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Incentives for wetland creation
ARTICLE IN PRESS
Journal of Environmental Economics and Management 50 (2005) 598–616 www.elsevier.com/locate/jeem
Incentives for wetland creation Anne-Sophie Cre´pin The Beijer International Institute of Ecological Economics, The Royal Swedish Academy of Sciences, 10405 Stockholm, Sweden Received 9 January 2002 Available online 31 May 2005
Abstract When information about soil quality is complete, wetland creation with a take-it-or-leave-it contract, which specifies wetland size and transfer, yields higher social benefits than if a uniform contract, which offers a payment proportional to the wetland size, had been used. This result points to a paradox because uniform contracts have been used a lot in practice. This article concentrates on the presence of asymmetric information about soil quality as a possible explanation for this paradox. It shows that the choice of instrument for wetland creation has welfare implications. Different contracts typically yield quite different social welfare surpluses and distribution between interest groups. It is not obvious, which of four contracts studied dominates when a farm characteristic affecting costs is unknown to the social planner. The probability distribution of the characteristic, the size of the excess burden, the elasticity of costs and benefits to wetland size and the cost of acquiring missing information influence the outcome. r 2005 Elsevier Inc. All rights reserved. Keywords: Asymmetric information; Voluntary incentives; Wetlands
1. Introduction Several countries and the European Union (EU) use subsidy systems to support wetland1 creation on farmland. These incentives give opportunities to enhance environmental quality while Fax:+46 8 15 24 64.
E-mail address: [email protected]. Wetlands are land areas with water near the surface during large parts of the year. They enhance biodiversity and produce ecosystem services [3,8]. 1
0095-0696/$ - see front matter r 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2005.01.005
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obtaining a desired reduction of traditional agricultural production. The authorities in the United States (US) and in EU countries have used many different kinds of incentives to encourage wetland creation on arable land.2 Why so many different incentives? This article discusses reasons that support the choice of wetland creation incentives that are in practice, and focuses on two incentives rather similar to the most frequently used. The studied incentives are called uniform and take-it-or-leave-it (TOL) contracts. The uniform contract, which is similar to incentives proposed in England and Sweden, offers a payment that is proportional to the surface of wetland created and allows farmers to choose the wetland size. In the TOL contract, social planners set wetland size and transfer. This contract looks like incentives proposed in the Wetland Reserve Program of the Farm Bill Act 2002 and in the Ka¨vlinge River Area in Sweden [22]. One can show that a TOL contract would produce larger social benefits than a uniform contract if all information necessary to calculations was available. So why have uniform contracts been used so much in practice? This article focuses on asymmetric information as one possible explanation among many others. Suppose farmers have better knowledge than the planner about farm-specific characteristics that affect the cost of wetland creation, such as soil quality. If farmers can choose wetland size, they will do that according to all their knowledge. This is more than the planner can ever do. So asymmetric information may imply that a uniform contract could yield higher social welfare than a TOL contract. Nevertheless, this is not completely obvious because farmers have objectives that differ from the social planners’ objectives when choosing the wetland size. When there is asymmetric information, other contracts than uniform and pure TOL contracts are relevant. In practice, social planners may use some kinds of information gathering procedures—for example land inspection—together with TOL contracts. This supports the asymmetric information hypothesis. Most of the relevant literature would probably advocate use of screening mechanisms that consist of a selection of contracts, conveniently chosen, so that farmers would pick the contract that corresponds to the true characteristics of the land. In this paper, a general contract of that kind is designed to maximize social welfare. Here, the relation between a social planner and a farmer is a typical principal–agent relationship with adverse selection. Green and Laffont [9], Dasgupta [6], and Baron and Myerson [2] provided pioneering work on optimal incentives in such situation. Bourgeon et al. [5], Bourgeon and Chambers [4], Hueth [13] and Jayet [14] applied the tools developed by Baron and Myerson and others in the context of land use incentives and policies to reduce overproduction in agriculture. Gren [10] discussed efficient contracts for converting arable land into pollutants sinks.3 Smith [21], Wu and Babcock [26] and Segerson and Miceli [20] gave other relevant contributions to the field. General contracts are hardly used but they are studied here because they have been designed as optimal contracts so they could give valuable information on how existing programs can be improved and help comparisons between contracts. The paper shows that contract choice can create welfare gains and that this choice depends on the distribution of the unknown characteristic, on the elasticity of costs and benefits to wetland 2
See for examples the Farm Bill Act 2002, the England rural Development Programme, Lindahl [15] and documentation from the Swedish department of agriculture (available in Swedish on the Web: http://www.sjv.se) 3 A pollutant sink is here a wetland aiming at reducing nutrient leakage from agriculture.
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size changes, on the interest groups’ bargaining power, on excess burden, and on information acquisition costs. Similar subsidy systems have also been used, for example, to conserve meadows or pasture lands. This suggests that the results obtained could be generalized even for other landuse incentives: Wetland creation can be reinterpreted as any amenity production that the social planner wants to encourage on agricultural land. This paper is organized like this: Section 2 presents the model. Section 3 presents derived characteristics of information gathering, and uniform, TOL and general contracts. Section 4 compares the different contracts. Section 5 discusses the results.
2. Model A wetland creation program is a situation in which a social planner and a farmer trade environmental benefits4 from wetland creation on the farmer’s land. In exchange the farmer receives a transfer (t) per unit of wetland created. Consider y 2 ½0; y, a farm characteristic that represents soil quality affecting the production of goods, other than wetlands. Let q 2 Rþ denote the wetland size. Assume that wetland creation programs do not affect other sectors in the economy than those represented here. Wetland creation costs consist of fix cost, construction cost and the alternative cost of land.5 Assume that these cost components together depend only on wetland size and on soil quality. The cost function is denoted cðq; yÞ.6 Typically the authorities do not own the land so the social welfare surplus W ðq; t; yÞ from wetland creation of size q on farm y is the sum of the environmental surplus (ES), the farmer’s profit (FS) and taxpayers’ surplus (TS), respectively. If the authorities instead created a wetland on land that they owned the potential social surplus Oðq; yÞ would instead consist of the environmental surplus less the wetland creation cost corrected for a positive excess burden l. The environmental surplus is the net environmental benefit7 bðqÞ, which depends on wetland size. The taxpayers’ surplus is the transfer that they must pay tq, corrected for the excess burden l. This gives expressions for W and O. W ðq; t; yÞ bðqÞ þ FS ð1 þ lÞtq, Oðq; yÞ bðqÞ ð1 þ lÞcðq; yÞ. The key assumptions (H1)–(H5) help clarify the results. They are justified if the alternative cost of the land is the main cost component. q2 cðq; yÞ 40, qq2 4
(H1)
These benefits are mainly recreation, increased biodiversity and water-cleaning (SOU 1994:82 and Mitsch and Gosselink [17]). So¨derqvist [23] found some evidence of private benefits for farmers but they should not be included here. 5 For a more detailed analysis of costs for wetland creation, see [22]. 6 If there is a fix cost we assume cð0; yÞX0 and cðq; yÞXcð0; yÞ for all positive wetland sizes q. 7 This is the environmental benefit less the environmental cost.
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qcðq; yÞ 40, qq
(H2)
qcðq; yÞ 40, qy
(H3)
q2 cðq; yÞ 40, qyqq
(H4)
d 2 bðqÞ p0. dq2
(H5)
The marginal cost is likely to increase if the wetland size increases because land available for alternative use becomes rare (H1). Creating a larger wetland respectively using land of higher quality for wetland creation yield a higher alternative cost ((H2) and (H3), respectively). Assumption (H4) reflects the usual Spence–Mirrlees condition and means that the same increase in wetland size yields a higher increase in costs on a high-quality plot (high y) compared to a lowquality plot. Finally, the environmental surplus is concave (H5). 2.1. Contracts A wetland creation program results in a contract ðt; qÞ. In a uniform contract, the social planner decides the transfer; the farmer can choose to select a wetland size q and receive the amount tq or reject the contract. In a TOL contract, the social planner decides transfer and wetland size; the farmer chooses to accept the contract or not. The farmer selects a profit-maximizing wetland size if given the opportunity and rejects any contract that yields negative profits. The social planner knows this strategy and can use backward induction to determine, which contract to propose. The farmer’s profit from choosing contract ðt; qÞ is pðq; t; yÞ ¼ tq cðq; yÞ. Wetlands’ effects on the farmer’s other traditional agricultural production enter only through the alternative cost of the land included in cðq; yÞ.8 Let tðq; yÞ denote the minimum transfer that the farmer requires to accept a contract. Let q ðt; yÞ (X0) denote the profit-maximizing wetland size for any transfer t and land quality y. Given that (H1) holds and if tXtðq ; yÞ, the first-order conditions for profit maximization: t qcðq;yÞ qq ¼ 0 gives the optimal wetland size. Otherwise a wetland size equal to zero is profit maximizing. The welfare surplus from wetland creation is W ðq; t; yÞ ¼ Oðq; yÞ lpðq; t; yÞ. This corresponds to the potential social welfare surplus less the excess burden of the farmer’s profit. If there are several farmers, the welfare surplus is the sum of all farmers’ surpluses. If the
8
Accounting for private benefits from wetland creation (e.g. irrigation) does not influence the results: c could be the net costs. So¨derqvist [23] discusses private benefits from wetland creation for farmers.
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Table 1 Contract properties with complete information Uniform contract ( u )
TOL contract ( tol )
t¼
qcðq u ;yÞ qq
tðq tol ; yÞ ¼
q solves
qOðq u ;yÞ qq
¼l
W¼
Oðq u ; yÞ
FS ¼
qcðq u ;yÞ qq bðq u Þ
ES ¼ TS ¼
q2 cðq u ;yÞ
q 2 qq u qcðqu ;yÞ
l qq qu
cðq u ; yÞ
q u cðq u ; yÞ
ð1 þ lÞ
qcðq u ;yÞ qq
q u
qOðq tol ;yÞ ¼ qq
Oðqtol ; yÞ
cðq tol ;yÞ q tol
0
0 bðq tol Þ ð1 þ lÞcðq tol ; yÞ
farmer rejects the contract, W ¼ ES ¼ FS ¼ TS ¼ 0. The planner’s problems are:9 max
fW ðq; t; yÞ; 0g
s.t.
t ¼ tðq; yÞ;
max
fW ðq; t; yÞ; 0g
s.t.
q ¼ q ðt; yÞ:
q;t
t
ðTake-it-or-leave-itÞ;
ðUniformÞ;
The constraints can be substituted in respective objective functions and when (H1) and (H5) hold, the first-order conditions for maxima are necessary and sufficient. Table 1 summarizes the results derived from these conditions.10 Indices u and tol denote the optimal measures for respective contract. 2.2. Uniform contracts versus take-it-or-leave-it contracts Excess burden (l) is essential for contract comparison. With no excess burden (l ¼ 0) wetland sizes maximize the potential welfare surplus (qO qq ) in both contracts so they are the same. Environmental surpluses are the same as well. Allowing the farmer to choose wetland size and qcðq ;yÞ make a non-negative profit ( qqu q u cðq u ; yÞ) does not incur a social cost so the social welfare surpluses are identical. Transfers differ so the farmer prefers a uniform contract that yields at least zero profit compared to a TOL contract that always yields zero profit. The taxpayers would rather qcðq Þ finance a TOL contract because q tol ¼ q u so cðq tol ; yÞX qqu q u otherwise the farmer would have rejected the uniform contract. qcðq ;yÞ Consider now a positive excess burden l40. A positive farmer profit ( qqu q u cðq u ; yÞ40) would then induce a social cost. Fig. 1 represents society’s marginal benefits and marginal costs of
9
The constraint in the take-it-or-leave-it program must hold with equality because taxes are costly so a larger transfer would induce larger social costs. 10 See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm
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2 (1 + λ ) ∂c(q, θ ) + λ ∂ c (q2, θ ) q
Marginal costs and benefits
∂q
∂q
b
(1 + λ )∂ c(q, θ ) q
c d
db(q ) dq
e a
q u*
* qtol
q
Fig. 1. Contract comparison when information is complete.
wetland creation as functions of wetland size to illustrate this.11 The marginal benefit function (db dq) is 2the same in both contracts. The difference between the marginal cost functions is the term q cðq ;yÞ l qq2u q u , which is positive (H1). So q u oq tol and the environmental benefit is higher in the TOL contract: ðabdq tol Þ4ðabcq u Þ. The social welfare is higher in the TOL contract: ðebdÞ4ðebcÞ— because the planner has two instruments available in the TOL contract (t and q) but only one in the uniform contract (t). Using two instruments instead of one allows the planner to control that the farmer does not make more profit than necessary and hence lowers social costs. The farmer would prefer the uniform contract because it supplies her with a surplus at least as large as in the TOL contract. It is difficult to tell which contract the taxpayers would prefer. On one hand, they must give a higher transfer in a uniform contract; on the other hand, they finance a smaller wetland. But at least for small excess burden, continuity implies that taxpayers prefer a TOL contract.
3. Contracts under asymmetric information From now on, suppose instead that the farmer knows the true soil quality y, but that the social planner knows only the distribution of y. Let f ðyÞ be the density function with cumulative density function F ðyÞ.12 The social planner cannot implement the optimal TOL contract unless the farmer reveals the true y. Unfortunately, the farmer would have incentives to lie about y because, due to assumption (H3), stating a higher soil quality than the true one would fool the authorities to 11
The graphs represent linear functions but the results would not be affected if they were not, as long as (H1), (H2) and (H5) hold. 12 If instead the social planner proposes wetland creation programs to a population of farmers who are only differentiated by their soil quality, the soil quality among farms is then distributed according to f.
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believe that costs are higher than they really are. This would entitle to a larger transfer without affecting the true cost and hence yield a higher profit. Soil quality being the farmer’s private information, the social planner knows only an expected value of the social welfare function to maximize. The planner can choose to acquire the missing information or provide a contract based on available information. Both solutions are associated with welfare costs so to compare contracts, the cost of information acquisition must be set in relation with the cost of providing suboptimal contracts. In addition to that, if the social planner chooses to act upon available information, she may set the transfer so low that if the farmer has a high y, accepting the contract is not profitable. Given assumption (H3), this defines a virtual threshold farm: if the farm has a higher y than the threshold, the farmer rejects the contract. The rest of this section presents contracts characteristics when there is asymmetric information. 3.1. Information acquisition Suppose the social planner can acquire missing information directly at some cost I40, for example, by visiting the farm. After gathering information, the social planner faces the same problems as in the complete information case and thus selects the optimal TOL contract—see Section 2. The expected surpluses are, respectively, Z y ¼ Oðq tol ðyÞ; yÞf ðyÞ dy ð1 þ lÞI, W a
ig 0
FSa
ig ¼ 0, Z y ESa
¼ bðq tol ðyÞÞf ðyÞ dy, ig 0
TSa
ig ¼ ð1 þ lÞ
Z
y 0
! cðq tol ðyÞ; yÞf ðyÞ dy þ I .
The expected social welfare surplus consists here of the expected maximum potential welfare surplus obtained with a TOL contract with complete information, less the information cost. Information acquisition removes informational asymmetry and gives opportunity to reduce the farmer’s profit to a minimum, hence FSa
ig ¼ 0. The expected environmental surplus is the environmental surplus that the planner would expectRfrom a wetland of size q tol . The expected y taxpayers’ surplus is the sum of the expected transfer 0 cðq tol ; yÞf ðyÞ dy and the cost of acquiring information I, both with excess burden. In practice, the Ka¨vlinge river program [23] and the restoration cost-share agreements proposed in the Farm Bill act 2002 use similar incentives. In both programs, the authorities visit all program participation candidates. 3.2. Uniform contracts Let u characterize the virtual threshold farm in the uniform contract. The planner knows that wetland creation on a virtual threshold farm would yield zero profits and that the farmer chooses a profit-maximizing wetland size. The planner must determine the transfer ta
u that would
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maximize social welfare given these two constraints. This results in the problem Z u a
a
max ðOðqa
u ðyÞ; yÞ lðtqu ðyÞ cðqu ðyÞ; yÞÞÞf ðyÞ dy, t
s.t.
0 a a
tu qu ðuÞ
cðqa
u ðuÞ; uÞ ¼ 0, a
qcðqu ðyÞ; yÞ ta
¼ 0. u qq
Proposition 1. A necessary condition for a maximum in expression (1) is given by Eq. (4). Z u a
du qOðqa
a
u ðyÞ; yÞ dqu ðyÞ ðuÞ; uÞf ðuÞ ðyÞ f ðyÞ dy ¼ 0. þ lq Oðqa
u u dt qq dt 0
605
ð1Þ ð2Þ ð3Þ
(4)
Proof. Differentiate (1) with regard to t and use (2) and (3) to eliminate superfluous terms.13 & Condition (4) states that the transfer is optimal provided that the marginal effects of a change in transfer on the social welfare sum to zero. The first term represents the expected value of the marginal welfare change due to a change in the threshold plot. The second term represents the expected value of the marginal welfare change due to a change in wetland size. If the usual concavity conditions are satisfied,14 Eqs. (2)–(4) are sufficient to characterize optimal transfer, threshold plot and wetland size in a uniform contract. The expected surpluses are, respectively, Z u a
a
a
¼ ðOðqa
W a
u u ðyÞ; yÞ lðtðqu ðuÞ; uÞqu ðyÞ cðqu ðyÞ; yÞÞÞf ðyÞ dy, Z0 u a
a
FSa
ðtðqa
u ðuÞ; uÞqu ðyÞ cðqu ðyÞ; yÞÞf ðyÞ dy, u ¼ 0 Z u a
bðqa
ESu ¼ u ðyÞÞf ðyÞ dy, 0 Z u a
TSa
¼ ð1 þ lÞtðq ðuÞ; uÞ qa
u u ðyÞf ðyÞ dy. u 0
The expected social welfare surplus consists of the expected potential welfare surplus less the excess burden of the farmer’s profit. The expected farmer’s surplus equals the expected value of transfer less wetland creation cost. The environmental surplus is the expected environmental surplus that a wetland of size qa
u ðyÞ would yield. The taxpayers’ surplus is equal to the transfer with excess burden, times the expected size of the wetland created. All surpluses are equal to zero if y is higher than the threshold plot. 3.3. Take-it-or-leave-it contracts Let vpy characterize the threshold farm in a TOL program. The social planner must find out a
transfer (ta
tol ) and wetland size (qtol ) that maximize social welfare given that the farmer only 13 14
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm This is not obvious and should be verified in each specific case.
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accepts contracts that yield non-negative profits Z v a
a a
max ðOðqa
tol ; yÞ þ lcðqtol ; yÞ lttol qtol Þf ðyÞ dy, a a
qtol ;ttol
s.t.
0 a a
ttol qtol
cðqa
tol ; vÞ ¼ 0.
ð5Þ ð6Þ
Proposition 2. If qa
tol 40, necessary conditions for a maximum in expression (5) are given by (7) and (8)
Z v qOðqa
qcðqa
dv a
a
tol ; yÞ tol ; yÞ Oðqtol ; vÞf ðvÞ l ttol f ðyÞ dy ¼ 0, ð7Þ þ qq qq dq 0 dv ð8Þ lqa
Oðqa
tol ; vÞf ðvÞ tol F ðvÞ ¼ 0. dt Proof. Differentiate with regard to q and t and use (6) to eliminate terms.15 & If the usual concavity conditions are satisfied,16 these conditions, together with (6), characterize an optimal TOL program under asymmetric information. Condition (7) states that wetland size is optimal if the marginal effects of a change in wetland size on the social welfare sum to zero. The first term represents the effect of the threshold plot change. The second term represents the direct effect of a change in wetland size. Condition (8) states that the transfer is optimal if expected potential welfare gains from transforming the threshold plot equal expected excess burden from creating a wetland of the given size. The expected surpluses are, respectively, Z v a
a
a
ðOðqa
W tol ¼ tol ; yÞ lðcðqtol ; vÞ cðqtol ; yÞÞÞf ðyÞ dy, Z0 v a
FSa
ðcðqa
tol ; vÞ cðqtol ; yÞÞf ðyÞ dy, tol ¼ 0 Z v ESa
¼ bðqa
tol Þf ðyÞ dy, tol 0 Z v a
TStol ¼ ð1 þ lÞ cðqa
tol ; vÞf ðyÞ dy. 0
The expected social welfare surplus is the expected potential welfare surplus less the excess burden from the farmer’s profit. The expected farmer’s surplus is the expected value of the difference between the transfer and the farmer’s true cost for wetland creation. The environmental surplus is the expected environmental surplus that a wetland of size qa
tol would yield. The taxpayers’ surplus is the expected transfer with excess burden. All surpluses equal zero if y is higher than the threshold characteristic. 3.4. General contracts The so-called revelation principle17 states that if the desired allocation can be implemented through some mechanism, then it can also be implemented through a direct truthful mechanism, where agents reveal their private information. Here, such a mechanism would consist of a menu of 15
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm This is not obvious and should be verified in each specific case. 17 Dasgupta et al. [7], and Myerson [18] were the first to discuss it. 16
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contracts, that specify wetland size and compensation level. The menu of contracts must fulfill incentive compatibility and individual rationality constraints. The results in this section are a standard application of incentives theory with adverse selection.18 The optimal transfer and the social planner’s objective can be written as (9) and (10). Z 1 y qcðq; iÞ cðq; yÞ ðq; yÞ ¼ ta
di þ , ð9Þ g q y qy q Z y F ðyÞ qcðq; yÞ max W ðq; yÞ ¼ Oðq; yÞ l f ðyÞ dy. ð10Þ q f ðyÞ qy 0 3
cðq;yÞ Proposition 3. If qqyqq 2 X0 and given assumptions (H1)–(H5), a necessary and sufficient condition for a maximum in expression (10) is given by (11)
qOðq; yÞ F ðyÞ q2 cðq; yÞ ¼l . qq f ðyÞ qyqq
(11)
Proof. Follows directly from differentiation of (10). & Condition (11) states that, on the margin, the effect of a change in wetland size on the potential welfare surplus must equal the excess burden of the change in the compensation that the planner must pay to make the farmer reveal y. The wetland size is non-increasing in y so we obtain a separating equilibrium.19 Let qa
g be the a
R qcðq ;iÞ cðqa
y g g ;yÞ 1 optimal wetland size solving (11). The corresponding transfer is then ta
di þ . g ¼ qa
y qy qa
g g This wetland creation program yields the following surpluses: Z y F ðyÞ qcðqa
g ; yÞ a
a
Oðqg ; yÞ l Wg ¼ f ðyÞ dy, qy f ðyÞ 0 Z y qcðqa
g ; yÞ a
FðyÞ FSg ¼ dy, qy 0 Z y ESa
¼ bðqa
g Þf ðyÞ dy, g 0
TSa
g
Z y
¼ ð1 þ lÞ 0
F ðyÞ qcðqa
g ; yÞ a
þ cðqg ; yÞ f ðyÞ dy. qy f ðyÞ
The expected social welfare surplus is the expected potential social welfare surplus less the excess burden of the transfer that would make the farmer reveal y. The farmer’s expected surplus reflects the necessity to keep the transfer non-increasing in y. The environmental surplus is the expected environmental benefit that a wetland of size qa
g would yield. The taxpayers’ expected surplus is the sum, with excess burden, of the expected farmer’s surplus and the true cost of wetland creation. 18
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm. The reader is also referred to Chapter 2.3 in [19] for computations with a similar model. 19 See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm. (H4) is essential for this result to hold [19].
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Table 2 Contract properties with asymmetric information Uniform contract ta
u ¼ qa
u solves u solves W a
u ¼ FS a
u ¼ ES a
u ¼ TS a
u ¼ Take-it-or-leave-it-contract ta
tol ¼ qa
tol solves v solves W a
tol ¼ FS a
tol ¼ ES a
tol ¼ TS a
tol ¼
cðqa
u ðuÞ;uÞ ¼ tðqa
u ðuÞ; uÞ qa
u ðuÞ qcðqa
a
u ðyÞ;yÞ tu ¼ qq
a
R u a
qOðqa
du u ðyÞ;yÞ dqu ðyÞ f ðyÞ dy Oðqa
u ðuÞ; uÞf ðuÞ dt ¼ 0 lqu ðyÞ qq dt Ru a
a
a
a
½Oðq ðyÞ; yÞ lðqu ðyÞtðqu ðuÞ; uÞ cðqu ðyÞ; yÞÞf ðyÞ dy R0u a u a
ðq ðyÞtðqa
u ðuÞ; uÞ cðqu ðyÞ; yÞÞf ðyÞ dy R0u u a
0 bðqu ðyÞÞf ðyÞ dy R u a
ð1 þ lÞtðqa
u ðuÞ; uÞ 0 qu ðyÞf ðyÞ dy
cðqa
;vÞ tol qa
tol
¼ tðqa
tol ; vÞ
dv Oðqa
tol ; vÞf ðvÞ dq þ
R v qOðqa
;yÞ tol 0
qq
f ðyÞ dy ¼ l
R v 0
ta
tol
qcðqa
;yÞ tol qq
f ðyÞ dy
a
Oðqa
; vÞf ðvÞ dv dt ¼ lqtol F ðvÞ R v tol a
a
ðOðqtol ; yÞ lðcðqtol ; vÞ cðqa
tol ; yÞÞÞf ðyÞ dy R0v a
a
ðcðq ; vÞ cðq ; yÞÞf ðyÞ dy tol tol R0v a
0 bðqtol ÞfRðyÞ dy v ð1 þ lÞ 0 cðqa
tol ; vÞf ðyÞ dy
4. Contracts comparison Tables 2 and 3 summarize contracts characteristics. Recall that the general contract consists of an optimal screening mechanism. The uniform contract offers a payment that is proportional to the surface of wetland created and allows farmers to choose the wetland size. The TOL contract proposes a given wetland size and transfer. All these contracts use available information only. In the informationgathering program, the authorities gather the necessary information to offer an optimal contract. It is straightforward to verify that the general contract yields a higher expected social welfare surplus than that obtained with a uniform or a TOL contract.20 One could say that general contracts are optimal contracts based on available information whereas uniform and TOL contracts are suboptimal. The farmer never prefers the information-gathering program, which leaves her for sure with zero profit from wetland creation, whereas the other contracts may yield positive profits. Again it is useful to underline the role played by the excess burden (l) to compare the contracts further. 4.1. No excess burden 4.1.1. Contract characteristics The general and information gathering contracts produce wetland size and environmental surplus that are identical to those obtained with the TOL contract with complete information 20
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm
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Table 3 Contract properties with asymmetric information General contract ta
g ¼
R y qcðqa
g ;iÞ 1 qy qa
y g
qa
g solves
qOðq;yÞ qq
¼l
di þ
cðqa
g ;yÞ qa
g
2 a
F ðyÞ q cðqg ;yÞ qyqq f ðyÞ
a
R y F ðyÞ qcðqg ;yÞ a
f ðyÞ dy qy 0 Oðqg ; yÞ l f ðyÞ a
Ry qcðqg ;yÞ dy 0 F ðyÞ qy Ry a
0 bðqg Þf ðyÞ dy R y ðyÞ qcðqa
g ;yÞ ð1 þ lÞ 0 Ff ðyÞ þ cðqa
g ; yÞ f ðyÞ dy qy
W a
g ¼ FS a
g ¼ ES a
g ¼ TS a
g ¼
Information gathering ta
ig ¼ qa
ig solves
tðq tol ðyÞ; yÞ qOðq;yÞ qq ¼ 0
W a
ig ¼
Ry
FS a
ig ES a
ig
¼ ¼
0 Ry
TS a
ig
¼
0
Oðq tol ðyÞ; yÞf ðyÞ dy ð1 þ lÞI
bðq tol ðyÞÞf ðyÞ dy R y ð1 þ lÞ 0 ðcðq tol ðyÞ; yÞÞf ðyÞ dy þ I 0
a
(q tol ¼ qa
ig ¼ qg ) because, in these contracts, the wetland size maximizes the potential social
welfare surplus (qOðq;yÞ qq ¼ 0). The TOL wetland size with asymmetric information maximizes the R v qOðqa ;yÞ expected potential social welfare surplus instead ( 0 qqtol f ðyÞ dy ¼ 0). In the uniform contract, qcðqa
u ðyÞ;yÞ qq
¼ ta
u ). The transfer in the general contracts R y qcðqa
g ;iÞ di; which is positive and exceeds the transfer with information gathering by the term q1a
y qy g
wetland size maximizes the farmer’s profit (
represents the average informational rent per unit of wetland. Contract characteristics in TOL and uniform contracts depend on plot distribution: the lower the variance of y, the more the results obtained in Section 2 are likely to hold. If variance is relatively high, comparisons are more difficult. Fig. 2 illustrates wetland sizes in each contract. Diagram A shows a case in which a uniform contract yields a smaller wetland than a TOL contract and diagram B shows the alternative case. The optimal TOL wetland size is found at the R v qcðq;yÞ intersection of the curves db qq f ðyÞ dy. The optimal uniform wetland size is found at the dq and 0 intersection of
qcðq;yÞ qq
cðqa
u ðuÞ;uÞ . qa
u ðuÞ qcðq;yÞ db 21 qq with dq.
with ta
u ¼
at the intersection of
The optimal wetland size in the general contract is found
Rv qcðq;yÞ qcðqa ;yÞ a
Here we assume that 8q; 0 qcðq;yÞ qq f ðyÞ dyo qq and tu 4 qq . This is not always true but does not affect the result that wetland sizes can be smaller or larger in the TOL compared with the uniform contract. 21
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Marginal costs and benefits
Marginal costs and benefits
∂c(q, θ ) ∂q
∂ c(q, θ ) ∂q
∂c(q, θ ) f (θ )dθ ∂q 0 v
tu
tu
∫
a*
a*
v
∫
0
∂c(q, θ ) f (θ )dθ ∂q
db(q ) dq q
a* q a* qua* qtol
(A)
db(q ) dq q
a* q a* qtol qua*
(B)
Fig. 2. Wetland size in uniform and TOL contracts: (A) Elastic costs, unelastic benefits and (B) elastic benefits, unelastic costs. Marginal costs and benefits
Elastic costs, Unelastic benefits ∂c(q, θ ) ∂q
Range for tu and
ttol
a*
∂c(q,θ ) ∂q
db(q ) dq
db(q ) dq
ttol
Range Range for
(A)
∂c(q, θ ) ∂q
Range
a*
qua*
∂ c(q, θ ) ∂q
∂c(q,0) ∂q
for tu and
for
Elastic benefits, Unelastic costs
Marginal costs and benefits
a* qtol
a*
a*
∂c(q,0) ∂q
q Range for (B)
a* qtol
q Range for
qua*
Fig. 3. Contract comparison.
Fig. 3 illustrates how the maximum range for transfer and wetland size (i.e. with u ¼ v ¼ y) depends on the elasticity of wetland creation benefits and costs to changes in wetland size.22 In 22
The curve qcðq;yÞ qq .
R v qcðq;yÞ 0
qq
f ðyÞ dy is not drawn in the diagram but must obviously be located between the curves qcðq;0Þ qq and
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Fig. 3A, benefits from wetland creation are relatively inelastic to wetland size, which narrows the range of possible transfer sizes in both contracts. The range of TOL wetland sizes is large— because of high variance in y. In contrast to that, a more elastic cost narrows the wetland size range in the uniform contract. So if costs are elastic, a uniform contract is likely to yield a wetland size closer to qa .23 In Fig. 3B, benefits are much more elastic to wetland size so the range of possible TOL wetland sizes is small even though the variance in y is high. Here as well, a cost, which is more elastic to wetland size, narrows the wetland size range in the uniform contract. So if costs are very inelastic, a TOL is likely to yield a wetland size closer to qa compared with a uniform contract. These results relate to the traditional discussion about whether one should regulate price or quantities [25]. Transforming the TOL threshold plot into a wetland yields no potential welfare surplus, but transforming the uniform contract threshold plot yields a potential social welfare surplus equal to the average marginalvalue of a change in the threshold plot on the potential social welfare surplus R u qOðqa
ðyÞ;yÞ dqa
f ðyÞ u ðyÞ u dy). So threshold plots differ in both contracts unless they are both ( 0 qq dt f ðuÞdu dt
equal to y; whether u4v or v4u depends on plot distribution. 4.1.2. Welfare surpluses The expressions of the social welfare surpluses are limited to the potential welfare surplus O except in the information gathering contract. The wetland sizes being the same in general and information gathering contract, the expected social welfare surpluses differ only by the term a
Io0. The social welfare is higher in the general contract (W a
g 4W ig ) because the informational rent corresponds to a transfer between interest groups, which is free of charges due to zero excessburden. In contrast, the cost of acquiring information is a pure welfare loss. Also the only difference between the expected taxpayers surpluses in those contracts are the terms representing the surplus that the planner must pay to make the farmer reveal the true y and the cost of acquiring the missing information, respectively. Z y qcðq tol ; yÞ a
a
FðyÞ dy4I. TSig 4TSg 3 qy 0 Ry qcðqa ;yÞ The expected farmer’s surplus in the general contract is 0 FðyÞ qyg dy, which is positive (H3), and thus larger than the farmer’s surplus in the information gathering contract. The social welfare difference between uniform and TOL contracts depends on wetland size and threshold characteristic Z u Z v a
a
a
a
ðOðqu ðyÞ; yÞ Oðqtol ; yÞÞf ðyÞ dy ðOðqa
W u W tol ¼ tol ; yÞÞf ðyÞ dy 0 u |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} a
b
a is the difference in welfare surpluses due to different wetland sizes. The information in Table 1 together with assumptions (H1) and (H5) imply that q tol and thus qa maximize O 23
Recall that qa is at the intersection of
qcðq;yÞ qq
and
dbðqÞ dq .
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Table 4 Contracts comparisons Case 1
Case 2
Case 3
Elastic costs Inelastic costs a
a
a
jqa
tol q jojqu q j a4b a
W a
tol oW u ðyÞ
Inelastic costs Elastic benefits a
a
a
jqa
tol q j4jqu q j aob a
W a
tol 4W u ðyÞ
Elastic costs and benefits or Inelastic costs and benefits a
a
a
jqa
tol q j_jqu q j a_b a
W a
tol _W u ðyÞ
and if O is symmetric, 8y;
a
a
a
a
a
Oðqa
u ðyÞ; yÞ4Oðqtol ; yÞ () jqtol q j4jqu ðyÞ q j.
So if O is not too asymmetric, so that 8y; q; Oðqa q; yÞ Oðqa þ q; yÞ, one would expect a wetland size close to qa to yield a higher potential social welfare from wetland creation than a wetland size that is not so close. b is the difference in welfare surpluses due to differences in threshold plots. It is the expected social welfare surplus obtained from creating a wetland using a TOL contract on plots with characteristics qOðq;yÞ between the two thresholds. Note that b40 because Oðqa
tol ; vÞ ¼ 0 and qy o0 (H3). If wetland creation costs are relatively elastic compared to benefits (case A in Fig. 3 and case 1 a
in Table 4), it is likely that Oðqa
u ðyÞ; yÞ4Oðqtol ; yÞ for most values of y implying that a would be positive and if a is large enough the gain in welfare surplus due to the opportunity to create wetland of size closer to optimal size could be larger than the loss due to differences in threshold plots. A uniform contract would then most probably yield higher social welfare than a TOL contract. If costs of wetland creation were relatively inelastic compared to benefits (case B in Fig. 3 and case 2 in Table 4), a would probably be negative and the TOL contract would yield higher social welfare than the uniform contract. When costs and benefits are neither very elastic nor inelastic, it is difficult to tell which effect dominates (case 3 in Table 4). It is difficult to compare each interest group’s surpluses in the TOL, uniform, and general contracts. If the distribution of plot characteristics has low variance, by continuity, the results obtained with complete information still yield. The farmer would rather sign a uniform contract whereas the taxpayers would prefer a TOL contract. If plot characteristics have high variance, the differences in respective surpluses must be calculated from case to case. There is no evidence that the farmer’s surplus should be higher in the uniform contract. If the transfer can be determined accurately but not the wetland size, as in case A, the farmer’s surplus could very well be much higher in the TOL but it could also be much lower. If the farmer had a plot with a high characteristic— higher than the threshold farm’s—she might prefer a general contract that yields non-negative profits for sure to a TOL or a uniform contract that would yield a negative profit and be refused. 4.2. A positive excess burden By continuity, the results obtained in Section 4.1 must hold at least for small excess burden but they may not hold if excess burden is large. When l40, the general contract does not always yield
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a higher social welfare than the information gathering contract. Relation (12) gives a necessary and sufficient condition for that statement to remain true. Z y 1 F ðyÞ qcðqa
g ; yÞ
a
Oðqtol ; yÞ Oðqg ; yÞ þ l f ðyÞ dy DðlÞX0. (12) I4 qy 1þl 0 f ðyÞ So if information is cheap, information gathering yields a higher social welfare surplus than a general contract. The term DðlÞ is always positive because (H3) and Oðq tol ; yÞ4Oðqa
g ; yÞ for all farm characteristics. The general contract yields smaller wetlands and higher farmer’s profit than information gathering because of the necessity to keep the transfer non-increasing in y so q tol ¼
a
a
a
qa
ig 4qg and FS tol ¼ FS ig pFS g . Information gathering yields a lower taxpayers’ surplus than if information had been complete (TS tol 4TS a
ig ). The surplus is also lower for the taxpayers compared to the general contract if information is expensive enough— R y qcðqa
;yÞ F ðyÞ g a
I4 0 qy f ðyÞ þ cðqg ; yÞ cðqtol ; yÞ f ðyÞ dy. Similarly, (13) respectively (14) give necessary and sufficient conditions for a TOL, respectively, a uniform contract to yield a higher social welfare than information acquisition. ! Z y 1 (13) Oðq tol ðyÞ; yÞf ðyÞ dy W a
I4 tol , ð1 þ lÞ 0 1 I4 ð1 þ lÞ
Z
y 0
! . Oðq tol ðyÞ; yÞf ðyÞ dy W a
u
(14)
So if information is cheap, information gathering yields a higher social welfare surplus than a TOL contract or a uniform contract. Further contract comparisons are not obvious except for some considerations about wetland size. Proposition 4. The Spence–Mirrlees condition (H4) is necessary and sufficient for the wetland size in the TOL contract to decrease when the excess burden increases. Proof. Using the equations for wetland size and threshold plot one can show24 that 1 0 Z v dv C BZ v qOðqa
qcðqa
dqC B a
tol ; yÞ tol ; yÞ . f ðyÞ dy ¼ lB f ðyÞ dy q ta
FðvÞ tol tol dv C A @ 0 qq qq 0 dt |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} S
So the sign of S determines whether wetland size increases or decreases when excess burden increases: if S is positive, the TOL wetland size decreases when l increases. Using condition dv dv a
a
ta
tol qtol ¼ cðqtol ; vÞ to calculate dq and dt , and integrating S by parts, we obtain R v q2 cðqa
;yÞ tol S ¼ 0 qqqy FðyÞ dy. So S40 if and only if (H4) holds. & What happens with wetland size in a uniform contract depends on the sign of 24
du dl.
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm
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5. Discussion This article shows that the choice of instrument for wetland creation has important welfare implications and may yield quite different social welfare surpluses and distribution between interest groups. An appropriate instrument choice could result in social welfare gains. This article also indicates situations in which respective contract is preferable. If excess burden is zero or very small, one can measure a contract’s performance by how close to optimum the contract is with regard to wetland size, transfer and threshold plot. Uniform contracts seem a simple and rather accurate way to make farmers create wetlands if the farm characteristic has high variance and costs are relatively elastic to changes in wetland size: The social planner has a good idea about the optimal transfer and knows then that the farmer would pick a wetland size close to optimal with a uniform contract. If instead variance was low, or if wetland creation benefits were elastic as well, a TOL would be better because the social planner could pick a wetland size close to optimal. Screening mechanisms like in the general contract have been criticized for being of little practical use because the derived transfer scheme is often too complicated.25 In addition, general contracts yield small gains when uniform or TOL contracts are accurate. Uniform or TOL contracts are much more straightforward than general contracts, and the farmer need not work too hard to find out if they are worthwhile accepting. This may explain why general contracts have not been used. Another explanation, not studied in this article, could be the presence of other costs associated with this contract, for example, transaction costs.26 When costs are inelastic to wetland size, the social planner cannot pick a transfer close to optimal and a general contract or information gathering yield large social gains compared to TOL or uniform contracts. In such a situation, the cost of information determines, which contract is superior. When excess burden is large, picking suboptimal wetland sizes and transfer or making the farmer reveal the true plot characteristic induces a larger welfare loss. So information acquisition combined with a TOL contract gains advantages and might even be superior to all other alternatives. In this article, the authorities can only gather all the information necessary or none. If partial information acquisition was possible, one could create a wetland creation program superior to all other programs by combining partial information gathering with a screening mechanism. Empirical evidence shows that uniform contracts and information gathering associated with a TOL offer have been the main type of incentives used in practice for wetland creation. This indicates that acquiring information may have been cheap and/or excess burden large in cases when information gathering was preferred. In cases when uniform contracts were preferred one should verify that variance in the farm characteristic was high, and costs relatively elastic to changes in wetland size. Empirical verifications of these theoretical results require collecting information about land quality and the assessment of marginal costs and marginal benefit functions. Heimlich et al. [12], and Sundberg and So¨derqvist [24] have reviewed the major 25
Some of the weaknesses of those types of models are discussed, for example, in [11,16] or [1]. Such costs could be large for the farmer in a screening mechanism, which would require each contract to be compared to all others to chose the one that yields the highest profit. 26
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valuation studies in the field in the US and in Sweden. None of the studies discussed contained the information necessary to verify these theoretical results. This suggests that contracts may not be well designed and adapting the contracts to each particular situation could yield welfare gains. This requires collecting better information about land quality, and marginal costs and benefit functions. This article shows also that program choices have distributional impacts between taxpayers, farmers and people who value environmental quality. So interest groups may want to lobby for favorable wetland creation programs. In this lobbying game, the farmer has an advantage against the other players because she knows the true plot characteristic and can calculate the exact surpluses in each contract, not only expected values. In practice the farmers’ high bargaining power could be a factor explaining the use of uniform contracts rather than information acquisition. If this is true, today’s wetland creation program may reflect the fact that farmers in the US and in the Ka¨vlinge River basin have had less bargaining power than farmers in England or in the rest of Sweden. The incentives studied here are once and for all incentives. In practice, wetland creation programs are set for some period in time—most often 10–20 years—and can be renewed for further periods. If the game is repeated, the social planner may learn from the farmer’s choice in previous periods. If the farmer rejected the TOL contract in a previous period, the social planner knows only that the transfer was too low compared to the wetland size. In contrast to that the farmer’s choice of uniform or general contract implies that the social planner obtains the missing information about soil quality. She has then complete knowledge about soil quality in the beginning of the second period27 and can implement an optimal wetland creation from that point in time.
Acknowledgments I thank participants at several conferences and seminars for giving me valuable comments on earlier drafts. Special thanks to M. Dufwenberg, J. Ha¨ckner, P.-A. Jayet, T. Lindahl, K.-G. Lo¨fgren, K.-G. Ma¨ler, E. Nævdal, H. Scharin, T. So¨derqvist, and to two anonymous referees. I also thank J. Petersen from American Writing and Editing. This research was initiated within the research project Ecological-Economic Analysis of Wetlands: Functions, Values and Dynamics (ECOWET). Funding from the EU/DGXII Environment and Climate Programme (Contract No. ENV4-CT96-0273) and the Swedish Council for Planning and Coordination of Research (FRN) is gratefully acknowledged.
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Journal of Environmental Economics and Management 50 (2005) 598–616 www.elsevier.com/locate/jeem
Incentives for wetland creation Anne-Sophie Cre´pin The Beijer International Institute of Ecological Economics, The Royal Swedish Academy of Sciences, 10405 Stockholm, Sweden Received 9 January 2002 Available online 31 May 2005
Abstract When information about soil quality is complete, wetland creation with a take-it-or-leave-it contract, which specifies wetland size and transfer, yields higher social benefits than if a uniform contract, which offers a payment proportional to the wetland size, had been used. This result points to a paradox because uniform contracts have been used a lot in practice. This article concentrates on the presence of asymmetric information about soil quality as a possible explanation for this paradox. It shows that the choice of instrument for wetland creation has welfare implications. Different contracts typically yield quite different social welfare surpluses and distribution between interest groups. It is not obvious, which of four contracts studied dominates when a farm characteristic affecting costs is unknown to the social planner. The probability distribution of the characteristic, the size of the excess burden, the elasticity of costs and benefits to wetland size and the cost of acquiring missing information influence the outcome. r 2005 Elsevier Inc. All rights reserved. Keywords: Asymmetric information; Voluntary incentives; Wetlands
1. Introduction Several countries and the European Union (EU) use subsidy systems to support wetland1 creation on farmland. These incentives give opportunities to enhance environmental quality while Fax:+46 8 15 24 64.
E-mail address: [email protected]. Wetlands are land areas with water near the surface during large parts of the year. They enhance biodiversity and produce ecosystem services [3,8]. 1
0095-0696/$ - see front matter r 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2005.01.005
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obtaining a desired reduction of traditional agricultural production. The authorities in the United States (US) and in EU countries have used many different kinds of incentives to encourage wetland creation on arable land.2 Why so many different incentives? This article discusses reasons that support the choice of wetland creation incentives that are in practice, and focuses on two incentives rather similar to the most frequently used. The studied incentives are called uniform and take-it-or-leave-it (TOL) contracts. The uniform contract, which is similar to incentives proposed in England and Sweden, offers a payment that is proportional to the surface of wetland created and allows farmers to choose the wetland size. In the TOL contract, social planners set wetland size and transfer. This contract looks like incentives proposed in the Wetland Reserve Program of the Farm Bill Act 2002 and in the Ka¨vlinge River Area in Sweden [22]. One can show that a TOL contract would produce larger social benefits than a uniform contract if all information necessary to calculations was available. So why have uniform contracts been used so much in practice? This article focuses on asymmetric information as one possible explanation among many others. Suppose farmers have better knowledge than the planner about farm-specific characteristics that affect the cost of wetland creation, such as soil quality. If farmers can choose wetland size, they will do that according to all their knowledge. This is more than the planner can ever do. So asymmetric information may imply that a uniform contract could yield higher social welfare than a TOL contract. Nevertheless, this is not completely obvious because farmers have objectives that differ from the social planners’ objectives when choosing the wetland size. When there is asymmetric information, other contracts than uniform and pure TOL contracts are relevant. In practice, social planners may use some kinds of information gathering procedures—for example land inspection—together with TOL contracts. This supports the asymmetric information hypothesis. Most of the relevant literature would probably advocate use of screening mechanisms that consist of a selection of contracts, conveniently chosen, so that farmers would pick the contract that corresponds to the true characteristics of the land. In this paper, a general contract of that kind is designed to maximize social welfare. Here, the relation between a social planner and a farmer is a typical principal–agent relationship with adverse selection. Green and Laffont [9], Dasgupta [6], and Baron and Myerson [2] provided pioneering work on optimal incentives in such situation. Bourgeon et al. [5], Bourgeon and Chambers [4], Hueth [13] and Jayet [14] applied the tools developed by Baron and Myerson and others in the context of land use incentives and policies to reduce overproduction in agriculture. Gren [10] discussed efficient contracts for converting arable land into pollutants sinks.3 Smith [21], Wu and Babcock [26] and Segerson and Miceli [20] gave other relevant contributions to the field. General contracts are hardly used but they are studied here because they have been designed as optimal contracts so they could give valuable information on how existing programs can be improved and help comparisons between contracts. The paper shows that contract choice can create welfare gains and that this choice depends on the distribution of the unknown characteristic, on the elasticity of costs and benefits to wetland 2
See for examples the Farm Bill Act 2002, the England rural Development Programme, Lindahl [15] and documentation from the Swedish department of agriculture (available in Swedish on the Web: http://www.sjv.se) 3 A pollutant sink is here a wetland aiming at reducing nutrient leakage from agriculture.
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size changes, on the interest groups’ bargaining power, on excess burden, and on information acquisition costs. Similar subsidy systems have also been used, for example, to conserve meadows or pasture lands. This suggests that the results obtained could be generalized even for other landuse incentives: Wetland creation can be reinterpreted as any amenity production that the social planner wants to encourage on agricultural land. This paper is organized like this: Section 2 presents the model. Section 3 presents derived characteristics of information gathering, and uniform, TOL and general contracts. Section 4 compares the different contracts. Section 5 discusses the results.
2. Model A wetland creation program is a situation in which a social planner and a farmer trade environmental benefits4 from wetland creation on the farmer’s land. In exchange the farmer receives a transfer (t) per unit of wetland created. Consider y 2 ½0; y, a farm characteristic that represents soil quality affecting the production of goods, other than wetlands. Let q 2 Rþ denote the wetland size. Assume that wetland creation programs do not affect other sectors in the economy than those represented here. Wetland creation costs consist of fix cost, construction cost and the alternative cost of land.5 Assume that these cost components together depend only on wetland size and on soil quality. The cost function is denoted cðq; yÞ.6 Typically the authorities do not own the land so the social welfare surplus W ðq; t; yÞ from wetland creation of size q on farm y is the sum of the environmental surplus (ES), the farmer’s profit (FS) and taxpayers’ surplus (TS), respectively. If the authorities instead created a wetland on land that they owned the potential social surplus Oðq; yÞ would instead consist of the environmental surplus less the wetland creation cost corrected for a positive excess burden l. The environmental surplus is the net environmental benefit7 bðqÞ, which depends on wetland size. The taxpayers’ surplus is the transfer that they must pay tq, corrected for the excess burden l. This gives expressions for W and O. W ðq; t; yÞ bðqÞ þ FS ð1 þ lÞtq, Oðq; yÞ bðqÞ ð1 þ lÞcðq; yÞ. The key assumptions (H1)–(H5) help clarify the results. They are justified if the alternative cost of the land is the main cost component. q2 cðq; yÞ 40, qq2 4
(H1)
These benefits are mainly recreation, increased biodiversity and water-cleaning (SOU 1994:82 and Mitsch and Gosselink [17]). So¨derqvist [23] found some evidence of private benefits for farmers but they should not be included here. 5 For a more detailed analysis of costs for wetland creation, see [22]. 6 If there is a fix cost we assume cð0; yÞX0 and cðq; yÞXcð0; yÞ for all positive wetland sizes q. 7 This is the environmental benefit less the environmental cost.
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qcðq; yÞ 40, qq
(H2)
qcðq; yÞ 40, qy
(H3)
q2 cðq; yÞ 40, qyqq
(H4)
d 2 bðqÞ p0. dq2
(H5)
The marginal cost is likely to increase if the wetland size increases because land available for alternative use becomes rare (H1). Creating a larger wetland respectively using land of higher quality for wetland creation yield a higher alternative cost ((H2) and (H3), respectively). Assumption (H4) reflects the usual Spence–Mirrlees condition and means that the same increase in wetland size yields a higher increase in costs on a high-quality plot (high y) compared to a lowquality plot. Finally, the environmental surplus is concave (H5). 2.1. Contracts A wetland creation program results in a contract ðt; qÞ. In a uniform contract, the social planner decides the transfer; the farmer can choose to select a wetland size q and receive the amount tq or reject the contract. In a TOL contract, the social planner decides transfer and wetland size; the farmer chooses to accept the contract or not. The farmer selects a profit-maximizing wetland size if given the opportunity and rejects any contract that yields negative profits. The social planner knows this strategy and can use backward induction to determine, which contract to propose. The farmer’s profit from choosing contract ðt; qÞ is pðq; t; yÞ ¼ tq cðq; yÞ. Wetlands’ effects on the farmer’s other traditional agricultural production enter only through the alternative cost of the land included in cðq; yÞ.8 Let tðq; yÞ denote the minimum transfer that the farmer requires to accept a contract. Let q ðt; yÞ (X0) denote the profit-maximizing wetland size for any transfer t and land quality y. Given that (H1) holds and if tXtðq ; yÞ, the first-order conditions for profit maximization: t qcðq;yÞ qq ¼ 0 gives the optimal wetland size. Otherwise a wetland size equal to zero is profit maximizing. The welfare surplus from wetland creation is W ðq; t; yÞ ¼ Oðq; yÞ lpðq; t; yÞ. This corresponds to the potential social welfare surplus less the excess burden of the farmer’s profit. If there are several farmers, the welfare surplus is the sum of all farmers’ surpluses. If the
8
Accounting for private benefits from wetland creation (e.g. irrigation) does not influence the results: c could be the net costs. So¨derqvist [23] discusses private benefits from wetland creation for farmers.
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Table 1 Contract properties with complete information Uniform contract ( u )
TOL contract ( tol )
t¼
qcðq u ;yÞ qq
tðq tol ; yÞ ¼
q solves
qOðq u ;yÞ qq
¼l
W¼
Oðq u ; yÞ
FS ¼
qcðq u ;yÞ qq bðq u Þ
ES ¼ TS ¼
q2 cðq u ;yÞ
q 2 qq u qcðqu ;yÞ
l qq qu
cðq u ; yÞ
q u cðq u ; yÞ
ð1 þ lÞ
qcðq u ;yÞ qq
q u
qOðq tol ;yÞ ¼ qq
Oðqtol ; yÞ
cðq tol ;yÞ q tol
0
0 bðq tol Þ ð1 þ lÞcðq tol ; yÞ
farmer rejects the contract, W ¼ ES ¼ FS ¼ TS ¼ 0. The planner’s problems are:9 max
fW ðq; t; yÞ; 0g
s.t.
t ¼ tðq; yÞ;
max
fW ðq; t; yÞ; 0g
s.t.
q ¼ q ðt; yÞ:
q;t
t
ðTake-it-or-leave-itÞ;
ðUniformÞ;
The constraints can be substituted in respective objective functions and when (H1) and (H5) hold, the first-order conditions for maxima are necessary and sufficient. Table 1 summarizes the results derived from these conditions.10 Indices u and tol denote the optimal measures for respective contract. 2.2. Uniform contracts versus take-it-or-leave-it contracts Excess burden (l) is essential for contract comparison. With no excess burden (l ¼ 0) wetland sizes maximize the potential welfare surplus (qO qq ) in both contracts so they are the same. Environmental surpluses are the same as well. Allowing the farmer to choose wetland size and qcðq ;yÞ make a non-negative profit ( qqu q u cðq u ; yÞ) does not incur a social cost so the social welfare surpluses are identical. Transfers differ so the farmer prefers a uniform contract that yields at least zero profit compared to a TOL contract that always yields zero profit. The taxpayers would rather qcðq Þ finance a TOL contract because q tol ¼ q u so cðq tol ; yÞX qqu q u otherwise the farmer would have rejected the uniform contract. qcðq ;yÞ Consider now a positive excess burden l40. A positive farmer profit ( qqu q u cðq u ; yÞ40) would then induce a social cost. Fig. 1 represents society’s marginal benefits and marginal costs of
9
The constraint in the take-it-or-leave-it program must hold with equality because taxes are costly so a larger transfer would induce larger social costs. 10 See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm
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2 (1 + λ ) ∂c(q, θ ) + λ ∂ c (q2, θ ) q
Marginal costs and benefits
∂q
∂q
b
(1 + λ )∂ c(q, θ ) q
c d
db(q ) dq
e a
q u*
* qtol
q
Fig. 1. Contract comparison when information is complete.
wetland creation as functions of wetland size to illustrate this.11 The marginal benefit function (db dq) is 2the same in both contracts. The difference between the marginal cost functions is the term q cðq ;yÞ l qq2u q u , which is positive (H1). So q u oq tol and the environmental benefit is higher in the TOL contract: ðabdq tol Þ4ðabcq u Þ. The social welfare is higher in the TOL contract: ðebdÞ4ðebcÞ— because the planner has two instruments available in the TOL contract (t and q) but only one in the uniform contract (t). Using two instruments instead of one allows the planner to control that the farmer does not make more profit than necessary and hence lowers social costs. The farmer would prefer the uniform contract because it supplies her with a surplus at least as large as in the TOL contract. It is difficult to tell which contract the taxpayers would prefer. On one hand, they must give a higher transfer in a uniform contract; on the other hand, they finance a smaller wetland. But at least for small excess burden, continuity implies that taxpayers prefer a TOL contract.
3. Contracts under asymmetric information From now on, suppose instead that the farmer knows the true soil quality y, but that the social planner knows only the distribution of y. Let f ðyÞ be the density function with cumulative density function F ðyÞ.12 The social planner cannot implement the optimal TOL contract unless the farmer reveals the true y. Unfortunately, the farmer would have incentives to lie about y because, due to assumption (H3), stating a higher soil quality than the true one would fool the authorities to 11
The graphs represent linear functions but the results would not be affected if they were not, as long as (H1), (H2) and (H5) hold. 12 If instead the social planner proposes wetland creation programs to a population of farmers who are only differentiated by their soil quality, the soil quality among farms is then distributed according to f.
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believe that costs are higher than they really are. This would entitle to a larger transfer without affecting the true cost and hence yield a higher profit. Soil quality being the farmer’s private information, the social planner knows only an expected value of the social welfare function to maximize. The planner can choose to acquire the missing information or provide a contract based on available information. Both solutions are associated with welfare costs so to compare contracts, the cost of information acquisition must be set in relation with the cost of providing suboptimal contracts. In addition to that, if the social planner chooses to act upon available information, she may set the transfer so low that if the farmer has a high y, accepting the contract is not profitable. Given assumption (H3), this defines a virtual threshold farm: if the farm has a higher y than the threshold, the farmer rejects the contract. The rest of this section presents contracts characteristics when there is asymmetric information. 3.1. Information acquisition Suppose the social planner can acquire missing information directly at some cost I40, for example, by visiting the farm. After gathering information, the social planner faces the same problems as in the complete information case and thus selects the optimal TOL contract—see Section 2. The expected surpluses are, respectively, Z y ¼ Oðq tol ðyÞ; yÞf ðyÞ dy ð1 þ lÞI, W a
ig 0
FSa
ig ¼ 0, Z y ESa
¼ bðq tol ðyÞÞf ðyÞ dy, ig 0
TSa
ig ¼ ð1 þ lÞ
Z
y 0
! cðq tol ðyÞ; yÞf ðyÞ dy þ I .
The expected social welfare surplus consists here of the expected maximum potential welfare surplus obtained with a TOL contract with complete information, less the information cost. Information acquisition removes informational asymmetry and gives opportunity to reduce the farmer’s profit to a minimum, hence FSa
ig ¼ 0. The expected environmental surplus is the environmental surplus that the planner would expectRfrom a wetland of size q tol . The expected y taxpayers’ surplus is the sum of the expected transfer 0 cðq tol ; yÞf ðyÞ dy and the cost of acquiring information I, both with excess burden. In practice, the Ka¨vlinge river program [23] and the restoration cost-share agreements proposed in the Farm Bill act 2002 use similar incentives. In both programs, the authorities visit all program participation candidates. 3.2. Uniform contracts Let u characterize the virtual threshold farm in the uniform contract. The planner knows that wetland creation on a virtual threshold farm would yield zero profits and that the farmer chooses a profit-maximizing wetland size. The planner must determine the transfer ta
u that would
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maximize social welfare given these two constraints. This results in the problem Z u a
a
max ðOðqa
u ðyÞ; yÞ lðtqu ðyÞ cðqu ðyÞ; yÞÞÞf ðyÞ dy, t
s.t.
0 a a
tu qu ðuÞ
cðqa
u ðuÞ; uÞ ¼ 0, a
qcðqu ðyÞ; yÞ ta
¼ 0. u qq
Proposition 1. A necessary condition for a maximum in expression (1) is given by Eq. (4). Z u a
du qOðqa
a
u ðyÞ; yÞ dqu ðyÞ ðuÞ; uÞf ðuÞ ðyÞ f ðyÞ dy ¼ 0. þ lq Oðqa
u u dt qq dt 0
605
ð1Þ ð2Þ ð3Þ
(4)
Proof. Differentiate (1) with regard to t and use (2) and (3) to eliminate superfluous terms.13 & Condition (4) states that the transfer is optimal provided that the marginal effects of a change in transfer on the social welfare sum to zero. The first term represents the expected value of the marginal welfare change due to a change in the threshold plot. The second term represents the expected value of the marginal welfare change due to a change in wetland size. If the usual concavity conditions are satisfied,14 Eqs. (2)–(4) are sufficient to characterize optimal transfer, threshold plot and wetland size in a uniform contract. The expected surpluses are, respectively, Z u a
a
a
¼ ðOðqa
W a
u u ðyÞ; yÞ lðtðqu ðuÞ; uÞqu ðyÞ cðqu ðyÞ; yÞÞÞf ðyÞ dy, Z0 u a
a
FSa
ðtðqa
u ðuÞ; uÞqu ðyÞ cðqu ðyÞ; yÞÞf ðyÞ dy, u ¼ 0 Z u a
bðqa
ESu ¼ u ðyÞÞf ðyÞ dy, 0 Z u a
TSa
¼ ð1 þ lÞtðq ðuÞ; uÞ qa
u u ðyÞf ðyÞ dy. u 0
The expected social welfare surplus consists of the expected potential welfare surplus less the excess burden of the farmer’s profit. The expected farmer’s surplus equals the expected value of transfer less wetland creation cost. The environmental surplus is the expected environmental surplus that a wetland of size qa
u ðyÞ would yield. The taxpayers’ surplus is equal to the transfer with excess burden, times the expected size of the wetland created. All surpluses are equal to zero if y is higher than the threshold plot. 3.3. Take-it-or-leave-it contracts Let vpy characterize the threshold farm in a TOL program. The social planner must find out a
transfer (ta
tol ) and wetland size (qtol ) that maximize social welfare given that the farmer only 13 14
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm This is not obvious and should be verified in each specific case.
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accepts contracts that yield non-negative profits Z v a
a a
max ðOðqa
tol ; yÞ þ lcðqtol ; yÞ lttol qtol Þf ðyÞ dy, a a
qtol ;ttol
s.t.
0 a a
ttol qtol
cðqa
tol ; vÞ ¼ 0.
ð5Þ ð6Þ
Proposition 2. If qa
tol 40, necessary conditions for a maximum in expression (5) are given by (7) and (8)
Z v qOðqa
qcðqa
dv a
a
tol ; yÞ tol ; yÞ Oðqtol ; vÞf ðvÞ l ttol f ðyÞ dy ¼ 0, ð7Þ þ qq qq dq 0 dv ð8Þ lqa
Oðqa
tol ; vÞf ðvÞ tol F ðvÞ ¼ 0. dt Proof. Differentiate with regard to q and t and use (6) to eliminate terms.15 & If the usual concavity conditions are satisfied,16 these conditions, together with (6), characterize an optimal TOL program under asymmetric information. Condition (7) states that wetland size is optimal if the marginal effects of a change in wetland size on the social welfare sum to zero. The first term represents the effect of the threshold plot change. The second term represents the direct effect of a change in wetland size. Condition (8) states that the transfer is optimal if expected potential welfare gains from transforming the threshold plot equal expected excess burden from creating a wetland of the given size. The expected surpluses are, respectively, Z v a
a
a
ðOðqa
W tol ¼ tol ; yÞ lðcðqtol ; vÞ cðqtol ; yÞÞÞf ðyÞ dy, Z0 v a
FSa
ðcðqa
tol ; vÞ cðqtol ; yÞÞf ðyÞ dy, tol ¼ 0 Z v ESa
¼ bðqa
tol Þf ðyÞ dy, tol 0 Z v a
TStol ¼ ð1 þ lÞ cðqa
tol ; vÞf ðyÞ dy. 0
The expected social welfare surplus is the expected potential welfare surplus less the excess burden from the farmer’s profit. The expected farmer’s surplus is the expected value of the difference between the transfer and the farmer’s true cost for wetland creation. The environmental surplus is the expected environmental surplus that a wetland of size qa
tol would yield. The taxpayers’ surplus is the expected transfer with excess burden. All surpluses equal zero if y is higher than the threshold characteristic. 3.4. General contracts The so-called revelation principle17 states that if the desired allocation can be implemented through some mechanism, then it can also be implemented through a direct truthful mechanism, where agents reveal their private information. Here, such a mechanism would consist of a menu of 15
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm This is not obvious and should be verified in each specific case. 17 Dasgupta et al. [7], and Myerson [18] were the first to discuss it. 16
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contracts, that specify wetland size and compensation level. The menu of contracts must fulfill incentive compatibility and individual rationality constraints. The results in this section are a standard application of incentives theory with adverse selection.18 The optimal transfer and the social planner’s objective can be written as (9) and (10). Z 1 y qcðq; iÞ cðq; yÞ ðq; yÞ ¼ ta
di þ , ð9Þ g q y qy q Z y F ðyÞ qcðq; yÞ max W ðq; yÞ ¼ Oðq; yÞ l f ðyÞ dy. ð10Þ q f ðyÞ qy 0 3
cðq;yÞ Proposition 3. If qqyqq 2 X0 and given assumptions (H1)–(H5), a necessary and sufficient condition for a maximum in expression (10) is given by (11)
qOðq; yÞ F ðyÞ q2 cðq; yÞ ¼l . qq f ðyÞ qyqq
(11)
Proof. Follows directly from differentiation of (10). & Condition (11) states that, on the margin, the effect of a change in wetland size on the potential welfare surplus must equal the excess burden of the change in the compensation that the planner must pay to make the farmer reveal y. The wetland size is non-increasing in y so we obtain a separating equilibrium.19 Let qa
g be the a
R qcðq ;iÞ cðqa
y g g ;yÞ 1 optimal wetland size solving (11). The corresponding transfer is then ta
di þ . g ¼ qa
y qy qa
g g This wetland creation program yields the following surpluses: Z y F ðyÞ qcðqa
g ; yÞ a
a
Oðqg ; yÞ l Wg ¼ f ðyÞ dy, qy f ðyÞ 0 Z y qcðqa
g ; yÞ a
FðyÞ FSg ¼ dy, qy 0 Z y ESa
¼ bðqa
g Þf ðyÞ dy, g 0
TSa
g
Z y
¼ ð1 þ lÞ 0
F ðyÞ qcðqa
g ; yÞ a
þ cðqg ; yÞ f ðyÞ dy. qy f ðyÞ
The expected social welfare surplus is the expected potential social welfare surplus less the excess burden of the transfer that would make the farmer reveal y. The farmer’s expected surplus reflects the necessity to keep the transfer non-increasing in y. The environmental surplus is the expected environmental benefit that a wetland of size qa
g would yield. The taxpayers’ expected surplus is the sum, with excess burden, of the expected farmer’s surplus and the true cost of wetland creation. 18
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm. The reader is also referred to Chapter 2.3 in [19] for computations with a similar model. 19 See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm. (H4) is essential for this result to hold [19].
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Table 2 Contract properties with asymmetric information Uniform contract ta
u ¼ qa
u solves u solves W a
u ¼ FS a
u ¼ ES a
u ¼ TS a
u ¼ Take-it-or-leave-it-contract ta
tol ¼ qa
tol solves v solves W a
tol ¼ FS a
tol ¼ ES a
tol ¼ TS a
tol ¼
cðqa
u ðuÞ;uÞ ¼ tðqa
u ðuÞ; uÞ qa
u ðuÞ qcðqa
a
u ðyÞ;yÞ tu ¼ qq
a
R u a
qOðqa
du u ðyÞ;yÞ dqu ðyÞ f ðyÞ dy Oðqa
u ðuÞ; uÞf ðuÞ dt ¼ 0 lqu ðyÞ qq dt Ru a
a
a
a
½Oðq ðyÞ; yÞ lðqu ðyÞtðqu ðuÞ; uÞ cðqu ðyÞ; yÞÞf ðyÞ dy R0u a u a
ðq ðyÞtðqa
u ðuÞ; uÞ cðqu ðyÞ; yÞÞf ðyÞ dy R0u u a
0 bðqu ðyÞÞf ðyÞ dy R u a
ð1 þ lÞtðqa
u ðuÞ; uÞ 0 qu ðyÞf ðyÞ dy
cðqa
;vÞ tol qa
tol
¼ tðqa
tol ; vÞ
dv Oðqa
tol ; vÞf ðvÞ dq þ
R v qOðqa
;yÞ tol 0
f ðyÞ dy ¼ l
R v 0
ta
tol
qcðqa
;yÞ tol qq
f ðyÞ dy
a
Oðqa
; vÞf ðvÞ dv dt ¼ lqtol F ðvÞ R v tol a
a
ðOðqtol ; yÞ lðcðqtol ; vÞ cðqa
tol ; yÞÞÞf ðyÞ dy R0v a
a
ðcðq ; vÞ cðq ; yÞÞf ðyÞ dy tol tol R0v a
0 bðqtol ÞfRðyÞ dy v ð1 þ lÞ 0 cðqa
tol ; vÞf ðyÞ dy
4. Contracts comparison Tables 2 and 3 summarize contracts characteristics. Recall that the general contract consists of an optimal screening mechanism. The uniform contract offers a payment that is proportional to the surface of wetland created and allows farmers to choose the wetland size. The TOL contract proposes a given wetland size and transfer. All these contracts use available information only. In the informationgathering program, the authorities gather the necessary information to offer an optimal contract. It is straightforward to verify that the general contract yields a higher expected social welfare surplus than that obtained with a uniform or a TOL contract.20 One could say that general contracts are optimal contracts based on available information whereas uniform and TOL contracts are suboptimal. The farmer never prefers the information-gathering program, which leaves her for sure with zero profit from wetland creation, whereas the other contracts may yield positive profits. Again it is useful to underline the role played by the excess burden (l) to compare the contracts further. 4.1. No excess burden 4.1.1. Contract characteristics The general and information gathering contracts produce wetland size and environmental surplus that are identical to those obtained with the TOL contract with complete information 20
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm
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Table 3 Contract properties with asymmetric information General contract ta
g ¼
R y qcðqa
g ;iÞ 1 qy qa
y g
qa
g solves
qOðq;yÞ qq
¼l
di þ
cðqa
g ;yÞ qa
g
2 a
F ðyÞ q cðqg ;yÞ qyqq f ðyÞ
a
R y F ðyÞ qcðqg ;yÞ a
f ðyÞ dy qy 0 Oðqg ; yÞ l f ðyÞ a
Ry qcðqg ;yÞ dy 0 F ðyÞ qy Ry a
0 bðqg Þf ðyÞ dy R y ðyÞ qcðqa
g ;yÞ ð1 þ lÞ 0 Ff ðyÞ þ cðqa
g ; yÞ f ðyÞ dy qy
W a
g ¼ FS a
g ¼ ES a
g ¼ TS a
g ¼
Information gathering ta
ig ¼ qa
ig solves
tðq tol ðyÞ; yÞ qOðq;yÞ qq ¼ 0
W a
ig ¼
Ry
FS a
ig ES a
ig
¼ ¼
0 Ry
TS a
ig
¼
0
Oðq tol ðyÞ; yÞf ðyÞ dy ð1 þ lÞI
bðq tol ðyÞÞf ðyÞ dy R y ð1 þ lÞ 0 ðcðq tol ðyÞ; yÞÞf ðyÞ dy þ I 0
a
(q tol ¼ qa
ig ¼ qg ) because, in these contracts, the wetland size maximizes the potential social
welfare surplus (qOðq;yÞ qq ¼ 0). The TOL wetland size with asymmetric information maximizes the R v qOðqa ;yÞ expected potential social welfare surplus instead ( 0 qqtol f ðyÞ dy ¼ 0). In the uniform contract, qcðqa
u ðyÞ;yÞ qq
¼ ta
u ). The transfer in the general contracts R y qcðqa
g ;iÞ di; which is positive and exceeds the transfer with information gathering by the term q1a
y qy g
wetland size maximizes the farmer’s profit (
represents the average informational rent per unit of wetland. Contract characteristics in TOL and uniform contracts depend on plot distribution: the lower the variance of y, the more the results obtained in Section 2 are likely to hold. If variance is relatively high, comparisons are more difficult. Fig. 2 illustrates wetland sizes in each contract. Diagram A shows a case in which a uniform contract yields a smaller wetland than a TOL contract and diagram B shows the alternative case. The optimal TOL wetland size is found at the R v qcðq;yÞ intersection of the curves db qq f ðyÞ dy. The optimal uniform wetland size is found at the dq and 0 intersection of
qcðq;yÞ qq
cðqa
u ðuÞ;uÞ . qa
u ðuÞ qcðq;yÞ db 21 qq with dq.
with ta
u ¼
at the intersection of
The optimal wetland size in the general contract is found
Rv qcðq;yÞ qcðqa ;yÞ a
Here we assume that 8q; 0 qcðq;yÞ qq f ðyÞ dyo qq and tu 4 qq . This is not always true but does not affect the result that wetland sizes can be smaller or larger in the TOL compared with the uniform contract. 21
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Marginal costs and benefits
Marginal costs and benefits
∂c(q, θ ) ∂q
∂ c(q, θ ) ∂q
∂c(q, θ ) f (θ )dθ ∂q 0 v
tu
tu
∫
a*
a*
v
∫
0
∂c(q, θ ) f (θ )dθ ∂q
db(q ) dq q
a* q a* qua* qtol
(A)
db(q ) dq q
a* q a* qtol qua*
(B)
Fig. 2. Wetland size in uniform and TOL contracts: (A) Elastic costs, unelastic benefits and (B) elastic benefits, unelastic costs. Marginal costs and benefits
Elastic costs, Unelastic benefits ∂c(q, θ ) ∂q
Range for tu and
ttol
a*
∂c(q,θ ) ∂q
db(q ) dq
db(q ) dq
ttol
Range Range for
(A)
∂c(q, θ ) ∂q
Range
a*
qua*
∂ c(q, θ ) ∂q
∂c(q,0) ∂q
for tu and
for
Elastic benefits, Unelastic costs
Marginal costs and benefits
a* qtol
a*
a*
∂c(q,0) ∂q
q Range for (B)
a* qtol
q Range for
qua*
Fig. 3. Contract comparison.
Fig. 3 illustrates how the maximum range for transfer and wetland size (i.e. with u ¼ v ¼ y) depends on the elasticity of wetland creation benefits and costs to changes in wetland size.22 In 22
The curve qcðq;yÞ qq .
R v qcðq;yÞ 0
f ðyÞ dy is not drawn in the diagram but must obviously be located between the curves qcðq;0Þ qq and
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Fig. 3A, benefits from wetland creation are relatively inelastic to wetland size, which narrows the range of possible transfer sizes in both contracts. The range of TOL wetland sizes is large— because of high variance in y. In contrast to that, a more elastic cost narrows the wetland size range in the uniform contract. So if costs are elastic, a uniform contract is likely to yield a wetland size closer to qa .23 In Fig. 3B, benefits are much more elastic to wetland size so the range of possible TOL wetland sizes is small even though the variance in y is high. Here as well, a cost, which is more elastic to wetland size, narrows the wetland size range in the uniform contract. So if costs are very inelastic, a TOL is likely to yield a wetland size closer to qa compared with a uniform contract. These results relate to the traditional discussion about whether one should regulate price or quantities [25]. Transforming the TOL threshold plot into a wetland yields no potential welfare surplus, but transforming the uniform contract threshold plot yields a potential social welfare surplus equal to the average marginalvalue of a change in the threshold plot on the potential social welfare surplus R u qOðqa
ðyÞ;yÞ dqa
f ðyÞ u ðyÞ u dy). So threshold plots differ in both contracts unless they are both ( 0 qq dt f ðuÞdu dt
equal to y; whether u4v or v4u depends on plot distribution. 4.1.2. Welfare surpluses The expressions of the social welfare surpluses are limited to the potential welfare surplus O except in the information gathering contract. The wetland sizes being the same in general and information gathering contract, the expected social welfare surpluses differ only by the term a
Io0. The social welfare is higher in the general contract (W a
g 4W ig ) because the informational rent corresponds to a transfer between interest groups, which is free of charges due to zero excessburden. In contrast, the cost of acquiring information is a pure welfare loss. Also the only difference between the expected taxpayers surpluses in those contracts are the terms representing the surplus that the planner must pay to make the farmer reveal the true y and the cost of acquiring the missing information, respectively. Z y qcðq tol ; yÞ a
a
FðyÞ dy4I. TSig 4TSg 3 qy 0 Ry qcðqa ;yÞ The expected farmer’s surplus in the general contract is 0 FðyÞ qyg dy, which is positive (H3), and thus larger than the farmer’s surplus in the information gathering contract. The social welfare difference between uniform and TOL contracts depends on wetland size and threshold characteristic Z u Z v a
a
a
a
ðOðqu ðyÞ; yÞ Oðqtol ; yÞÞf ðyÞ dy ðOðqa
W u W tol ¼ tol ; yÞÞf ðyÞ dy 0 u |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} a
b
a is the difference in welfare surpluses due to different wetland sizes. The information in Table 1 together with assumptions (H1) and (H5) imply that q tol and thus qa maximize O 23
Recall that qa is at the intersection of
qcðq;yÞ qq
and
dbðqÞ dq .
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Table 4 Contracts comparisons Case 1
Case 2
Case 3
Elastic costs Inelastic costs a
a
a
jqa
tol q jojqu q j a4b a
W a
tol oW u ðyÞ
Inelastic costs Elastic benefits a
a
a
jqa
tol q j4jqu q j aob a
W a
tol 4W u ðyÞ
Elastic costs and benefits or Inelastic costs and benefits a
a
a
jqa
tol q j_jqu q j a_b a
W a
tol _W u ðyÞ
and if O is symmetric, 8y;
a
a
a
a
a
Oðqa
u ðyÞ; yÞ4Oðqtol ; yÞ () jqtol q j4jqu ðyÞ q j.
So if O is not too asymmetric, so that 8y; q; Oðqa q; yÞ Oðqa þ q; yÞ, one would expect a wetland size close to qa to yield a higher potential social welfare from wetland creation than a wetland size that is not so close. b is the difference in welfare surpluses due to differences in threshold plots. It is the expected social welfare surplus obtained from creating a wetland using a TOL contract on plots with characteristics qOðq;yÞ between the two thresholds. Note that b40 because Oðqa
tol ; vÞ ¼ 0 and qy o0 (H3). If wetland creation costs are relatively elastic compared to benefits (case A in Fig. 3 and case 1 a
in Table 4), it is likely that Oðqa
u ðyÞ; yÞ4Oðqtol ; yÞ for most values of y implying that a would be positive and if a is large enough the gain in welfare surplus due to the opportunity to create wetland of size closer to optimal size could be larger than the loss due to differences in threshold plots. A uniform contract would then most probably yield higher social welfare than a TOL contract. If costs of wetland creation were relatively inelastic compared to benefits (case B in Fig. 3 and case 2 in Table 4), a would probably be negative and the TOL contract would yield higher social welfare than the uniform contract. When costs and benefits are neither very elastic nor inelastic, it is difficult to tell which effect dominates (case 3 in Table 4). It is difficult to compare each interest group’s surpluses in the TOL, uniform, and general contracts. If the distribution of plot characteristics has low variance, by continuity, the results obtained with complete information still yield. The farmer would rather sign a uniform contract whereas the taxpayers would prefer a TOL contract. If plot characteristics have high variance, the differences in respective surpluses must be calculated from case to case. There is no evidence that the farmer’s surplus should be higher in the uniform contract. If the transfer can be determined accurately but not the wetland size, as in case A, the farmer’s surplus could very well be much higher in the TOL but it could also be much lower. If the farmer had a plot with a high characteristic— higher than the threshold farm’s—she might prefer a general contract that yields non-negative profits for sure to a TOL or a uniform contract that would yield a negative profit and be refused. 4.2. A positive excess burden By continuity, the results obtained in Section 4.1 must hold at least for small excess burden but they may not hold if excess burden is large. When l40, the general contract does not always yield
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a higher social welfare than the information gathering contract. Relation (12) gives a necessary and sufficient condition for that statement to remain true. Z y 1 F ðyÞ qcðqa
g ; yÞ
a
Oðqtol ; yÞ Oðqg ; yÞ þ l f ðyÞ dy DðlÞX0. (12) I4 qy 1þl 0 f ðyÞ So if information is cheap, information gathering yields a higher social welfare surplus than a general contract. The term DðlÞ is always positive because (H3) and Oðq tol ; yÞ4Oðqa
g ; yÞ for all farm characteristics. The general contract yields smaller wetlands and higher farmer’s profit than information gathering because of the necessity to keep the transfer non-increasing in y so q tol ¼
a
a
a
qa
ig 4qg and FS tol ¼ FS ig pFS g . Information gathering yields a lower taxpayers’ surplus than if information had been complete (TS tol 4TS a
ig ). The surplus is also lower for the taxpayers compared to the general contract if information is expensive enough— R y qcðqa
;yÞ F ðyÞ g a
I4 0 qy f ðyÞ þ cðqg ; yÞ cðqtol ; yÞ f ðyÞ dy. Similarly, (13) respectively (14) give necessary and sufficient conditions for a TOL, respectively, a uniform contract to yield a higher social welfare than information acquisition. ! Z y 1 (13) Oðq tol ðyÞ; yÞf ðyÞ dy W a
I4 tol , ð1 þ lÞ 0 1 I4 ð1 þ lÞ
Z
y 0
! . Oðq tol ðyÞ; yÞf ðyÞ dy W a
u
(14)
So if information is cheap, information gathering yields a higher social welfare surplus than a TOL contract or a uniform contract. Further contract comparisons are not obvious except for some considerations about wetland size. Proposition 4. The Spence–Mirrlees condition (H4) is necessary and sufficient for the wetland size in the TOL contract to decrease when the excess burden increases. Proof. Using the equations for wetland size and threshold plot one can show24 that 1 0 Z v dv C BZ v qOðqa
qcðqa
dqC B a
tol ; yÞ tol ; yÞ . f ðyÞ dy ¼ lB f ðyÞ dy q ta
FðvÞ tol tol dv C A @ 0 qq qq 0 dt |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} S
So the sign of S determines whether wetland size increases or decreases when excess burden increases: if S is positive, the TOL wetland size decreases when l increases. Using condition dv dv a
a
ta
tol qtol ¼ cðqtol ; vÞ to calculate dq and dt , and integrating S by parts, we obtain R v q2 cðqa
;yÞ tol S ¼ 0 qqqy FðyÞ dy. So S40 if and only if (H4) holds. & What happens with wetland size in a uniform contract depends on the sign of 24
du dl.
See appendix available on http://www.beijer.kva.se/Staff/Anne-SophieCr%E9pin/Anne-Sophie.htm
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5. Discussion This article shows that the choice of instrument for wetland creation has important welfare implications and may yield quite different social welfare surpluses and distribution between interest groups. An appropriate instrument choice could result in social welfare gains. This article also indicates situations in which respective contract is preferable. If excess burden is zero or very small, one can measure a contract’s performance by how close to optimum the contract is with regard to wetland size, transfer and threshold plot. Uniform contracts seem a simple and rather accurate way to make farmers create wetlands if the farm characteristic has high variance and costs are relatively elastic to changes in wetland size: The social planner has a good idea about the optimal transfer and knows then that the farmer would pick a wetland size close to optimal with a uniform contract. If instead variance was low, or if wetland creation benefits were elastic as well, a TOL would be better because the social planner could pick a wetland size close to optimal. Screening mechanisms like in the general contract have been criticized for being of little practical use because the derived transfer scheme is often too complicated.25 In addition, general contracts yield small gains when uniform or TOL contracts are accurate. Uniform or TOL contracts are much more straightforward than general contracts, and the farmer need not work too hard to find out if they are worthwhile accepting. This may explain why general contracts have not been used. Another explanation, not studied in this article, could be the presence of other costs associated with this contract, for example, transaction costs.26 When costs are inelastic to wetland size, the social planner cannot pick a transfer close to optimal and a general contract or information gathering yield large social gains compared to TOL or uniform contracts. In such a situation, the cost of information determines, which contract is superior. When excess burden is large, picking suboptimal wetland sizes and transfer or making the farmer reveal the true plot characteristic induces a larger welfare loss. So information acquisition combined with a TOL contract gains advantages and might even be superior to all other alternatives. In this article, the authorities can only gather all the information necessary or none. If partial information acquisition was possible, one could create a wetland creation program superior to all other programs by combining partial information gathering with a screening mechanism. Empirical evidence shows that uniform contracts and information gathering associated with a TOL offer have been the main type of incentives used in practice for wetland creation. This indicates that acquiring information may have been cheap and/or excess burden large in cases when information gathering was preferred. In cases when uniform contracts were preferred one should verify that variance in the farm characteristic was high, and costs relatively elastic to changes in wetland size. Empirical verifications of these theoretical results require collecting information about land quality and the assessment of marginal costs and marginal benefit functions. Heimlich et al. [12], and Sundberg and So¨derqvist [24] have reviewed the major 25
Some of the weaknesses of those types of models are discussed, for example, in [11,16] or [1]. Such costs could be large for the farmer in a screening mechanism, which would require each contract to be compared to all others to chose the one that yields the highest profit. 26
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valuation studies in the field in the US and in Sweden. None of the studies discussed contained the information necessary to verify these theoretical results. This suggests that contracts may not be well designed and adapting the contracts to each particular situation could yield welfare gains. This requires collecting better information about land quality, and marginal costs and benefit functions. This article shows also that program choices have distributional impacts between taxpayers, farmers and people who value environmental quality. So interest groups may want to lobby for favorable wetland creation programs. In this lobbying game, the farmer has an advantage against the other players because she knows the true plot characteristic and can calculate the exact surpluses in each contract, not only expected values. In practice the farmers’ high bargaining power could be a factor explaining the use of uniform contracts rather than information acquisition. If this is true, today’s wetland creation program may reflect the fact that farmers in the US and in the Ka¨vlinge River basin have had less bargaining power than farmers in England or in the rest of Sweden. The incentives studied here are once and for all incentives. In practice, wetland creation programs are set for some period in time—most often 10–20 years—and can be renewed for further periods. If the game is repeated, the social planner may learn from the farmer’s choice in previous periods. If the farmer rejected the TOL contract in a previous period, the social planner knows only that the transfer was too low compared to the wetland size. In contrast to that the farmer’s choice of uniform or general contract implies that the social planner obtains the missing information about soil quality. She has then complete knowledge about soil quality in the beginning of the second period27 and can implement an optimal wetland creation from that point in time.
Acknowledgments I thank participants at several conferences and seminars for giving me valuable comments on earlier drafts. Special thanks to M. Dufwenberg, J. Ha¨ckner, P.-A. Jayet, T. Lindahl, K.-G. Lo¨fgren, K.-G. Ma¨ler, E. Nævdal, H. Scharin, T. So¨derqvist, and to two anonymous referees. I also thank J. Petersen from American Writing and Editing. This research was initiated within the research project Ecological-Economic Analysis of Wetlands: Functions, Values and Dynamics (ECOWET). Funding from the EU/DGXII Environment and Climate Programme (Contract No. ENV4-CT96-0273) and the Swedish Council for Planning and Coordination of Research (FRN) is gratefully acknowledged.
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