#### 2.1. A Regulated Open Access Fishery with Coastal-Habitat Linkages

The starting point for the valuation approach developed in this paper is the dynamic model of coastal-habitat-fishery linkages developed in Barbier [

6]. The underlying assumption of the model is that a near-shore fishery depends on a coastal wetland habitat, such as salt marsh or mangroves, as a breeding habitat and nursery. Consequently, any change in the coastal wetland habitat is likely to affect the biological growth of the fishery, which is usually modeled through some influence on carrying capacity.

Defining

X_{t} as the stock of fish measured in biomass units, any net change in growth of this stock over time can be represented as

Thus, any expansion in the fish stock occurs as a result of biological growth in the current period $F\left({X}_{t},{S}_{t}\right)$ net of any harvesting $h\left({X}_{t},{E}_{t}\right)$, which is the function of the stock as well as fishing effort E_{t}. The influence of the wetland habitat area S_{t} as a breeding ground and habitat on growth of the fish stock is assumed to be positive $\partial F/\partial {S}_{t}>0$, as an increase in wetland area will mean more carrying capacity for the fishery and thus greater biological growth.

As the near-shore fishery is open access, effort in the next period will adjust in response to the profits made in the current period. Letting

$p\left({h}_{t}\right)$ represent landed fish price per unit harvested,

w the unit cost of effort and

$\varphi >0$ the adjustment coefficient, then total effort in the fishery changes according to

Assume that biological growth is characterized by a logistic function

$F\left({X}_{t},{S}_{t}\right)=r{X}_{t}\left(1-{X}_{t}/K\left({S}_{t}\right)\right)$, and harvesting by a Schaefer production process

${h}_{t}=q{X}_{t}{E}_{t}$, where

q is the catchability coefficient,

r is the intrinsic growth rate and

$K\left({S}_{t}\right)=\alpha \mathrm{ln}{S}_{t}$ is the impact of coastal wetland area on carrying capacity

K_{t} of the fishery. The market demand function for harvested fish is iso-elastic, i.e.,

$p\left({h}_{t}\right)=k{h}_{t}^{\eta},\eta =1/\epsilon 0$. Substituting these expressions into Equations (1) and (2) yields

Following Homans and Wilen [

13], it is assumed that an outside regulatory body imposes a simple quota rule to ensure that current harvest does not over-exploit the stock. Here, the regulatory rule is that harvest must always be a fixed proportion

b of the current stock, i.e.,

${h}_{t}=b{X}_{t}$. Thus,

b represents the quota on current harvest-stock ratio, or the regulatory quota for short. Since the Schaefer production function dictates that

${h}_{t}=b{X}_{t}=q{X}_{t}{E}_{t}$, the implication of this rule is that effort will be fixed at

$E=b/q$. Total effort in the fishery now depends on the regulator’s decision on how large a proportion

b of the stock can be safely fished. This can be stated in terms of the following proposition:

**Proposition** **1.** If a regulatory rule is imposed that harvest is a fixed proportion b of the current stock, then total effort in the fishery is constant and determined by the size of the regulatory quota b, i.e., $E=b/q$.

Fixing effort in the fishery implies that Equation (4) becomes

$k{\left(b{X}_{t}\right)}^{\eta +1}=wE=wb/q$. This implies that rents in the fishery will be totally dissipated. Intuitively, as total effort by all fishers is fixed, some will be able to fish enough to make profits, but others will not. The latter will leave the fishery to be replaced by those attracted by the profits, but overall effort will remain the same, and the process will repeat itself until eventually zero rents are earned throughout the fishery. The result is a unique value for fish biomass

Thus, fish stock is also constant in the regulated fishery. Note that the impact of a change in the regulatory quota on the stock will depend on the elasticity of demand for harvested fish ε. That is, if demand is relatively inelastic

$-1<\epsilon <0$ (implying

$\eta <-1$), then

$dX/db<0$. However, for elastic demand

$\epsilon <-1$ (

$-1<\eta <0$), then

$dX/db>0$. The following proposition follows:

**Proposition** **2.** If the market demand for fish is relatively inelastic $-1<\epsilon <0$, then the fish stock will decrease (increase) with a positive (negative) change in the regulatory quota b; if the market demand is relatively elastic $\epsilon <-1$, the fish stock will increase (decrease) with a positive (negative) change in b.

As fish biomass is unchanging and governed by (5), then (3) becomes

Since the right-hand side of Equation (6) is positive, an important implication is:

**Proposition** **3.** The regulatory quota b must always be less than the intrinsic growth rate r of the fish stock.

Equations (5) and (6) can be solved to determine the regulatory quota b that yields this equilibrium outcome for the fishery. Once b is known, it is possible to find X from Equation (5), E from Proposition 1, and then harvest h.

Valuing the impact of the change in coastal habitat area

S_{t} can now be determined by examining how this change influences the equilibrium harvest outcome

h and thus the consumer surplus for marketed fish. For example, if

h^{0} is the initial harvest in the fishery and

h^{1} is harvest after the change in coastal habitat area occurs, then the resulting change in consumer surplus

CS will be

However, the value of this habitat–fishery linkage will depend on whether or not the regulatory quota b is adjusted in response to the change in S.

In the case where such an adjustment occurs, then the solution for

b depends on the current size of the coastal habitat area, i.e.,

$b=b\left({S}_{t}\right)$. From substituting Equations (5) in (6), one can find

As Equation (8) is currently specified, the impact of a change in S_{t} on the regulatory quota $db/d{S}_{t}$ is ambiguous. Once this effect is known, Propositions 1 and 2 can be invoked to determine the impacts on fishing effort E and stock X, respectively. The ensuing changes in harvest and consumer surplus follow.

In the case where the regulatory quota b does not change, fishing stock adjusts in response to the change in coastal habitat area, i.e., from Equation (6).

As this impact is always positive, it leads to

**Proposition** **4.** If the regulatory quota b does not adjust in response to a change in the coastal habitat area S_{t}, then fish stock will increase (decrease) in response to an increase (decrease) in S_{t}.

Because there is no adjustment to b, then fishing effort remains unchanged (Proposition 1). However, there is an impact on harvest, since $dh=bdX=\frac{b\left(r-b\right)\alpha}{rS}dS$. The result is a change in consumer surplus as indicated by Equation (7), which is the value attributed to the decline or increase in the coastal habitat supporting the fishery.

To summarize, the regulatory rule ${h}_{t}=b{X}_{t}$ imposed on the open access fishery with coastal habitat linkages leads to a bioeconomic equilibrium that is fully recursive. Valuing any changes in the coastal habitat supporting the fishery will depend on whether or not the regulatory quota b is adjusted in response to these changes. If the regulatory quota adjusts for any change in S_{t}, the result will be changes in both fishing effort and stock. Although rents are still fully dissipated, the resulting change in harvest will impact consumer surplus. If b does not adjust, then effort is unchanged but the stock of fish will respond to any change to coastal habitat area. Both harvest and consumer surplus are again impacted. However, these differing impacts are sufficiently important that they can affect significantly the value attributed to the coastal-habitat-fishery linkage.

#### 2.2. Case Study: Mangrove-Dependent Fisheries, Thailand

The above approach for valuing coastal habitat support for a regulated fishery is illustrated through application to the mangrove-dependent demersal and shellfish fisheries in Thailand, based on data from Barbier [

6].

Up to 38,000 households in around 2500 coastal communities engage in small-scale fishing activities, which are largely open access [

6]. These communities are located along the Southern Gulf of Thailand and Andaman Sea (Indian Ocean) coasts. Gill nets and both motorized and non-motorized small boats are the most common form of fishing gear used by artisanal fishers. Although a license fee and permit are required for fishing in coastal waters, officials do not strictly enforce the law and users do not pay. Currently, there is no legislation for supporting community-based fishery management, and regulation of the fisheries is negligible.

Based on data from Barbier [

15] that identifies which of Thailand’s artisanal demersal and shellfish fisheries depend on mangroves for breeding and nurseries, Barbier [

6] employs pooled time-series and cross-sectional regressions that yield the key biological parameters (

r, α), economic parameters (

k,

w,

q) for the two fisheries. This allows determination of the key relationships in Equations (5)–(9) necessary for valuing coastal-habitat linkages in a regulated open access fishery. In addition, evidence from domestic fish markets in Thailand suggest that the demand for fish is fairly inelastic, and an elasticity of −0.5 is assumed for the iso-elastic market demand function. These key parameter estimates for Thailand’s mangrove-dependent demersal and shellfish fisheries are summarized in

Table 1. In addition, the table indicates the estimated area of mangroves along the Gulf of Thailand and Andaman Sea supporting these fisheries.

The parameter estimates in

Table 1 are used in the model developed here to estimate the value of mangrove–fishery linkages for an open access fishery that is regulated according to the rule

${h}_{t}=b{X}_{t}$. The first step is solving conditions in Equations (5) and (6) to find the corresponding regulatory quota

b, and then

X,

E, and

h for each fishery. The second step is determining the changes in consumer surplus resulting from annual average changes in mangrove deforestation, depending on whether the regulatory quota adjusts or not.

In this valuation exercise, two different calculations of annual mangrove deforestation rates are used, based on high and low estimates for Thailand over 1996 to 2004 [

6]. The low estimate by the Royal Thai Forestry department is 3.44 km

^{2}; the high value by the UN Food and Agricultural Organization is 18.0 km

^{2}.