Conservation Procurement Auctions

with Bidirectional Externalities�

Pak-Sing Choiy, Ana Espínola-Arredondoz, and Félix Muñoz-Garcíax

School of Economic SciencesWashington State University

Pullman, WA 99164

August 21, 2017

Abstract

This study analyzes a conservation procurement auction with bidirectional externalities,

that is, conservation output can a¤ect the costs of individuals dedicated to market production,

and vice versa. The procurer does not observe bidders� e¢ ciency in conservation or market

production. Each market failure alone (asymmetric information or the presence of externali-

ties) deviates optimal output away from the �rst best. Their coexistence, however, rather than

producing larger output ine¢ ciencies, can move optimal output closer to the �rst best when neg-

ative conservation externalities are minor. In this setting, the bene�t from acquiring information

about bidders�types is small. In contrast, when conservation externalities are substantial, the

procurer would have strong incentives to acquire information before designing the auction.

Keywords: Mechanism Design, Bidirectional Externalities, Conservation Procurement

Auction.

JEL classification: D44, D62, D82, Q15, Q51.

�We would like to thank David Lewis for his insightful comments and suggestions and all participants in theAssociation of Environmental and Resource Economists session at the 91st annual Western Economic AssociationInternational conference. We also thank seminar participants at the University of Barcelona, and at the First CatalanEconomics Society Conference.

yAddress: 301F Hulbert Hall, Washington State University, Pullman, WA 99164. E-mail: paksing.choi@wsu.edu.zAddress: 111C Hulbert Hall, Washington State University, Pullman, WA 99164. E-mail: anaespinola@wsu.edu.xAddress: 103G Hulbert Hall, Washington State University, Pullman, WA 99164. E-mail: fmunoz@wsu.edu.

1

1 Introduction

Procurement auctions are often used to conserve territories rich in biodiversity, or protect endan-

gered species. Examples include the Conservation Reserve Program (CRP) in the United States,

the Bush Tender Programme in Australia, and the Countryside Stewardship Scheme in the United

Kingdom.1 The CRP, for instance, retires highly erodible and other environmentally sensitive crop-

land from production.2 The participation in a conservation program usually implies the suspension

of all market activities and the dedication of the land to conservation, thus requiring a payment to

landowners.

Conservation activities can generate externalities, potentially increasing (or decreasing) the

costs of landowners who do not dedicate their land to conservation. For instance, river watershed

restoration projects in Portland, Oregon, increased home prices by 37% for properties located

on the restoration site, thus re�ecting a positive externality from the conservation program to

the housing market.3 In contrast, a¤orestation projects increase upstream water use, imposing a

negative externality on non-participating farmers located downstream; see Nordblom et al. (2012).

Externalities can also stem from non-participants to participants of the conservation program. In

the U.S. Midwest, for example, non-participating landowners often expand their production to

areas that were not previously cultivated, a phenomenon known as slippage. Common crops in

this area, like wheat, corn, and grain sorghum, require an intensive use of pesticides, thus making

conservation more di¢ cult and expensive.4

Our paper examines how the existence of externalities distorts conservation output in procure-

ment auctions (such as acreage of farmland dedicated to conservation, or biodiversity), and its

corresponding payments to landowners. Unlike previous studies, we allow for bidirectional exter-

nalities, whereby landowners participating in the conservation program can generate externalities

on those dedicated to market activities, and vice versa. In this context, a negative (positive)

externality from conservation to market activities, increases (decreases, respectively) production

costs. Similarly, a negative (positive) externality from market to conservation activities increases

1As of May 2016, the CRP covers about 24.2 million acres, and has 652,305 contracts with 365,771 farms par-ticipating in the program, totaling an annual rental payment of US$1.7 billion. In the case of the Bush TenderProgramme, it signed 586 contracts with 465 landowners from 2001 to 2012, with total payments of AUS$17.51 mil-lion. For more details on the CRP, see Latacz-Lohmann and Van der Hamsvoort (1997) and Hellerstein et al.(2015),Stoneham et al. (2003) for programs in Australia, and Dobbs and Pretty (2004) for programs in the United Kingdom.

2 In the Georgia Irrigation Reduction Auction studied by Cummings et al. (2004), farmers suspend irrigation ofthe land to conserve water for downstream users. In particular, farmers turn their irrigation permit over to theregulator during the drought season in exchange for a one-time lump-sum compensation. Similarly, in the MarylandAgricultural Land Preservation Foundation program, farmers yield their land development rights for a certain periodof time upon subscription; see Horowitz et al. (2009). The compensation was shown to be 5% to 15% above thereservation values.

3See Jarrad et al. (2016). Prior studies also found a positive e¤ect of watershed restoration on property prices.Streiner and Loomis (1995), for instance, use a hedonic price model to show that urban stream restoration projectsincrease property values by 3-13% in California. (The range depends on whether the main bene�ts of the project arereduced �ood damage, revegetation, or enhanced aesthetics.) For other studies �nding similar results using contingentvaluation methods, see Loomis et al. (2000) and Holmes et al. (2004).

4Leathers and Harrington (2000) report an average annual slippage of 53% for the 1988-1994 period. Other studiesreport an average slippage rate of 33% in the period between 1956 and 1985; see Joyce and Skold (1987).

2

(decreases) conservation costs. In addition, the procurer is unable to observe the landowners�ef-

�ciency level either in the conservation, the market activity, or both. This is a common feature

in CRP auctions, where the procurer has imperfect predictors of soil quality and landowners�abil-

ities. We show that each market failure alone (asymmetric information or externalities) deviates

optimal output away from the �rst best. However, we demonstrate that their coexistence, rather

than producing larger output ine¢ ciencies, can move optimal output closer to the �rst best under

certain conditions.

We �rst analyze the case in which the procurer has complete information as our benchmark

(observing e¢ ciency levels in both activities for all bidders). In the absence of externalities, the

regulator balances the marginal bene�t of additional units of conservation against its marginal cost,

which leads to a �rst-best outcome. When negative (positive) externalities from conservation to

production are present, market production becomes less (more) attractive, thus reducing (increas-

ing) the procurer�s payment to induce the participation of landowners a¤ected by the externality.

As a consequence, the auction becomes less expensive to implement, leading the procurer to increase

(decrease) optimal conservation output. A similar (opposite) argument applies when market pro-

duction generates positive (negative) externalities on conservation costs since landowners require a

lower (higher) compensation to participate.

Under an incomplete information setting, we develop a direct revelation mechanism that induces

landowners to truthfully reveal their private information. For comparison purposes, we �rst present

the case in which externalities are absent. As in Myerson (1981), the procurer increases conservation

output until its marginal bene�t coincides with its virtual marginal cost, where the latter includes

not only marginal costs but also information rents to induce truth-telling. Therefore, the auction

becomes more expensive than under complete information, yielding a lower conservation output.

However, in our setting, the regulator has two sources of uncertainty: he does not observe bidders�

market nor their conservation e¢ ciency, entailing information rents stemming from both unknown

parameters.

When conservation externalities are present, the procurer must also consider the external e¤ect

that every bidder i�s conservation output imposes on those producing market goods. Similar to the

complete information setting, negative externalities increase landowner j�s market cost, thus reduc-

ing the compensation that the procurer needs to o¤er. The auction then becomes less expensive,

leading the procurer to induce a larger conservation output, relative to the setting without exter-

nalities. Consequently, such output approaches the �rst best when the conservation externality is

minor. When the externality is substantial, however, optimal output can lie further away from the

�rst best. In the �rst case, the presence of externalities ameliorates the market imperfection that

stems from asymmetric information, thus becoming an �ally�of the regulator; while in the second

case externalities augment ine¢ ciencies.

Uninformed procurers often use auctions to reduce their information asymmetry, seeking to

decrease output ine¢ ciencies. Information rents, however, lead to output distortions relative to the

�rst best. Our �ndings indicate that externalities can reduce such output distortion, ultimately

3

helping the uninformed procurer approach the �rst best. This occurs, in particular, when conser-

vation externalities are minor. When they are substantial, however, the above output distortion is

emphasized, providing the regulator with strong incentives to acquire information about bidders�

e¢ ciency (soil quality and landowners�abilities) before the design of the auction. In contrast, when

conservation externalities are minor, the acquisition of information becomes less bene�cial.

A similar argument applies when landowners dedicated to market activities produce negative

externalities which increase conservation costs. In this context, the procurer needs to increase the

compensation to landowners dedicated to conservation, thus making the program more expensive

to implement, ultimately leading to a decrease in conservation output. Therefore, this externality

further reduces optimal output, relative to the incomplete information context without externali-

ties. Conservation output in this case becomes further away from the �rst best, augmenting the

ine¢ ciency stemming from asymmetric information alone. Hence, the regulator has the strongest

incentives to acquire information about bidders�types; which holds regardless of the intensity of

the externality.

Our results can be a valuable tool for procurers designing conservation programs in areas with

little information about landowners�conservation costs, or about their current market e¢ ciency,

when bidirectional externalities exist. Similarly, our model extends to the procurement of utility

contracts in regions where competing �rms have no prior experience delivering such utility (e.g.,

water treatment and distribution contracts). In that setting, bidirectional externalities could arise

if, for instance, water treatment improves health conditions in the region, thus increasing labor

productivity of those �rms still dedicated to market activities and, in addition, polluting market

activities raise the costs of the water company. In addition, our �ndings shed light on the conse-

quences of ignoring one or both types of externalities. For instance, if the regulator considers a

negative externality from conservation to market activities (but ignores externalities from market to

conservation), we show that the conservation output is excessive (insu¢ cient) when the externality

he ignores is negative (positive, respectively). Therefore, the conservation program would be too

passive as it jeopardizes biodiversity, or too aggressive as it hurts market activities.

Related literature. Several papers have analyzed the e¤ects of negative externalities on

auctions. For instance, Jehiel et al. (1996, 1999 and 2000) and Figueroa and Skreta (2011) consider

that a bidder�s payo¤ from not winning the auction is a¤ected by who gets the object.5 Espinola-

Arredondo (2008) assumes that bidders�payo¤s have two components, revenue and costs, where

only costs are a¤ected by externalities. In particular, she considers that the production cost of those

bidders losing the auction is a¤ected not only by the identity of the winner but also by the output

decision (namely, conservation level) of the winning bidder.6 Similarly, our paper considers that

externalities a¤ect the bidders�conservation/production cost. However, we examine bidirectional

5Filiz-Ozbay and Ozbay (2007) study an externality created by the bidder to herself, and Bartling and Netzer(2016) experimentally analyze players�motives to a¤ect other players�monetary payo¤s.

6 In addition, she considers that only a single e¢ ciency parameter is unobserved by the procurer, while our modelallows for two parameters (conservation and market e¢ ciencies).

4

externalities: those produced by the winning bidders developing the conservation program, and

also by the losing bidders still operating in the market.

Hansen (1988), Desgagne (1988) and Dasgupta and Spulber (1990) examine two-dimensional

bid auctions.7 In addition, Che (1993) studies a score-based system of two-dimensional bid auctions

(quality, price) in order to implement an optimal mechanism, and Branco (1997) also analyzes a

multidimensional bid auction, but considers the impact of costs�correlation on the design of mul-

tidimensional mechanisms. Similarly, we examine a direct revelation mechanism in which every

bidder truthfully reveals his two-dimensional type, e¢ ciency in conservation and in market activi-

ties, since the former a¤ects the bidder�s ability to generate conservation while the latter increases

the compensation that the procurer needs to o¤er to achieve participation.

Finally, several authors have analyzed procurement auctions for environmental investments,

since they are considered to be more cost-e¢ cient than uniform-rate payment schemes. This is

mainly due to the heterogeneity of conservation bene�ts and costs across di¤erent landowners

(Latacz-Lohmann and Van der Hamsvoort, 1997), despite the fact that auctions generally entail

information rents and higher administrative costs; see Kirwan et al. (2005) and Connor et al.

(2008).8 We focus on procurement auctions as a tool to promote biodiversity where, in addition,

we allow for externalities to a¤ect both the costs of landowners producing conservation output and

those continuing their market activities. We show that, the output distortion from asymmetric

information can be ameliorated by the presence of externalities.

Our paper is structured as follows. Section 2 develops the model, Section 3 analyzes output

and payments under complete information, while section 4 examines them under incomplete infor-

mation. Last, section 5 discusses our main results and conclusions.

2 Model

ConsiderN landowners producing a homogenous market good. In order to promote biodiversity, the

regulator conducts a procurement auction. When landowner i implements a conservation project,

he dedicates all his land to a prede�ned environmental service, such as biodiversity enrichment,

and refrains from alternative land use activities, such as market production (e.g., agricultural

produce). Let �Ki denote landowner i�s cost e¢ ciency, where the superscriptK = fC;Mg representsconservation or market production, respectively. As we discuss below, higher values of �Ki imply

lower costs in activity K.9 Let �i =��Mi ; �

Ci

�be landowner i�s e¢ ciency pair, where �Mi 2 �M and

�Ci 2 �C ; and � � (�1; : : : ; �N ) be the e¢ ciency pro�le for all landowners, such that � 2 � where �7Bichler (2000) experimentally examines multi-attribute auctions, and Asker and Cantillon (2010) study a pro-

curement auction considering price and quality. For a literature review, see Rochet and Stole (2003).8Additionally, studies have shown that uniform-rate payment schemes are prone to adverse selection problems,

since they attract landowners with low conservation e¢ ciency (e.g., poor soil quality); see Osterberg (2001), Hynesand Garvey (2009), and Quillérou et al. (2010).

9For a given market production, the cost function decreases in landowner i�s ability in conducting market produc-tion (e.g., planting and harvesting corn). Due to his experience in market production, however, this ability could beless useful for conservation (e.g., wetland rehabilitation, installing native grasses, or longleaf pine, as usually requestedin CRP programs by the USDA).

5

is the Cartesian product �M ��C . E¢ ciency parameter �Ki is only observable to landowner i, butits distribution, �Ki � F (�Ki ;K) where �Ki 2

h�K ; �

Ki, is common knowledge.10 Hence, we allow

for di¤erent distribution functions for conservation and market e¢ ciency, i.e., F (�;K) is activity-dependent. In addition, we consider that bidders and procurer exhibit symmetric priors over types.

We also assume that the production and conservation e¢ ciency parameters are independently

distributed.11 Furthermore, our model allows for market production to generate an externality

on conservation, and vice versa; thus allowing for bidirectional externalities, but we do not allow

externalities within an activity. That is, landowner i�s conservation (market) activity does not

a¤ect landowner j�s conservation (market) costs.

The utility when landowner i undertakes conservation is

ui�qCi ; �

Ci ; C

�= ti(qCi ; C)� Ci(qCi ; qM�i; �Ci ; C) (1a)

and if, instead, he continues market activities his utility is

ui�qMi ; �

Mi ;M

�= pqMi � Ci(qMi ; qC�i; �Mi ;M) (1b)

where ti(qCi ; C) in expression (1a) denotes the payment to landowner i when he engages in conser-

vation; and pqMi in (1b) represents the market revenue for a given price p > 0 when he produces qMiunits of market output. In addition, the second term in the above expressions, Ci(qKi ; q

J�i; �

Ki ;K)

represents landowner i�s cost in activity K, which is a function of: (i) his own output qKi ; (ii) the

externalities that activity J 6= K of other landowners impose on him as described by the vector

qJ�i ��qJ1 ; :::; q

Ji�1; q

Ji+1; :::; q

JN

�; and (iii) his e¢ ciency in activity K, �Ki . Finally, when q

Ki = 0,

costs are normalized to zero.

When the procurer observes the e¢ ciency parameters from all landowners, he can anticipate

the externalities that each of them will su¤er and/or impose on others, and thus their costs in

either activity. Therefore, the procurer can design the pro�le of conservation output and payments

such that landowners do not have incentives to cut their output after experiencing externalities; as

we examine in sections 3 and 4.

2.1 Assumptions

We next describe how landowner i�s total cost in activity K, and his marginal cost, MCi � CiqKi,

are a¤ected by his output decisions and e¢ ciency.

10F (�Ki ;K) being common knowledge can be interpreted as that the distribution of possible technologies availableto develop activity K is well known, even if the speci�c technology of a particular landowner is unobservable.11 Intuitively, a landowner�s market e¢ ciency does not a¤ect his e¢ ciency in conservation because a di¤erent skill

set might be required for each activity. Instead, e¢ ciency parameters could be positive correlated, if landowners whoare e¢ cient in market production are also e¢ cient in conservation; or negatively, if the opposite occurs. In bothcontexts, however, the procurer could bene�t from correlated e¢ ciencies since inducing the truthful revelation of asingle e¢ ciency parameter (e.g., market) could help him infer the other parameter (e.g., conservation). Our problem,hence, is more involved as it requires thruthful revelation of both e¢ ciency parameters.

6

Assumption 1. Total and marginal costs of landowner i in activity K increase in his own

output, and decrease in his e¢ ciency on that activity at a decreasing rate. In addition, marginal

costs satisfy MCiqKi �

Ki� 0:

Since marginal costs are decreasing in e¢ ciency, MCi�Ki� 0, the single-crossing condition holds.

The last part of Assumption 1 states that the convexity of the cost function decreases as landowner

i becomes more e¢ cient. That is, increasing output becomes less expensive when the landowner is

more e¢ cient in activity K. Given the similarities between negative and positive externalities, we

next present our assumptions for the case of negative externalities, and at the end of this subsection

discuss the main di¤erences with positive externalities. Assumptions 2-3 describe how costs are

a¤ected by negative externalities.

Assumption 2. Total and marginal costs of landowner i in activity K increase in landowner

j�s output in activity J (negative externality), where j 6= i and J 6= K . This increase is attenuated

by landowner i�s e¢ ciency in activity K.

Hence, total and marginal costs increase with negative externalities, and such e¤ects diminish in

landowner i�s e¢ ciency. When he is relatively ine¢ cient in activity K, a given increase in negative

externalities from landowner j, qJj , yields a large increase in landowner i�s cost. However, when he

is relatively e¢ cient, such an increase is smaller.

Assumption 3. Landowner i�s total costs in activity K are convex in the externality generatedby landowner j, but this e¤ect is attenuated by landowner i�s e¢ ciency in activity K.

Intuitively, not only landowner i�s costs increase in bidder j�s production, but at an increasing

rate, thus re�ecting that landowner i�s costs are convex in negative externalities, as depicted in

Figure 1.12 Also, the e¢ ciency of landowner i attenuates the convexity of his cost function; as

indicated in the approximately linear curve in Figure 1 (high e¢ ciency). In order to illustrate our

model and results, we next present a parametric example, which is further developed throughout

the paper.

12For illustration purposes, Figure 1 considers two e¢ ciency levels �KLi and �KH

i which represent low and highlevels of e¢ ciency respectively, satisfying �KL

i < �KHi .

7

Fig 1. E¤ect of negative externalities on costs.

Example 1. Consider the cost function13

Ci�qKi ; q

J�i; �

Ki ;K

�=qKi

�qKi + �

JPj 6=i q

Jj

�1 + �Ki

for activity K. Following Jehiel et al. (1996), �J � 0 measures the intensity of negative exter-

nalities from all the other N � 1 landowners dedicated to activity J 6= K.14 Let us next examineAssumptions 1-3. In particular, the marginal cost is MCi = 1

1+�Ki

�2qKi + �

JPj 6=i q

Jj

�which is

unambiguously positive and increasing in output qKi . Furthermore, total and marginal costs are

decreasing in e¢ ciency �Ki at a decreasing rate, i.e., Ci�Ki

= � qKi

(1+�Ki )2

�qKi + �

JPj 6=i q

Jj

�� 0,

Ci�Ki �

Ki=

2qKi

(1+�Ki )3

�qKi + �

JPj 6=i q

Jj

�� 0, MCi

�Ki= � 1

(1+�Ki )2

�2qKi + �

JPj 6=i q

Jj

�� 0 and

MCi�Ki �

Ki= 2

(1+�Ki )3

�2qKi + �

JPj 6=i q

Jj

�� 0. Assumption 2 is also satis�ed given that landowner

i�s total and marginal costs increase in other landowners�output, CiqJj=

�JqKi1+�Ki

� 0 and MCiqJj=

�J

1+�Ki� 0; which are attenuated in landowners i�s e¢ ciency, �Ki . Finally, Assumption 3 weakly

holds due to the linearity of the cost function in externalities, that is, CiqJj q

Jj= 0. �

Remark. In the case of positive externalities, landowner i�s total and marginal costs decrease13Other costs functions also satisfy Assumptions 1-3, but are not as compact. In addition, this function: (i)

places e¢ ciency parameter �Ki in the denominator, thus illustrating that higher values of �Ki decrease both total andmarginal costs; (ii) helps visualize the e¤ect of the externalities in the last term of the numerator through parameter�J ; and (iii) guarantees positive and increasing marginal costs as required.14For simplicity, this functional form assumes that the intensity of negative externality is symmetric across landown-

ers. The externality that each of them experiences can, however, be di¤erent if output levels are di¤erent, that is,�JP

j 6=i qJj 6= �J

Pj 6=k q

Jk for two landowners i and k.

8

in other landowner�s output; and such a decrease is attenuated by landowner i�s own e¢ ciency. In

addition, landowner i�s costs are convex in externalities. That is, having received a certain level of

positive externality from landowner j, landowner i has less room for further cost reduction upon a

higher level of externality.15

2.2 Market output

We next study the market activity of landowner i. (All proofs are relegated to the appendix.)

Lemma 1. Landowner i chooses an optimal market output, qM�i , that maximizes (1b) which

solves

p =MCi�qM�i ; qC�i; �

Mi ;M

�(2)

that is independent of others�market output. In addition, qM�i and market pro�t, ui

�qM�i ; �Mi ;M

�,

increase in landowner i�s production e¢ ciency, �Mi .

Landowner i increases his market output until the point where market price coincides with his

marginal costs which include the external e¤ect that conservation output from other landowners

imposes on him.

2.3 Regulator�s payo¤

The bene�t that landowner i generates when producing conservation output qCi is

W i�qCi�= V i

�qCi�� (1 + �) ti

�qCi ; C

�(3)

where V i�qCi�denotes the value that the procurer assigns to conservation, which is increasing

and concave in qCi ; and � � 0 represents the shadow cost of raising public funds.16 Since the

procurer does not observe �, he takes the expected bene�t from each landowner i and sums over

all landowners, that is,

EW (q; t) =NXi=1

�iE��W i�qCi��

(4)

where �i denotes the weight that the procurer assigns to landowner i, subject to 0 < �i � 1

andPNi=1 �i = 1; q �

�qM ; qC

�represents the pro�le of market and conservation output, where

qK ��qK1 ; : : : ; q

KN

�; and t �

�pqM ; tC

�is the pro�le of market revenue and conservation payment,

respectively, where tC ��t1(C); : : : ; tN (C)

�and qM �

�qM1 ; : : : ; q

MN

�.

15 If landowner j imposes a positive externality while landowner k generates a negative externality, then the twoexternalities o¤set each other, entailing that landowner i�s costs can increase or decrease, depending on which e¤ectdominates.16For instance, the CRP started to rank bids since 1996 using the Environmental Bene�ts Index, which considers

the environmental services that the retired parcel of land expects to produce, captured by V i in our model, and thecost of the landowner�s payment, ti in our setting; see Hellerstein et al. (2015).

9

3 Complete information

As a benchmark for future comparisons, we next describe the optimal contract (i.e., output and

payment pro�les) under complete information. In this context, the regulator observes��Ci ; �

Mi

�for

every landowner i, and chooses which landowners are selected for the conservation project, and

how much conservation output qCi each produces, leaving the remaining landowners to choose their

market production according to Lemma 1. For compactness, letMBi � V iqCirepresent the marginal

bene�t from additional units of conservation output, and MECi �Pj 6=i

�j�iCjqCi

�q̂Mj ; q

C�j ; �

Mj ;M

�denote the marginal external cost that landowner i�s conservation output imposes on other landown-

ers� costs, where q̂Mj is the contingent output that landowner j produces if he were to continue

market production.

Lemma 2 [Complete information]. When the procurer observes every landowner i�s e¢ -ciency pair �i =

��Ci ; �

Mi

�, he chooses the conservation output qC��i that solves

MBi = (1 + �)�MCi �MECi

�(5)

and the payment is

ti�qCi ; C

�= Ci

�qCi ; q

M�i; �

Ci ; C

�+�pq̂Mi � Ci

�q̂Mi ; q

C�i; �

Mi ;M

��where q̂Mi is the contingent market output of landowner i that solves (2), if landowner i�s expected

bene�t is positive. Otherwise, conservation output and payment are zero.

Hence, under no externalities, MECi becomes nil, and the procurer chooses landowner i�s

output by solving MBi = (1 + �)MCi, i.e., balancing the marginal value of additional units of

conservation and its marginal conservation cost, which yields the �rst-best outcome. However,

when negative (positive) conservation externalities are present, MECi is positive (negative) since

landowner i�s output increases (decreases) the production costs of other landowners, entailing that

(1+ �)�MCi �MECi

�lies below (above, respectively) (1+ �)MCi; as depicted in Figure 2. As a

consequence, the presence of negative (positive) conservation externalities induces a larger (smaller)

optimal output than when externalities are absent. Intuitively, when other landowners�contingent

production costs become higher, their market pro�t shrinks such that the procurer needs to o¤er

them a smaller compensation to induce their participation in the program.

10

Fig 2. Complete info., with and without negative ext.

In contrast, if negative production externalities exist (from landowners dedicated to market

activities to those doing conservation), landowner i�s marginal conservation cost MCi increases,

and MECi = 0 since landowner i does not generate externalities on landowners dedicated to

market. These e¤ects reduce landowner i�s optimal conservation output in expression (5). Finally,

the optimal payment in lemma 2 compensates landowner i for undertaking the conservation activity

(�rst term) and the cessation of market activity (term in brackets). Speci�cally, in the case of

negative production externalities, landowner i experiences an increase in his conservation cost,

while his market cost is una¤ected, ultimately increasing the payment relative to that when his

conservation output imposes externalities on market activities.

Example 2. Continuing our above parametric example, we can now evaluate expression (5),assuming that the procurer assigns a value V i

�qCi�= qCi to conservation output, where �i = 1 for

every landowner i. For simplicity, we assume that �Ki 2 [0; 1] for every landowner i and activity K.In a setting with two landowners, MECi =

�CqMj1+�Mj

. In Appendix 1, we evaluate MECi at q̂Mi , the

pro�t-maximizing market output solving (2). Using expression (5) we obtain

qC��i =11+� +

p�C

2

21+�Ci

+ (�C)2

2(1+�Mj )

(6)

11

4 Incomplete information

As described in previous sections, each landowner privately observes his e¢ ciency pair (�Mi ; �Ci ).

The procurer, in contrast, does not observe these e¢ ciency parameters, and uses a Direct Revelation

Mechanism (DRM) to maximize expected welfare in equation (4).17 In particular, in a DRM

� : �M ��C ! R2N+ the procurer asks each landowner i to report his production and conservation

e¢ ciency. Using this information, the procurer chooses the output and payment pro�les (q; t) that

solve

maxq;t

EW (q; t)

subject to:

1. Bayesian Incentive Compatibility:

U i��Ci ; �

Ci ; C

�� U i

��̂C

i ; �Ci ; C

�for all �Ci ; �̂

C

i 2 �C where �̂C

i 6= �Ci (7)

U i��Mi ; �

Mi ;M

�� U i

��̂M

i ; �Mi ;M

�for all �Mi ; �̂

M

i 2 �M where �̂M

i 6= �Mi (8)

2. Individual Rationality:

U i��C ; �C ; C

�� U i

��M; �M;M�

(9)

For compactness, we denote U i��Ki ; �

Ki ;K

�� ui

�qKi ; �

Ki ;K

�, where the �rst argument in U i (�)

represents landowner i�s report, the second argument denotes his true type, and the last element

re�ects his activity. Condition (7) says that landowner i prefers to truthfully reveal his conservation

e¢ ciency, �Ci , rather than report a false �̂C

i 6= �Ci . A similar argument applies to condition (8),

which guarantees truthful reporting of market e¢ ciency �Mi . Condition (9) implies that, even if

landowner i is the least e¢ cient in conservation and the most e¢ cient in production, he still has

incentives to submit his bid.18 Hence, any other landowner, who is more e¢ cient in conservation

or less e¢ cient in production, will also submit his bid. Before solving the DRM, we present two

de�nitions.

De�nition 1. Landowner i�s virtual conservation cost is

~Ci�qCi ; q

M�i; �

Ci ; C

�� Ci

�qCi ; q

M�i; �

Ci ; C

��1� F

��Ci ; C

�f��Ci ; C

� Ci�Ci

�qCi ; q

M�i; �

Ci ; C

�Thus, VMCi � ~Ci

qCi

�qCi ; q

M�i; �

Ci ; C

�represents his Virtual Marginal Conservation Cost.

17 If the government owned the land to be dedicated to conservation, it would observe its cost e¢ ciency, thus,reducing the mechanism to one in which only market costs are unknown. We analyze this mechanism in section 4.2.18While the procurer seeks that every landowner submits a bid, and thus reveals his e¢ ciency, the procurer might

choose only a subset of landowners for the conservation program, thus identifying bidders above a critical type asin Jehiel et al. (1999); which we discuss in Proposition 1. If condition (9) were violated, the procurer would not beable to infer all bidders�types, and thus he would not necessarily choose the most e¢ cient bidder(s) to undertake theconservation program.

12

In the context of CRP auctions, for example, the procurer could be uncertain about landowners�

conservation costs and needs to construct their virtual conservation cost. In particular, ~Ci (�)comprises landowner i�s actual conservation cost, Ci

�qCi ; q

M�i; �

Ci ; C

�, and his information rent,

�1�F(�Ci ;C)f(�Ci ;C)

Ci�Ci(�) � 0, to truthfully reveal his e¢ ciency �Ci , as in Myerson (1981), since Ci�Ci � 0

by Assumption 1. Hence, VMCi can also be expressed as

VMCi =MCi �1� F

��Ci ; C

�f��Ci ; C

� Ci�Ci q

Ci(�)

which, by the single-crossing property, entails that VMCi > MCi. As a consequence, landowner

i requires a more generous compensation to increase conservation output when the procurer is

uninformed about his e¢ ciency than otherwise.

De�nition 2. Landowner j�s virtual contingent production cost is

~Cj�q̂Mj ; q

C�j ; �

Mj ;M

�� Cj

�q̂Mj ; q

C�j ; �

Mj ;M

�+F��Mj ;M

�f��Mj ;M

�Cj�Mj

�q̂Mj ; q

C�j ; �

Mj ;M

�Thus, V ECi �

Pj 6=i

�j�i~CjqCi

�q̂Mj ; q

C�j ; �

Mj ;M

�denotes the Virtual External Cost of bidder i.

Intuitively, V ECi helps the procurer identify the externality that an increase in landowner i�s

conservation output imposes on other landowners dedicated to market. Speci�cally, the procurer

�rst identi�es the virtual contingent production cost of every landowner dedicated to market activ-

ities, which comprises his actual production cost, Cj�q̂Mj ; q

C�j ; �

Mj ;M

�, and his information rent,

F(�Mj ;M)f(�Mj ;M)

Cj�Mj

�q̂Mj ; q

C�j ; �

Mj ;M

�. Second, V ECi evaluates the increase in this virtual production

cost from a marginal increase in landowner i�s output. Therefore, V ECi can be expressed as

V ECi =MECi +Xj 6=i

�j�i

F��Mj ;M

�f��Mj ;M

�Cj�Mj q

Ci

(�) ;

which by Assumption 2 entails that MECi > V ECi. Hence, landowners j 6= i require an infor-

mation rent to truthfully reveal their types, which increases the procurer�s cost of implementing

output qCi due to his lack of information.

4.1 Optimal output pro�le

We next solve the DRM by �nding the optimal output levels that the procurer assigns to each

landowner.

Proposition 1. The DRM truthfully implements the regulator�s payo¤ function EW (�) inBayesian Nash Equilibrium, yielding an optimal output pro�le q� = (q�1; : : : ; q

�N ), where landowner

i�s market output is qM�i = 0, and his conservation output, qC�i , solves

13

MBi = (1 + �)�VMCi � V ECi

�(10)

if �Ci � ~�Ci

��Mi ; �

C�i; �

M�i�. Otherwise, landowner i keeps its market production as described in

Lemma 1, and conservation output is zero. In addition, the optimal conservation output qC�i in-

creases in landowner i�s own conservation e¢ ciency, �Ci .

We next analyze the optimal conservation output of landowner i arising from Proposition 1.

For illustration purposes, we �rst present the case in which externalities are absent; then the case

in which only conservation externalities are present; and �nally the setting where both conservation

and production externalities coexist.

4.1.1 Benchmark - Incomplete information without externalities

Under incomplete information, the procurer does not observe MCi but constructs the virtual

marginal cost VMCi, which includes the information rent to landowner i. In the case of no

externalities, V ECi = 0 in expression (10), and the procurer chooses conservation output as the

following Corollary describes.

Corollary 1 [No externalities, Myerson (1981)]. When externalities are absent and theprocurer does not observe every landowner i�s e¢ ciency pair �i =

��Ci ; �

Mi

�, market output is zero,

and a conservation output qC�0

i solves

MBi = (1 + �)VMCi

if �Ci � ~�Ci

��Mi�. Otherwise, landowner i keeps its market production as described in Lemma 1.

Therefore, as in standard mechanism design problems without externalities, the procurer equates

the marginal bene�t with the virtual marginal cost; as illustrated in Figure 3. When landowner i�s

conservation e¢ ciency is the highest, �C, his conservation costs are lower than those of all other

landowners, implying that information rents are nil, i.e., F (�C; C) = 1 entailing 1�F (�C ;C)

f(�C;C)

= 0 (�no

distortion at the top�). In contrast, when �C � �Ci < �C, the procurer induces truthful revelation

of e¢ ciency by paying information rents.19 This is illustrated in Figure 3, where the information

rent is depicted by the shaded area between (1 + �)VMCi and (1 + �)MCi. Hence, output

under incomplete information, qC�0

i , is lower than under complete information, qC��i . Intuitively,

information rents make the conservation program more expensive for the procurer, who responds

by reducing conservation output.

19The opposite result arises in market production. When landowner i�s market e¢ ciency is the lowest, �M , hisproduction cost cannot be further increased. Therefore, F (�M ;M) = 0, entailing that landowner i extracts noinformation rent; see De�nition 2. This is a �no distortion at the bottom�result, implying that his actual and virtualproduction costs coincide. When �M < �Mi � �M , however, landowner i captures an information rent.

14

Fig 3. Information rent in conservation.

Information rents grow as landowners�marginal cost decreases more rapidly for a given increase

in their conservation e¢ ciency �Ci , i.e., second term in VMCi is larger in absolute value. In Figure

3, this e¤ect implies that curve (1+�)VMCi su¤ers a large upward shift, thus reducing conservation

output. Similarly, when the shadow cost of raising public funds, �, increases, both curves in Figure

3 shift upward, ultimately shrinking conservation output. If marginal costs are extremely sensitive

to changes in �Ci , parameter � is su¢ ciently high, or both, the procurer refrains from inducing

conservation output since his payment would be too high.

4.1.2 Introducing Externalities

Conservation Externalities. If, however, landowner i imposes negative conservation externali-ties on landowners dedicated to market activities, V ECi becomes positive in expression (10). In-

tuitively, landowner i�s externality increases marginal costs for market output of other landowners.

Figure 4a depicts the optimal conservation output with and without negative conservation external-

ities. Under no externalities, the marginal bene�t and VMCi functions cross at conservation output

qC�0i . In the presence of negative conservation externalities, however, the (1 + �)

�VMCi � V ECi

�curve lies below the (1 + �)VMCi curve which, because of the concavity of the bene�t function,

entails a higher conservation output than that in the absence of externalities. Relative to the case

of no externalities, landowner j�s market cost increases, reducing his market pro�ts, ultimately de-

creasing the compensation that the procurer needs to o¤er to induce him to submit a bid. Hence,

the procurer sets a higher conservation output when negative conservation externalities are present

than otherwise. (The opposite argument applies in the case of positive conservation externalities.)

If the marginal bene�t from additional units of conservation is constant (i.e., MBi curve is �at),

15

the presence of negative externalities entails a large increase in conservation output since additional

conservation still produces signi�cant bene�ts. If, in contrast, the MBi curve is vertical, the pres-

ence of externalities does not a¤ect the amount of conservation being implemented, as further units

only generate negligible bene�ts.

When V ECi is small (i.e., when conservation externalities are relatively minor) optimal output

approaches the �rst best depicted at point A in Figure 4a. That is, in a context of incomplete

information, the presence of small conservation externalities becomes an �ally�of the regulator since

they ameliorate output ine¢ ciencies emerging from his lack of information. However, if conservation

externalities are substantial, they can induce larger output ine¢ ciencies than those arising from

asymmetric information alone. (Graphically, this occurs when the conservation externality curve

passes through point A0 in Figure 4a.)

More explicitly, we can evaluate the output distortion stemming from each market failture

as the di¤erence between the �rst-best outcome and the second best output implemented by the

mechanism. In particular, ine¢ ciencies from asymmetric information alone are given by

ODAsyInfo � qFBi � qC�0

i ;

where qFBi denotes the �rst-best outcome, and qC�0

i represents the optimal outcome in an incomplete

information context when externalities are absent (found in Corollary 1 and illustrated in Figure

4a). Similarly, the output distorsion arising from both market failures (asymmetric information

and externalities) is

ODBoth � qFBi � qC�i ;

where qC�i was found in Proposition 1. Hence, the presence of externalities reduces the output

distortion arising from asymmetric information alone if ODBoth < ODAsyInfo or, rearranging, if

qC�i < qC�0i ; which holds when externalities produce a small downward shift in the (1+�)VMCi curve

(see Figure 4a). Example 3 below shows that this occurs when the negative conservation externality,

�C , lies below a speci�c cuto¤ �C . Hence, small (large) externalities can reduce (enlarge) the

ine¢ ciencies that the regulator faces due to his lack of information.

16

Fig 4a. Negative conservation externalities from i. Fig 4b. Negative production externalities to i.

Production Externalities. If market activities from other landowners impose negative ex-

ternalities on landowner i, his marginal conservation cost increases, implying that VMCi shifts

upwards; ultimately increasing the right-hand side of (10). Figure 4b depicts this case, showing

that, since VMCi0 > VMCi, the auction becomes more expensive, leading the procurer to induce

a smaller optimal conservation output than without production externalities; see point B in Fig-

ure 4b. Therefore, the presence of production externalities moves output further away from the

�rst-best outcome. (The opposite result applies if market activities generate positive externalities

on the costs of landowners dedicated to conservation, where VMCi0 < VMCi, thus entailing a

higher conservation output. In this case, the positive production externality becomes an �ally�

of the regulator when the externality is minor.) Finally, when both conservation and production

externalities coexist, conservation output decreases relative to the case in which only conservation

externalities are present; as depicted in Figure 4b, where qC�1

i decreases to qC�2

i .

Example 3. Consider the cost function in Examples 1 and 2, and assume that �Ki � U [0; 1]for every i and K, thus yielding

VMCi =2qMi + �CqCj�1 + �Mi

�2 and V ECi =�CqCj�1 + �Mj

�2Inserting them in expression (10), yields an output level of

qC�i =

�1 + �Mj

�2 �1 + �Ci

�2 �2 + p�C (1 + �)

�(1 + �)

h8�1 + �Mj

�2+ (�C)2

�1 + �Ci

�2i :

17

Last, we identify for which values of �C the presence of conservation externalities ameliorates the

output ine¢ ciency arising from asymmetric information alone. First, the output distortion from

asymmetric information is given by

ODAsyInfo � qFBi � qC�0

i

=1 + �Ci2 (1 + �)

��1 + �Ci

�24 (1 + �)

=

�1 + �Ci

� �1� �Ci

�4 (1 + �)

where qFBi is found by evaluating the complete-information result from Example 2 without ex-

ternalities, �C = 0, while qC�0

i is found by setting �C = 0 in the above output qC�i . Note that

ODAsyInfo is decreasing in landowner i�s e¢ ciency parameter �Ci , and becomes nil when �Ci = 1,

i.e., no distortion at the top. Second, the output distortion from externalities alone are

ODExt � qFBi � qCi��i

=1 + �Ci2 (1 + �)

�11+� +

p�C

2

21+�Ci

+ (�C)2

2(1+�Mj )

=1 + �Ci2 (1 + �)

�C��C�1 + �Ci

�� 2p (1 + �)

�1 + �Mj

��4�1 + �Mj

�+ (�C)2

�1 + �Ci

�where qCi��i was found in Example 2 (complete information output with externalities, see Lemma

2). In addition, ODExt increases in the size of the externality, �C , re�ecting that, as every unit of

conservation generates a larger increase in other landowners�market cost, their contingent market

pro�ts decrease, which ultimately reduces the compensation the regulator needs to o¤er them

to participate. Hence, the regulator sets a larger conservation output, which expands the output

distortion relative to the �rst-best outcome. Third, the output distortion from both market failures

(asymmetric information and externalities) is

ODBoth � qFBi � qC�i

=1 + �Ci2 (1 + �)

��1 + �Mj

�2 �1 + �Ci

�2 �2 + p�C (1 + �)

�(1 + �)

h8�1 + �Mj

�2+ (�C)2

�1 + �Ci

�2iwhere output qC�i was found above. Furthermore, ODBoth decreases in �C , when

�C � b�C �q16�1 + �Ci

�2+ 32p2 (1 + �)2

�1 + �Mj

�2 � 4 �1 + �Ci �2p (1 + �)

�1 + �Ci

� ;

which indicates that when externalities are small, �C � b�C , the conservation output that theregulator implements approaches the �rst best (smaller output distortion). Otherwise, conservation

output moves farther away from the �rst-best outcome. Finally, the output distortion stemming

from both externalities, ODBoth, is smaller than that arising from asymmetric information alone,

18

ODAsyInfo, if

�C � �C �4p (1 + �)

�1 + �Mj

�2�1 + �Ci

�2 :

As discussed above, when the conservation externality is minor, the presence of externalities amelio-

rates output distortions.20 Otherwise, the conservation externality augments the output distortion

originating from asymmetric information alone. �

4.2 Layers of uncertainty

Previous sections consider that the procurer can either observe the pro�le of pair types, � =��C ; �M

�, in the complete information setting; or that he cannot observe the pro�le of �C nor �M .

We next analyze optimal output choices when the procurer observes landowners�market e¢ ciency

alone, i.e., �M but not �C , or their conservation e¢ ciency alone, i.e., �C but not �M .

Corollary 2. When the procurer only observes �M ( �C), he chooses the conservation output

qC�i that solves

MBi = (1 + �)�VMCi �MECi

�and (11)

MBi = (1 + �)�MCi � V ECi

�(12)

respectively, if �Ci � ~�Ci

��Mi ; �

C�i; �

M�i�. Otherwise, conservation output becomes qC�i = 0.

Hence, when the procurer only observes market e¢ ciency �M , he does not need to consider the

virtual external cost since the procurer can anticipate how landowner j�s observed production cost

will be a¤ected by landowner i�s conservation output. However, the procurer needs to consider the

virtual marginal cost of conservation, as he does not observe landowner i�s conservation e¢ ciency.

A similar argument applies to the case in which the procurer observes conservation e¢ ciency �Cialone in (12), whereby he uses the marginal cost of conservation and the virtual external cost. In

this case, the procurer does not observe landowner j�s production cost, and how he is a¤ected by

an increase in landowner i�s conservation output.

We can now compare expressions that identify optimal output levels in each information context.

Starting from the setting in which the procurer observes both �M and �C , i.e., MBi = (1 +

�)�MCi �MECi

�in expression (5), we see that its associated output is larger than that arising in

contexts in which the procurer only observes one e¢ ciency (either �M , as in expression 11, or �C as

in expression 12), which is in turn larger than in the model in which the procurer observes neither

�M nor �C (see expression 10). In particular, since VMCi lies aboveMCi, then VMCi�MECi >MCi �MECi, i.e., the right-hand side of (11) is larger than that of (5). Since MBi is weaklydecreasing, the output that solves (11) is smaller than that of (5); as depicted in Figure 5. A

similar argument applies to the comparison between expressions (12) and (5). Therefore, as the

20 If p � 1 and �C 2 [0; 1], condition �C � �C holds for all admissible parameter values. Intuitively, this occurswhen the price is not too low and the output from other landowners produces a less-than-proportional increase inlandowner i�s conservation cost.

19

procurer becomes less informed he needs to provide information rents to induce truth-telling in one

or both e¢ ciency parameters, raising the overall cost of the mechanism, and ultimately leading him

to reduce conservation output.

Fig 5. Only �M is observed.

4.3 Optimal payment pro�le

We next study the procurer�s optimal payment.

Proposition 2. The optimal payment for bidder i under incomplete information is

eti(qCi ; C) = ~Ci�qC�i ; qM�

�i ; �Ci ; C

�+hpq̂Mi � ~Ci

�q̂Mi ; q

C��i ; �

Mi ;M

�i(13)

if �Ci � ~�Ci

��Mi ; �

C�i; �

M�i�, and zero otherwise.

The optimal payment, eti(qCi ; C), is thus zero for those who continue the market activity; butfor those participating in the conservation program, it depends on the virtual conservation cost,~Ci�qC�i ; qM�

�i ; �Ci ; C

�, and the virtual contingent market pro�t, pq̂Mi � ~Ci

�q̂Mi ; q

C��i ; �

Mi ;M

�. There-

fore, optimal payments under complete information are evaluated at actual costs, while those under

incomplete information consider virtual costs, where the latter includes actual costs plus informa-

tion rents.

Let us compare the payment in di¤erent contexts. First, without externalities, landowner i re-

ceives ~Ci(qC0i ; �Ci ; C)+

hpbqMi � ~Ci(bqMi ; �Mi ;M)i. Other landowners can still produce positive output

levels in conservation and/or market activities, but in this setting they do not a¤ect landowners

i�s costs. (In the context of Example 1, the fact that landowner i is una¤ected by externalities

entails �C = 0.) Second, when negative conservation externalities exist, his payment becomes

20

~Ci(qC1i ; �Ci ; C) +

hpbqMi � ~Ci(bqMi ; qC1�i ; �Mi ;M)i. If the externality is relatively minor (�C � �C in

Example 3), conservation output is larger with than without externalities, thus producing two op-

posite e¤ects on landowner i�s payment: an increase in its virtual costs (�rst term), and a decrease

in its contingent market pro�t (second term). Hence, the payment is larger when externalities exist

than otherwise if, upon producing a larger conservation output, the landowner sees its cost increase

more signi�cantly than the increase in market costs that the externality generates. (The opposite

argument applies when the landowner enjoys a positive externality, which lowers its virtual conser-

vation costs and decreases its contingent market cost, yielding an ambigous e¤ect on the regulator�s

payment.)

Third, when production externalities are also considered, his payment becomes ~Ci(qC2i ; qM��i ; �

Ci ; C)+h

pbqMi � ~Ci(bqMi ; qC2�i ; �Mi ;M)i. As discussed above, the presence of negative (positive) externalitiesfrom market activities to conservation leads the regulator to decrease (increase) the conservation

output that he assigns to landowner i, which reduces (increases) i�s conservation cost, and ul-

timately its payment. Overall, the presence of a minor negative externality in conservation can

produces saving in the payment that the regulator needs to o¤er to induce landowner�s participa-

tion in the program; a result that is emphasized when externalities exist in production, or in both

activities.

5 Discussion

E¢ ciencies with/without externalities. Our results show that, in the absence of externalities, the

procurer implements a lower output level under incomplete than complete information, as he needs

to induce landowners to truthfully reveal their e¢ ciency. In the presence of negative conservation

externalities, optimal output approaches the �rst best if externalities are minor, but can lie further

away if they are substantial. Hence, when externalities are small, our results suggest that the

procurer would have little incentives to acquire information about �rms�e¢ ciency before designing

the auction.21 However, he would have larger e¢ ciency gains from acquiring information when

externalities from conservation and/or market production are substantial. In addition, our �ndings

indicate that the output reduction due to asymmetric information is emphasized (ameliorated)

when production (conservation) externalities exist, bringing optimal output further away (closer)

to the �rst best. Therefore, the procurer has more incentives to acquire information when he faces

production than conservation externalities.

Ignoring the presence of externalities. Consider a procurer who mistakenly assumes that a

conservation program does not generate any type of externalities on bidders dedicated to market

activities. The optimal conservation output he designs would be ine¢ ciently low (high), if negative

(positive) externalities exist. The opposite results apply when production externalities are ignored.

The only setting in which his policy recommendation could be accurate is that in which both types

21The procurer does not have incentives to acquire information about bidders�e¢ ciency after o¤ering the menu ofcontracts, since he cannot use such information to ameliorate bidders�information rents.

21

of externalities exactly o¤set each other in magnitude. A similar argument applies to settings

where two types of externalities coexist, but regulators only consider one type (e.g., a negative

externality from conservation to market activities). In this case, the regulator would implement an

insu¢ cient (excessive) conservation output when the externality he ignores is negative (positive,

respectively). Hence, the conservation program would be too passive as it does not adequately

promote biodiversity, or too aggressive as it hurts market activities.

Area-based approach. Regulatory authorities need to consider conservation programs in an

environmentally sensitive area as a whole, rather than spatially scattered pieces of farmland in

isolation of each other, due to the pervasive nature of bidirectional externalities. Scoring criteria

that evaluate the desirability of land projects need to consider the immediate neighborhoods, not

only because of spillover e¤ects on the surrounding areas, but also how other landowners�existing

and potential operations would a¤ect the compatibility of the projects. Therefore, it is important

to consider an area-based approach in land conservation for payment for environment services.

Indirect Revelation Mechanism. In an Indirect Revelation Mechanism (IRM), the procurer can

ask landowners to submit a bidimensional bid comprising (1) the conservation output they intend to

produce, and (2) the payment. The IRM would yield di¤erent output-payment pairs than the DRM

if the procurer implemented the output-payment pair submitted by every landowner. However, the

procurer does not have an incentive to implement these pairs due to the existence of externalities,

which he internalizes while the landowners ignore. As Branco (1997) noted, the procurer can

�adjust�the output-payment pairs by proposing a take-it-or-leave-it o¤er to the landowners in the

last stage of the IRM, which still preserves ex-ante incentive compatibility. Therefore, the DRM

and IRM (after allowing for last-stage �adjustments�by the procurer as described above) produce

the same outcome, that is, the same output-payment pair for each landowner i.

Further research. Our model considers that �rms sell at a given price p. However, a more

general setting could allow for a strictly decreasing demand function. In such a context, market

pro�ts could be larger than in our analysis, thus implying that landowners would require a larger

compensation from the procurer to dedicate their land to conservation. An alternative venue could

consider that the regulator simultaneously designs environmental policy (such as emission fees on

market activities) with the procurement auction, and could examine how such a setting reduces

payments for voluntary participation, ultimately saving public funds. In addition, it would be

interesting to analyze settings in which externalities occur within an activity, such as between

two landowners dedicated to conservation. Finally, a di¤erent setting could allow landowners to

dedicate only a portion of their land to conservation, leaving the rest to market activities. In

such a context, an activity from landowner i could increase/decrease the costs of the other activity

developed by the same landowner.

22

6 Appendix

6.1 Appendix 1 - Examples 2 and 3

Example 2: Complete Information. Substituting the optimal contingent market output,

q̂Mj =p(1+�Mj )��CqCi

2 , into MECi�qCi�, yields

MECi�qCi�=p�C

2���C�22

qCi1 + �Mj

:

Hence, expression (5) in the main body of the paper becomes

1

1 + �=

2qCi1 + �Ci

�"p�C

2���C�22

qCi1 + �Mj

#

as long as landowner j stops market production, that is qM��j = 0. After rearranging, we obtain

qC��i from the above �rst order condition.

qC��i =11+� +

p�C

2

21+�Ci

+ (�C)2

2(1+�Mj )

Evaluating this output level at �C = 0, we obtain the optimal conservation output when negative

externalities are absent, qFBi =1+�Ci2(1+�) .

Example 3: Incomplete Information. The virtual contingent production cost is

~Cj�qMj ; q

Ci ; �

Mj ;M

�=qMj

�qMj + �CqCi

��1 + �Mj

�2Therefore, the virtual contingent marginal production cost becomes

V ECi�qMj�=

�CqMj�1 + �Mj

�2Substituting the optimal virtual contingent output, q̂Mj =

p(1+�Mj )2��CqCi2 , into the above expression,

V ECi�q̂Ci�=p�C

2���C�22

qCi�1 + �Mj

�2 :Therefore, expression (10) in the main body of the paper becomes

1

1 + �=

4qCi�1 + �Ci

�2 �"p�C

2���C�22

qCi�1 + �Mj

�2#

23

as long as landowner j stops market production, that is qM�j = 0. After rearranging, we obtain qC�i

from the above �rst order condition.

qC�i =11+� +

p�C

2

4

(1+�Ci )2 +

(�C)2

2(1+�Mj )2

=

�1 + �Mj

�2 �1 + �Ci

�2 �2 + p�C (1 + �)

�(1 + �)

h8�1 + �Mj

�2+ (�C)2

�1 + �Ci

�2iEvaluating this output level at �C = 0, we obtain the optimal conservation output when negative

externalities are absent, qC�0

i =(1+�Ci )

2

4(1+�) .

6.2 Proof of Lemma 1

Di¤erentiating (1b) with respect to qMi , landowner i�s optimal market output, qM�i , satis�es

uiqMi

�qM�i ; �Mi ;M

�= p� Ci

qMi

�qM�i ; qC�i; �

Mi ;M

�= 0 (A1)

such that landowner i equates the marginal cost of production with the market price, that is,

p = CiqMi

�qM�i ; qC�i; �

Mi ;M

�. While we allow externalities from conservation to production, we do

not allow externalities among landowners who are still dedicated to market activities.

Di¤erentiating (A1) with respect to �Mi , and using the Implicit Function Theorem,

@qM�i

@�Mi= �

CiqMi �

Mi(qM�i ; qC�i; �

Mi ;M)

CiqMi q

Mi(qM�i ; qC�i; �

Mi ;M)

� 0

Totally di¤erentiating (A1) with respect to �Mi , and using the Envelope Theorem,

ui�Mi

�qM�i ; �Mi ;M

�= ui

qMi

�qM�i ; �Mi ;M

�| {z }=0 by Envelope Theorem

@qM�i

@�Mi| {z }�0

�Ci�Mi

�qMi ; q

C�i; �

Mi ;M

�| {z }�0 by Assumption 1

� 0

6.3 Proof of Lemma 2

When the procurer observes �Ci and �Mi , he solves the following maximization program.

maxq;t

W (q; t)

=maxqCi

NXi=1

�i�V�qCi�� (1 + �) ti

�qCi ; C

��by (3)

=maxqCi

NXi=1

�i�V�qCi�� (1 + �)

�ui�qCi ; �

Ci ; C

�+ Ci

�qCi ; q

M�i; �

Ci ; C

��by (1a)

The Individual Rationality constraint must be binding, otherwise the procurer could reduce the

24

residual utility and still induce the participation of landowner i. We thus obtain

ui�qCi ; �

Ci ; C

�= ui

�qMi ; �

Mi ;M

�= pqMi � Ci

�qMi ; q

C�i; �

Mi ;M

�by (1b)

such that we can rewrite the procurer�s maximization program as follows:

maxqCi

NXi=1

�i�V�qCi�� (1 + �)

�Ci�qCi ; q

M�i; �

Ci ; C

�+ pqMi � Ci

�qMi ; q

C�i; �

Mi ;M

��Di¤erentiating with respect to qCi , the optimal conservation output, q

C��i , we obtain

VqCi(qC��i ) = (1 + �)

hCiqCi(qC��i ; qM��

�i ; �Ci ; C)

+Xj 6=i

�j�i

�p� Cj

qMj(q̂Mj ; q

C���j ; �

Mj ;M)

�@qMj

@qCi� Cj

qCi(q̂Mj ; q

C���j ; �

Mj ;M)

!35where q̂Mj denotes landowner j�s contingent market output. Using p = Cj

qMj(q̂Mj ; q

C���j ; �

Mj ;M) from

Lemma 1, we �nd

VqCi(qC��i )| {z }

MBi(C)

= (1 + �)

266664CiqCi (qC��i ; qM���i ; �Ci ; C)| {z }

MCi(C)

�Xj 6=i

�j�iCjqCi(q̂Mj ; q

C���j ; �

Mj ;M)| {z }

MECi

377775And from the condensed maximization program above, we can infer that procurer�s payment func-

tion to landowner i, ti�qCi ; C

�, under complete information is

ti�qCi ; C

�= Ci

�qCi ; q

M�i; �

Ci ; C

�+�pq̂Mi � Ci

�q̂Mi ; q

C�i; �

Mi ;M

��6.4 Proof of Proposition 1

When the procurer observes neither �Ci nor �Mi , he solves the following maximization program.

maxq;t

E� [W (q; t)]

=maxqCi

NXi=1

�iE��V�qCi�� (1 + �) ti

�qCi ; C

��by (3)

=maxqCi

NXi=1

�iE��V�qCi�� (1 + �)

�ui�qCi ; �

Ci ; C

�+ Ci

�qCi ; q

M�i; �

Ci ; C

��by (1a)

The Individual Rationality constraint (9) must be binding, otherwise the procurer could reduce

25

the residual utility and still induce the participation of landowner i. We thus obtain

ui(qCi; �C ; C) = ui(qMi ; �

M;M)

where qCi� qCi

��C�and qMi � qMi

��M�. Output qK

iis only a function of �K for all K, since

�Ci and �Mi are independently distributed. (Payments, however, depend on both �Ci and �

Mi , as

shown in Proposition 2 below.) Applying Myerson�s Characterization Theorem (Myerson, 1981)

to the Bayesian Incentive Compatibility constraints (7) and (8) and substituting into the above

expression, yields

ui(qCi ; �Ci ; C) =pq

Mi � EqC�i

�Ci�qMi ; q

C�i; �

Mi ;M

���Z �

M

�Mi

EqC�i

hCi�Mi(qMi ; q

C�i; ��

M

i ;M)id��M

i

�Z �Ci

�CEqM�i

hCi�Ci(qCi ; q

M�i; ��

C

i ; C)id��C

i

such that by applying the Law of Iterated Expectation because the procurer takes expectation

directly of how landowners take expectation of the conservation-production e¢ ciency parameters

of each other, we can rewrite the procurer�s maximization program as follows:

maxqCi

NXi=1

�iE�

8>>>><>>>>:V�qCi�� (1 + �)

266664Ci�qCi ; q

M�i; �

Ci ; C

��Z �Ci

�CCi�Ci

�qCi ; q

M�i; ��

C

i ; C�d��C

i

+pqMi � Ci�qMi ; q

C�i; �

Mi ;M

��Z �

M

�Mi

Ci�Mi(qMi ; q

C�i; ��

M

i ;M)d��M

i

3777759>>>>=>>>>;

Using integration by parts, the procurer�s payo¤ function becomes

maxqCi

NXi=1

�iE�

nV (qCi )� (1 + �)

h~Ci(qCi ; q

M�i; �

Ci ; C) + pq

Mi � ~Ci(qMi ; q

C�i; �

Mi ;M)

io(A2)

Di¤erentiating (A2) with respect to qCi , the optimal conservation output, qC�i , satis�es

VqCi(qC�i )| {z }

MBi(C)

= (1 + �)

266664 ~CiqCi (qC�i ; qM��i ; �

Ci ; C)| {z }

VMCi(C)

�Xj 6=i

�j�i~CjqCi(q̂Mj ; q

C��j ; �

Mj ;M)| {z }

V ECi

377775 (A3)

26

In addition,

WqCi qCi(q�; t�) =VqCi qCi

(qC�i )� (1 + �)�CiqCi q

Ci(qC�i ; qM�

�i ; �Ci ; C)�

1� F (�Ci ; C)f(�Ci ; C)

CiqCi q

Ci �

Ci(qC�i ; qM�

�i ; �Ci ; C)

�+ (1 + �)

Xj 6=i

�j�i

"CjqCi q

Ci(q̂Mj ; q

C��j ; �

Mj ;M) +

F (�Mj ;M)

f(�Mj ;M)CjqCi q

Ci �

Mj(q̂Mj ; q

C��j ; �

Mj ;M)

#

By Assumption 1, the second term in the �rst bracket is negative such that the �rst bracket

is positive. Then, by Assumption 3, the second bracket is positive if the (second-order) direct

external e¤ect that landowner i�s negative externality dampens the curvature of landowner j�s

production cost curve, CjqCi q

Ci� 0, more than o¤sets the (third-order) indirect attenuation e¤ect

that landowner j�s production e¢ ciency weakens the positive external e¤ect from landowner i,F (�Mj ;M)

f(�Mj ;M)CjqCi q

Ci �

Mj� 0.

Di¤erentiating (A3) with respect to �Ci ,

@qC�i@�Ci

=(1 + �)hWqCi q

Ci(q�; t�)

i�1��1� @

@�Ci

�1� F (�Ci ; C)f(�Ci ; C)

��CiqCi �

Ci(qC�i ; qM�

�i ; �Ci ; C)� CiqCi �Ci �Ci (q

C�i ; qM�

�i ; �Ci ; C)

�

As the cumulative density function F (�Ci ; C) weakly increases in �Ci , the inverse hazard rate

1�F (�Ci ;C)f(�Ci ;C)

weakly decreases in �Ci such thath1� @

@�Ci

�1�F (�Ci ;C)f(�Ci ;C)

�i> 0. In addition, by Assumption

1, we can determine that: (1) CiqCi �

Ci(qC�i ; qM�

�i ; �Ci ; C) � 0, i.e., the single crossing condition; and

(2) CiqCi �

Ci �

Ci(qC�i ; qM�

�i ; �Ci ; C) = MCi

�Ci �Ci(qC�i ; qM�

�i ; �Ci ; C) � 0. Finally, if the regulator�s bene�t

function is strictly concave, WqCi qCi(q�; t�) < 0, optimal conservation output qC�i is monotonically

increasing in conservation e¢ ciency �Ci .

We next derive the contribution function of landowner i to the regulator�s payo¤, denoting Gito be the gain from producing conservation output, qCi . First, conducting an anti-derivative of (A3)

with respect to qCi ,

Gi(qi) =Gi(qC

i) +

Z qCi

qCi

VqCi(�qCi )d�q

Ci

� (1 + �)Z qCi

qCi

0@ ~CiqCi(�qCi ; q

M�i; �

Ci ; C)�

Xj 6=i

�j�i~CjqCi(q̂Mj ; (�q

Ci ; q

Ck ); �

Mj ;M)

1A d�qCi=Gi(qC

i) + V (qCi )� V (qCi )� (1 + �)

h~Ci(qCi ; q

M�i; �

Ci ; C)� ~Ci(qC

i; qM�i; �

C ; C)i

+ (1 + �)Xj 6=i

�j�i

h~Cj(q̂Mj ; (q

Ci ; q

Ck ); �

Mj ;M)� ~Cj(q̂M

00j ; (qC

i; qCk ); �

Mj ;M)

i

where qM00

j represents the contingent market output of landowner j 6= i under the externality

27

imposed by landowner i being the least e¢ cient in conservation, alongside other landowners k 6=fi; jg. Second, we evaluate the gain generated by type �C landowner i,

Gi(qCi) =V (qC

i)� (1 + �)

h~Ci(qC

i; qM�i; �

C ; C) + pq̂Mi � ~Ci(q̂Mi ; qC�i; �

Mi ;M)

i+ (1 + �)

Xj 6=i

�j�i

h~Cj(q̂M

00j ; (qC

i; qCk ); �

Mj ;M)� ~Cj(q̂M 0

j ; (0; qC0k ); �Mj ;M)

i

where qK0j is the output of landowner j 6= i in activity K without landowner i�s participation.

Third, combining the above results, the gain of type �Ci landowner i is

Gi(qi) =V (qCi )� (1 + �)

h~Ci(qCi ; q

M�i; �

C ; C) + pq̂Mi � ~Ci(q̂Mi ; qC�i; �

Mi ;M)

i+ (1 + �)

Xj 6=i

�j�i

h~Cj(q̂Mj ; (q

Ci ; q

Ck ); �

Mj ;M)� ~Cj(q̂M 0

j ; (0; qC0k ); �Mj ;M)

i

Fourth, let Li represent the loss from stopping the production of the market good qMi , which

implies the removal of production externality on other landowners, such that

Li(qi) � (1 + �)Xj 6=i

�j�i

h~Cj(qC0j ; (q

Mi ; q

M 0k ); �Cj ; C)� ~Cj(qCj ; (0; q

Mk ); �

Cj ; C)

i

Fifth, his contribution to the regulator�s payo¤ is found by taking the loss Li o¤ the gain Gi,

~W i(q) =Gi(qi) + Li(qi)

=V (qCi )� (1 + �)h~Ci(qCi ; q

M�i; �

Ci ; C) + pq̂

Mi � ~Ci(q̂Mi ; q

C�i; �

Mi ;M)

i+ (1 + �)

Xj 6=i

�j�i

h~Cj(q̂Mj ; (q

Ci ; q

Ck ); �

Mj ;M)� ~Cj(q̂M 0

j ; (0; qC0k ); �Mj ;M)

i+ (1 + �)

Xj 6=i

�j�i

h~Cj(qC0j ; (q̂

Mi ; q

M 0k ); �Cj ; C)� ~Cj(qCj ; (0; q

Mk ); �

Cj ; C)

i

where ~W (q) � 0 for all �Ci � ~�Ci

��Mi ; �

C�i; �

M�i�. This function considers landowner i�s bene�t in

(3) and also his weighted sum of externalities on other landowners, where qK0j represents the output

in activity K of landowner j without i�s participation (This contribution function is analogous

to the score function in Che (1993). As shown in the proof of Proposition 1, this function is

monotonic in �Ci , allowing for the existence of cuto¤ ~�Ci .) The bracket in the second line represents

landowner i�s marginal external e¤ect on others� virtual contingent production costs, which is

positive (negative) if his total weighted externalities are negative (positive) because the procurer

needs to compensate them for a lower (higher) forgone market pro�t. Similarly, the bracket in the

third line represents the e¤ect of landowner i�s market production on others�conservation costs,

which is positive (negative) if his externalities are negative (positive). Therefore, landowner i�s

market activity would entail a larger cost for participating landowners and the procurer, while his

28

participation in the program decreases those costs as his negative externality is absent, ultimately

yielding a positive welfare contribution.

Finally, we verify that ~W i(q) is monotonically increasing in �Ci ,

~W i�Ci(q) =

8<:VqCi (qCi )� (1 + �)24 ~Ci

qCi(qCi ; q

M�i; �

Ci ; C)�

Xj 6=i

�j�i~CjqCi(q̂Mj ; q

C�j ; �

Mj ;M)

359=; @qCi@�Ci

� (1 + �)��1� @

@�Ci

�1� F (�i; C)f(�Ci ; C)

��Ci�Ci(qCi ; q

M�i; �

Ci ; C)�

1� F (�Ci ; C)f(�Ci ; C)

Ci�Ci �

Ci(qCi ; q

M�i; �

Ci ; C)

�which, by (A3), the �rst brace is zero. Then, by Assumption 1, the whole term under the second

brace is negative such that ~W i�Ci(q) � 0 and ~W i(q) is monotonically increasing in �Ci . �

6.5 Proof of Corollary 2

When the procurer observes the pro�le of �M , but not that of �C , he only treats the observed

pro�le �M as a parameter. Following an approach similar to Myerson (1981), it is straightforward

to obtain expression (11). An analogous argument applies in the case that the procurer observes

the pro�le of �C , but not that of �M , obtaining expression (12). �

6.6 Proof of Proposition 2

Equating equation (4) with (A2), the procurer�s payment function to landowner i is

eti(qCi ; C) = ~Ci(qCi ; qM�i; �

Ci ; C) +

hpq̂Mi � ~Ci(q̂Mi ; q

C�i; �

Mi ;M)

iwhich is di¤erent from the gain function, Gi(qi), discussed in Proposition 1 and landowner i does

not compensate (or is not compensated) for the positive (negative) conservation externality on

others since this is already included in the payment function to other landowners j 6= i. �

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