been reduced and it is

in the interests of the landholder to improve the quality of the

soil through residue additions and nitrogen fixation.

0

10

20

30

40

50

60

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0.2

0.4

0.6

0.8

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20

30

40

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60

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(A)

Tre

e ar

ea, k

(hec

tare

s)R

ota

tio

n l

eng

th, T

(yea

rs)

(D)(C)

_ _ _ without carbon payments

____ with carbon payments

Discount rate = 15%

Optimal tree area (k)

Optimal cycle length (T)

Discount rate = 5%

0.0

0.2

0.4

0.6

0.8

1.0

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(B)

0

20

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60

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60

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Fir

ewo

od

har

ves

t (%

)

Soil carbon t (Mg C ha-1)Soil carbon t (Mg C ha-1)

(F)(E)Optimal harvest (hr)

Fig. 2 – Optimal management regimes obtained by solving the dynamic-programming model for ‘with carbon payment’ and

‘without carbon payment’ scenarios under two discount rates, at base-case values for the economic and biophysical

parameters.

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1456

Similar optimal-decision rules are observed with a lower

discount rate of 5% and carbon price of zero (right panel in

Fig. 2), but the lines shift to the right and the adoption of trees

(10% of the area) is triggered at a higher soil-carbon content of

20.5 Mg C ha�1 (Fig. 2B). At the lower discount rate a larger

commitment to trees becomes optimal at a slightly higher soil-

carbon value of 16.5 Mg C ha�1, involving the conversion of 60–

80% of the area to trees for longer rotations of between 43 and

50 years, and harvesting only 20% of pruned biomass (Fig. 2B, D

and F, respectively). When discount rates are lower, the

present value of the delayed benefits from trees is larger

making longer tree cycles optimal.

Carbon payments provide incentives to adopt trees earlier

in the soil degradation process (at higher St values) and to keep

trees for longer rotations (compare solid and dashed lines in

Fig. 2); and these effects are greater at higher discount rates.

The threshold values for the soil-carbon stock at which it

becomes optimal to convert part of the land from crops to trees

increase in the presence of carbon payments. This is because

trees become more financially competitive and because the

maintenance of soil-carbon stocks means liabilities from soil-

carbon losses are avoided. It is noticeable that it is never

optimal to switch entirely from crops to trees. This is because

the complementary interactions between the trees and the

crops exceed the competitive interactions.

4.2. Optimal state paths

The trajectories of the state variable (St) that result from

applying the optimal-decision rules over a period of 150 years

are plotted in Fig. 3. The associated optimal decisions that

drive the trajectories of soil-carbon stocks for the first 8 cycles

are listed in Table 3. If the initial soil quality is relatively good

(s0 = 33 Mg C ha�1) it is optimal to exploit the system by

Table 3 – Optimal decisions over eight cycles for the two carbon-price scenarios (scenario 1 = US$17.5; scenario 2 = US$0),at a high (15%) and low (5%) discount rate. A ‘cycle’ is a non-fixed period of time between optimal decisions.

Cycle/stage Optimal tree area (k*, ha) Optimal cycle length (T*, years)

15% discountrate

5% discount rate 15% discountrate

5% discountrate

1 2 1 2 1 2 1 2

1 0.9 0.9 0.8 0.8 43 24 44 44

2 0.1 0.1 0.1 0.1 41 9 11 11

3 0 0.1 0.1 0.1 1 9 13 13

4 0 0 0.1 0.1 1 1 13 13

5 0 0 0.1 0 1 1 15 1

6 0 0 0.1 0 1 1 15 1

7 0 0 0 0 1 1 1 1

8 0 0 0 0 1 1 1 1

Cycle/stage Optimal harvest (hr*, %) Cumulative NPV (US$ ha�1)

15% discountrate

5% discount rate 15% discount rate 5% discount rate

1 2 1 2 1 2 1 2

1 20 20 20 20 88.1 �52.4 396.3 206.6

2 100 100 100 100 89.0 �48.7 436.8 247.9

3 0 100 100 100 89.0 �47.4 466.0 277.4

4 0 0 100 100 89.0 �47.3 482.6 294.3

5 0 0 100 0 89.0 �47.3 493.1 295.4

6 0 0 100 0 89.0 �47.2 498.4 296.4

7 0 0 0 0 0 0 498.6 297.4

8 0 0 o o 0 0 498.9 298.3

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1 457

continuously planting maize crops annually which reduces

soil carbon for 44 years until it reaches an equilibrium value of

28.7 Mg C ha�1, where it can be maintained through the

addition of crop residues.

10

15

20

25

30

35

150100500

10

15

20

25

30

35

150100500

Carbon price

Time (years)

Soil

car

bon

(Mg

C h

a-1)

So

il c

arb

on

(Mg

C h

a-1)

Discount rate = 15%

Carbon pr

s0 = 33 Mg C ha-1

s0 = 33 Mg C ha-1

s0 = 12 Mg C ha-1

s0 = 12 Mg C ha-1

Fig. 3 – Optimal state paths associated with the optimal manag

programming model for ‘with carbon payment’ and ‘without car

case values for the economic and biophysical parameters.

When the initial soil quality is relatively poor

(s0 = 12 Mg C ha�1) it is optimal to build up soil carbon to a

plateau (22.11, 18.39, 22.0 or 21.08 Mg C ha�1 depending on the

price of carbon and the discount rate) by converting between

10

15

20

25

30

35

150100500

10

15

20

25

30

35

150100500

= US$17.5

Time (years)

Discount rate = 5%

ice = US$0

s0 = 33 Mg C ha-1

s0 = 33 Mg C ha-1

s0 = 12 Mg C ha-1

s0 = 12 Mg C ha-1

ement decisions obtained by solving the dynamic-

bon payment’ scenarios under two discount rates, at base-

0

10

20

30

40

50

150100500

0

10

20

30

40

50

150100500

Tota

l ca

rbon

(Mg

C h

a-1)

(B) Discount rate = 5%(A) Discount rate = 15%

Time (years) Time (years)

pc = $17.5

pc = $0

pc = $17.5

pc = $0

Fig. 4 – The trajectory of the total eligible-carbon stock associated with the optimal management regimes for the different

carbon prices ( pc) and discount rates for the poor-quality soil scenarios.

4 In situations where smallholders face labour, credit or con-sumption constraints and therefore their production and con-sumption decisions are non-separable, these findings andconclusions may well be different (e.g., see Angelsen, 1999).

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1458

10% and 90% of the area from crops to trees for between 42 and

111 years (the sum of the cycles for which k > 0) and returning

up to 80% of the pruned biomass to the system as residues

(Table 3). These stock changes equate to an average annual

increase in soil carbon of between 90 and 152 kg C ha�1, which

is similar to the range suggested by Nair et al. (2009) for soil-

carbon sequestration in multi-strata shaded perennial sys-

tems and homegardens of 100–250 kg C ha�1. Once these

plateaus have been reached it is then optimal to switch the

entire area back to a cropping system that can be maintained

at an equilibrium state through the addition of crop residues.

When the initial soil quality is high (s0 = 33 Mg C ha�1) it is

always optimal to plant crops and not to participate in the

carbon market, and the introduction of carbon payments and

the change in discount rate have no effect on the optimal soil-

carbon path. When the soil is degraded (s0 = 12 Mg C ha�1)

carbon payments provide an incentive to increase total carbon

stocks when the discount rate is high (Figs. 3 and 4 and Table 3).

In this situation, the time that land is planted to trees is

minimised because this incurs opportunity costs in the form of

forgone crop revenues. Without carbon payments, it is optimal

to convert from 90% trees to 90% crops within 24 years (Fig. 4A

and Table 3). Carbon payments cause the optimal rotation

length to increase from 24 to 43 years thereby increasing carbon

stocks. Lower discount rates (5%) imply a preference for longer

planning horizons and this is reflected in the longer tree

rotation of 44 years. In this case, carbon payments have little

effect on the optimal strategies as the positive effect of trees on

crop productivity drives the decisions.

Total eligible-carbon (Fig. 4) includes aboveground biomass

carbon as well as soil carbon, and this reflects the cumulative

stream of annual carbon payments. The trajectories of the

eligible carbon stock emphasise the positive effect that both

carbon price and discount rate have on the quantity of CERs

associated with optimal management regimes. The gradual

increase in total eligible carbon stock after the initial tree

rotation reflects the situation where it is optimal to plant trees

in only 10% of the area. Since no trees are grown in cases

where the initial soil-carbon level is high, total eligible-carbon

stock trajectories are the same as those presented in Fig. 3, and

are therefore not shown.

Comparing Fig. 4A and B illustrates an interesting result.

Introducing carbon payments (shifting from pc = 0 to pc = 17.5

in Fig. 4A) has a similar effect as decreasing the discount rate

in the absence of carbon payments (shifting from pc = 0 in

Fig. 4A to pc = 0 in Fig. 4B). This is because carbon payments

provide early cash flows and alleviate the constraint caused by

a high discount rate combined with delayed cash flows.

5. Summary and conclusions

In summary, our findings indicate that when soils are

relatively degraded and when carbon payments are available

or discount rates are low, it is optimal for a profit maximiser,

without labour and credit constraints, to adopt agroforestry

practices in the study area.4 Combining trees and crops takes

advantage of the positive effects of trees on soil quality, and

this has future benefits in the form of increased productivity.

The income provided by carbon payments partially counter-

acts the obstacles that high discount rates impose on the

adoption of trees. In these cases optimal management

involves a mix of tree-crop areas, tree-rotation lengths and

firewood-harvest regimes. Management strategies are sensi-

tive to the discount rate and the presence of carbon payments.

For example, with short planning horizons (high discount

rates) it is optimal to plant trees for 42–84 years (‘without’ and

‘with’ carbon payments, respectively). Lower rates of time

preference (5% discount rate) imply longer planning horizons

and result in optimal rotations of 81–111 years (‘without’ and

‘with’ carbon payments, respectively). In both cases, when the

soil-carbon level is sufficiently high to sustain crop productiv-

ity it is optimal to convert all the land back to crops. The soil-

carbon level at which this equilibrium is reached depends on

the price of carbon and the discount rate.

With low discount rates carbon payments have little effect

on optimal management, as decisions are driven by the ability

of trees to improve soil quality through nitrogen fixation and

soil amelioration. The resulting increase in crop productivity

translates into future financial benefits that are taken into

account in the dynamic programming model. Our results

e n v i r o n m e n t a l s c i e n c e & p o l i c y 1 4 ( 2 0 1 1 ) 4 5 1 – 4 6 1 459

demonstrate the importance of using a state-based approach.

Where the decisions made at any point in time are based on

the state of the system (soil quality) at that time.

Here we focused on technical aspects of carbon farming

through agroforestry. We considered profit maximisation as

the only objective and soil carbon as the state variable. Our

objective function could be extended to represent a utility

function of several variables, including profit and other

objectives such as food security. Alternatively, other objec-

tives of farmers could be incorporated as constraints, such as

setting a minimum cropping area to meet the food needs of the

household. Roshetko et al. (2007: 228) state that under

conditions of steady market demand, which characterise

many CDM projects, ‘‘. . .smallholder poly- or mono-culture

might be justified as segregated land-use subsystems in a

larger landscape mosaic’’. This is supported by the work of van

Noordwijk et al. (2008: 110) who show that a landscape

approach to managing carbon is necessary in the ‘‘complex,

adaptive integrated social-ecological systems that determine

land-use change’’.

Under current conditions at forest margins in Indonesia it

is easier to clear unprotected forests than to restore degraded

Imperata grasslands. Agroforests managed by smallholders,

however, have been shown to provide biodiversity, carbon

storage and rural livelihood services, and can help relieve

some of the pressure to harvest native forests (Tomich et al.,

2001; Pearce et al., 2003). This study has shown that payments

for carbon can make agroforestry systems profitable. This

may reduce the incentive to clear forest land and hence

contribute to climate mitigation as well as forest

conservation.

Acknowledgement

The authors gratefully acknowledge financial support from

the Australian Centre for International Agricultural Research

(ACIAR) under the project ‘‘Economic potential of land-use

change and forestry for carbon sequestration and poverty

reduction’’ (Project ID: PLIA/2002/066).

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Russell Wise is an Ecological Economist with experience as abioeconomic modeller within inter-disciplinary frameworks toimprove understanding of complex problems resulting from cli-mate and other drivers of change. Of particular interest is the use ofbioeconomics to investigate the potential of market-based mechan-isms to incentivise the early adoption of appropriate mitigation andadaptation strategies. Between 2006 and 2010 Russell led a team ofenvironmental economists at the CSIR in South Africa undertaking

inter-disciplinary research of the socio-economic benefits of pro-tecting and restoring natural capital and ecosystem services. Rus-sell is now a research scientist in the CSIRO’s Climate AdaptationFlagship and is evaluating adaptation options for coastal ecosys-tems and investigating institutional and cognitive barriers to adap-tation and mechanisms for overcoming these.

Oscar Cacho started his professional life as a marine biologist andlater became an economist. His research interests centre on theapplication of economics and biology (bioeconomics) to tackleproblems of sustainability in agriculture and natural resources.His recent work has been in two major areas: the role of carbonmarkets to deal with climate change and the economics of bio-security to protect native ecosystems. He has been part of aTechnical Advisory Group on Control of Invasive Species in theGalapagos Islands and a visiting expert at the Food and Agricul-tural Organisation of the United Nations (FAO). He is currentlyinvolved in a project on reduced deforestation and forest degra-dation in Indonesia.