Accumulation of Trace Metals by Mangrove Plants in Indian Sundarban Wetland: Prospects for Phytoremediation
Summary (4 min read)
1 Introduction
- Imagine a homeowner trying to sell her house to a prospective buyer.
- The authors depart from sequential screening by making the following assumptions.
- In particular, they show that under the same conditions as in the sequential screening model of Courty and Li (2000), the seller gives up no information rent for the additional private information—all the information rent arises from the ex ante private information that the buyer has at the time of contracting.
- The reason that discriminatory disclosure can be profitable is that an appropriate two-way partitioning, together with a selling mechanism, can achieve the same surplus with the dominated type as under the perfect signal structure, while reducing the information rent of the dominant type.
2.1 Basic Setup
- Consider the following two-period sequential screening model.
- For simplicity, the authors assume that all information of the buyer about ω besides his ex ante type θ is under the seller’s control.
- Given the consistency requirement that each G (·|θ, σ) is generated from the same prior distribution F (ω, θ), this can be achieved by requiring the corresponding conditional distributions functions {G (·|θ, σ)} to satisfy “convex order,” defined as follows: Definition 1 (Convex Order).
- For most of their results, the authors assume only that for all θ the signal structure corresponding to the distribution F (·|θ) of the true value when the seller fully discloses all the additional private information dominates any other σ in S.
- The literature has proposed several ways to quantity how informative signal structures are: (i) Blackwell (1951) sufficiency, (ii) Lehmann (1988) and Perciso (2000) accuracy, and (iii) Athey and Levin’s (2001) monotone information order with supermodular preferences.
2.2 Full Disclosure and Partial Disclosure
- The above framework incorporates the model of sequential screening of Courty and Li (2000) as a special case where the set of feasible signal structures is a singleton.
- This way of modeling full disclosure gives rise to what Eso and Szentes (2007) refer to as the “orthogonal” decomposition of all the private information about ω into θ, which the buyer always knows, and s~σ, which is independent of θ. 7.
- In orthogonal disclosure, since the distribution of sσ is independent of θ, the ordering of {F (·|θ)} by first-order stochastic dominance with respect to θ is passed on without change to the family of distributions {G(·|θ, σ)} with respect to θ for any σ.
- This is special because the signal realization depends on the true ex ante type θ only through the true value.
- Orthogonal disclosure is a special model in the framework the authors have set up here, and is no more natural than general disclosure policies that they study in an environment where the seller does not know the true type of the buyer when she releases additional private information.
3 Discrete Types
- The authors start with a discrete setting where the ex ante types is binary, θ ∈ Θ ≡ {H,L} , with probability fH and fL respectively.
- For convenience, the authors slightly adapt the notation to the binary setting.
- Suppose that under any signal structure σ, conditional on the ex ante type θ, the posterior estimate v of the true value ω is distributed according to Gθ(·|σ) over fixed, common support [ω, ω].
- Assume that Gθ(·|σ) has positive, continuous density gθ(·|σ) under the perfect signal structure σ = σ, and GH(·|σ) first-order stochastic dominates GL(·|σ).
- The unconditional mean values of the two types satisfy µH > µL.
3.1 A General Characterization
- An option contract (a, p) consists of a non-refundable advance payment a in period one for option of buying at price p in period two after the buyer forms posterior estimate v.
- If the authors impose the restriction on S that GH(v|σ) first-order stochastic dominates GL(v|σ) for any σ ∈ S, then they can strengthen Proposition 1 in two ways.
3.2 Direct Disclosure
- In Section 2, the authors have defined direct disclosure as a mapping σ : Θ×Ω → ∆S from reported ex ante type θ̃ and true value ω to a distribution over the signal space S. Monotone partition signal structures include the perfect signal structure as a special case.
- The advance payments âL and âH are chosen so that both (IRL) and (ICH) bind.
- This is why the authors need to exclude the possibility of full surplus extraction from the characterization in Proposition 1. with ε < 12 .
- Consider the following disclosure policy: if the buyer reports type H, the seller chooses σ which reveals the true value ω; if the buyer reports type L, the seller chooses σ[c] which only reveals to the buyer whether the true value ω is above or below c = 12 .
In contrast, if the seller discloses all information to both types of buyers, the problem reduces
- To sequential screening of Courty and Li (2000).
- The resulting allocation involves distortion and the type-H buyer enjoys strictly positive information rent.
- When condition (2) fails,14 the authors can apply Proposition 1 to characterize the optimal monotone partition signal structure σ[kL] for type L. Proposition 3 Suppose condition (2) fails.
3.3 Optimal Disclosure
- Note that condition (3) ensures that type H would not buy at the price of µ+L(c) when he learns nothing, which is weaker than condition (2) for full surplus extraction with direct disclosure.
- Then, for any signal structure σL for type L and its corresponding selling mechanism, there exists a binary signal structure for type L that reveals no information to deviating type H and is at least as profitable to the seller.
- Corollary 1 Suppose that condition (3) fails.
L that can be generated from partitioning continuous distributions of posterior estimates, the
- Optimal one is a generalized monotone two-way partition signal structure.
- Proposition 5 Suppose that condition (3) fails.
- The intuition behind Proposition 5 is clear from Corollary 1, which already suggests that the optimal signal structure for type L takes the form of a generalized monotone partition signal structure, because the latter maximizes the seller’s profit when the partition threshold is optimally chosen.
4 Continuous Types
- Given a signal structure σ ∈ S, each type θ is represented by a distribution G (v|θ, σ) of posterior estimate v.
- For the first two subsections, the authors restrict their attention to “continuous disclosure” where each distribution G (·|θ, σ) has a finite and positive density g (·|θ, σ).
4.1 A General Characterization
- By the revelation principle, the authors focus on direct revelation mechanisms {{x (θ, v) , y (θ, v)}} together with disclosure policy {σ(θ)}.
- That condition (AM), together with (FOC1), is sufficient for (IC1).
- This validates the firstorder approach and is used in the next subsection to generate sufficient conditions for the optimality of full disclosure.
4.2 When Full Disclosure Is Optimal
- In this subsection the authors identify information environments for which full disclosure is optimal among continuous disclosure policies.
- These information environments share a common theme that the disclosure policy does not affect the informativeness measure.
- The authors present two information environments studied in the literature, the first from Eso and Szentes (2007) and the second from Courty and Li (2000), in which informativeness measure I (θ, v, σ) is linear in v and independent of σ.
- Therefore, by Proposition 7, full disclosure is optimal if the virtual surplus function J (θ, v, σ) is also monotone in both θ and v. Example 2 Suppose type θ is drawn from support [ θ, θ ] with density f (·) and distribution F (·).
As a result, the informativeness measure is
- The aforementioned example of Eso and Szentes (2007) is a special case.
- For their next result, the authors assume that the family of distributions {G (·|θ, σ (θ))} is rotationordered.
- Therefore, the authors have the following proposition, and they omit its proof.
- Graphically, the rotation order requires that two distribution functions cross each other only once.
4.3 Full Disclosure Is Not Optimal under Hazard Rate Dominance
- So far in this section, the authors have restricted their attention to continuous disclosure policies that are associated with continuous and differentiable cumulative distributions {G (·|θ, σ (θ))} of posterior estimate v.
- The authors will add direct disclosure back to the seller’s feasible set of disclosure policies, and show that full disclosure is then not optimal in general.
- Let G (·|θ, σ) and g (·|θ, σ) denote its cumulative distribution and density respectively.
It is easy to see that distributions {G (ω|θ, σ)} are ordered in first-order stochastic dominance
- As a result, the sufficient conditions for the first-order approach are satisfied (Courty and Li, 2000).
- It can be verified that if the seller adopts the full disclosure policy, under the optimal mechanism the resulting allocation does not maximize the expected surplus, and the seller has to leave positive information rent to some high type buyers.
- The seller discloses to all types of buyer whether ω is above or below 12 , and charges price 3 4 in period two.
- This disclosure policy, together with the posted price, extracts all the surplus.
5 Discussion
- In this section the authors discuss how their analysis is related to Eso and Szentes (2007).
- First, the seller’s profit in the hypothetical setting is an upper-bound on what the seller can achieve in the original setting; and second, this upper-bound is attainable in the original setting.
- And thus their direct approach is more general.the authors.
- It is true that modeled as orthogonal disclosure, partial disclosure can never strictly raise the seller’s profit compared to full disclosure, which explains the claim about the optimality of full disclosure in Eso and Szentes (2007).
- In the continuous limit, however, this hypothetical profit can be approximated, consistent with the result of Eso and Szentes (2007).
5.1 Hypothetical Setting May Not Deliver Profit Upper-bound
- Consider first the discrete setting of Section 3.
- As the authors have shown in Section 3 and Section 4, full disclosure is not optimal in general, regardless of whether full surplus extraction is attainable.
- The seller’s choice is more constrained compared to the case with direct disclosure.
- The information content of the resulting quantile, however, depends on the underlying distribution of the original type-dependent signal.
5.2 Hypothetical Profit Is Not Attainable with Discrete Types
- The authors again take the setting with discrete ex ante types, but now assume orthogonal disclosure.
- Then the authors consider the original setting where the seller can release, without observing, the realized quantile.
- Denote by θi = θ + iδ the i-th type with θ0 = θ and θn = θ. Let π~σ (δ) denote the seller’s profit in the hypothetical setting, and π (δ) the maximal profit attained under the optimal menu of option contracts in the original setting.
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"Accumulation of Trace Metals by Man..." refers methods in this paper
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...Comparing our data with Effects Range Low (ERL) and Effect Range Medium (ERM) values (Long et al. 1995), majority of the trace metals (except Cu, Ni and Hg) showed lower concentrations than ERL....
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Frequently Asked Questions (13)
Q2. What are the main adaptive strategies for the removal of trace metals in mangrove plants?
These include sediment-plant interactions, modifications of anatomical structure of the plant organs as well as intracellular binding mechanisms.
Q3. What are the possible mechanisms responsible for restricted uptake and translocation within plants?
Possible physiological mechanisms responsible for restricted uptake and translocation within plants include cell wall immobilization, complexation with substances such as phytochelatins and barriers at the root endodermis (Baker and Walker 1990).
Q4. How many sediment samples were collected at each site?
Sediment samples were collected in triplicate from top 0–5 cm of the surface at each sampling site (Corsolini et al. 2012) over an area of 1m x 1m using a clean, acid-washed plastic scoop.
Q5. Why did Middleburg et al. (1996) have basic pH values?
According to Middleburg et al. (1996) mangrove sediments have basic pH values due to the limited buffer capacity of these sediments.
Q6. What was the method used for the determination of total metal(loid) contents?
The determination of total metal(loid) contents was performed using current analytical methods, including: Atomic Absorption Spectrometry (AAS, SOLAAR M Series equipment from Thermo–Unicam) for Co, Cr, Cu, Fe, Mn, Ni, Pb and Zn; coupled graphite furnace AAS for As and Cd; and a hydride generation system (HGS) linked to an atomic absorption for Hg.
Q7. What are the main reasons for the lack of standard norms and strict regulation about fuel being used?
The lack of standard norms and strict regulation about fuel being used in mechanized boats for ferrying and fishing throughout the year lead to deposition of metals.
Q8. What is the role of mangrove plants in extracting heavy metals from contaminated sites?
The present result suggests the role of mangrove plants in extracting heavy metals from contaminated sites might be dependent on sediment metal availability.
Q9. What are the mechanisms of sequestration of metals in mangrove plants?
These mechanisms include the sub-cellular compartmentalization of the metal, namely in vacuoles, and the sequestration of the metal by specially produced organic compounds, like phytochelatins, concentrating metal in the plants roots (Ross and Kaye 1994).
Q10. What is the role of the two organs in the plant?
Thus these two organs act as a barrier for metal translocation and protect the sensitive aerial parts of the plants from metal contamination (Pahalawattaarachchi et al. 2009).
Q11. What are the suggested mechanisms for reduced bioavailability of metals in sediments?
Suggested mechanisms for reduced bioavailability of metals in sediments are precipitation as sulphides under anaerobic conditions, organicD ownl oade dby [U nive rsid ade deT rasos-M onte se Alto Dou ro] at0 4:51 08 July 201 5Accumulation of Trace Metals by Mangrove Plants in Sundarban 889Fig.
Q12. What is the maximum value of the BCF in excoecaria agalloch?
The bio- concentration factor (BCF) showed its maximum value (15.5) in Excoecaria agallocha for Cd, suggesting that it can be considered as a high-efficient plant for heavy metal bioaccumulation.
Q13. What is the admixture of sand and clay in sediment samples?
Regarding texture, sediment samples exhibit a variable admixture of sand (1.80–15.45%), silt (32.58–38.93%) and clay (51.98–59.28%).