ARTICLE

# Adapting the designated area of geographical indications to climate change

Loïc Henry<fnref n="1" />,<fnref n="2" />

**Correspondence**

Loïc Henry, Université Paris-Dauphine PSL, LEDA, CNRS, IRD, 75016, Paris, France.
Email: loic.henry@dauphine.psl.eu

**Funding information**

Agence Nationale de la Recherche, Grant/Award Number: 16-CONV-0003

**Abstract**

This paper examines the agricultural supply relocation of products under geographical indication (GI) labels as an option to adapt to climate change. I develop a stylized framework that endogenously relates the delineation of the production area of the GI product to the distribution of specific geographical characteristics and their influence on the quality of the product and the corresponding comparative advantages. The model can then study how the GI production area responds to climate-related changes in the production conditions. The model shows that the GI production area can marginally expand as climate change worsens the production conditions, but it may disappear under more severe degradations. This opportunity to relocate current GIs hinges on striking a careful balance between mitigating climate-induced yield losses and altering quality, but it is also threatened by political economy barriers that govern the redistribution of GI rents.

**KEYWORDS**

adaptation, agriculture, climate change, geographical indication, land allocation, quality, wine

**JEL CLASSIFICATION**

L11, L15, Q13, Q54

# 1 | INTRODUCTION

One of the most pressing issues regarding climate change is its impacts on agricultural production (IPCC, 2019). As these impacts are likely to vary across space, reallocating crops to areas better suited to new climate conditions offers a promising adaptation margin (Costinot et al., 2016; Baldos et al., 2019; Gouel & Laborde, 2021). However, this type of adaptation may not be readily available

This is an open access article under the terms of the [Creative Commons Attribution License](https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2022 The Author. *American Journal of Agricultural Economics* published by Wiley Periodicals LLC on behalf of Agricultural & Applied Economics Association.

<footnote n="1">¹Université Paris-Dauphine PSL, LEDA, CNRS, IRD, Paris, France</footnote>

<footnote n="2">²Paris-Saclay Applied Economics, Université Paris-Saclay, INRAE, AgroParisTech, Palaiseau, France</footnote>
<figure><img src="image_1.png" /><figcaption>FIG URE 1 Number of GI labels in the EU quality labeling scheme. PDO designates protected designation of origin, PGI corresponds to protected geographical indication, and TSG is traditional speciality guaranteed. The PDO label is more binding, as the whole production process has to occur in the defined geographical area, whereas some stages of the production process within the defined area are needed for the PGI and TSG labels. DOOR database and eAmbrosia.</figcaption></figure>

for products that are defined precisely by where they are produced, as is the case for products with a geographical indication (GI hereafter) label.<fnref n="1" />

The quality of products under GI originates from a combination of climate, topography, geology, and soil characteristics that are specific to a region of production. The quality of wine, for example, is associated with the biophysical attributes of the land where the grapes have been grown. These characteristics, often termed as terroir, can be found only in some regions or even in very specific land parcels (Ay, 2021). To control quality, agricultural activities under GI are restricted in a designated production area, which is precisely delineated according to the presence of these characteristics. Well-known examples of GI products include Champagne, Napa Valley wines, and Parmigiano Reggiano cheese. Figure 1 illustrates the increasing number of products under GI labels in the EU. The EU commission reports a 7% share—and a corresponding amount of EUR 77 billion—for GI labeled products in the total sales value of the food and drink sector in the EU-28 in 2017. This share reaches 15% in France and 12% in Italy (European Commission and Directorate-General for Agriculture and Rural Development, 2021).

The restriction in the production area raises rent for landowners in the GI region, with possible welfare-deteriorating effects. However, it may also have welfare-enhancing effects. In particular, the GI label may alleviate the classical “lemons problem” (Akerlof, 1970). Thanks to the GI label, consumers can identify the origin of the product and its associated quality, thereby providing incentives to producers to supply high-quality goods (Mérel et al., 2021).

In this paper, I investigate the conditions under which the relocation of the supply of agricultural products under GI labels can be a strategy to adapt to climate change. To this end, I develop a

<footnote n="1">¹Geographical indications are labels that certify the geographical origin of a product so that it can be identified by consumers. The GI label grants property rights to the name of a location, to protect the producers from the misuse of their regional name. The WTO agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS, 1994) internationally recognizes GI labels as a legal tool comparable with trademark laws in that it enhances informational efficiency and restricts fraudulent behaviors (Menapace & Moschini, 2014). For details on these legal provisions, see Articles 22 and 23 of the TRIPS agreement.</footnote>
stylized framework to model the determinants of the decision to relocate. Specifically, it depends first on the ability to produce a good with sufficient quality outside the original area of production. Extending the exclusive production area to nearby parcels may mitigate climate impacts but at the expense of a change in the (real or perceived) quality of the product. Second, the GI protection system determines the degree of control in the definition of the production area. If carved in stone by the label, little margin is left for adaptation through land reallocation, and new adverse climate conditions may result in a significant drop in output. Third, the relocation redistributes the collective rent associated with the label. In this respect, the governance of GI labels plays an important role in shaping a rent-sharing agreement.

This model borrows from the industrial organization literature that assesses the welfare effects of GI labels (see Bonroy & Constantatos, 2015, for a recent review). These works examine the setting of quality in GIs and show that the level of differentiation depends on the shape of the variable costs of producing quality and on consumers' preferences regarding quality (Zago, 1999; Mérel & Sexton, 2012). This strand of the literature also studies the welfare effects of supply control instruments, such as minimum standard and specifications or controls on inputs and outputs (Lence et al., 2007; Moschini et al., 2008), to see how the associated collusive effect compares with the mitigation of information asymmetries.

However, these works do not explicitly model the link associated with terroir between the place of production, quality provision, and the opportunity cost in producing the regional product. I thus incorporate features related to both the agricultural economics literature on land use (Lichtenberg, 1989; Feng & Babcock, 2010) and to modern general equilibrium models that have recently been used to assess how the relocation of agricultural production mitigates climate change impacts (Costinot et al., 2016). These models represent the land allocation decision between parcels of heterogeneous productivity and across multiple agricultural commodities. I integrate this heterogeneity in land allocation decisions into a vertical differentiation model with an industry-level control on the designated production area. Thus, the GI supply comes from producers with heterogeneous productivity and quality in the GI product, and is restricted in an exclusive production area to control quality.

I then analyze how the GI production area adapts to climate change by including the following modeling features. First, the relocation considered occurs at the border of the existing area. Second, these parcels at the margins are assumed to produce a GI product of lower quality (Deconinck & Swinnen, 2021). Third, the model combines adaptation options (i) at the individual level, through modification of land allocation, and (ii) at the sectoral level—if allowed by the GI protection system—through the collective redefinition of the eligible parcels. Fourth, the relocation operates as climate change increases the opportunity cost of producing the GI uniformly across all producers. Fifth, the GI production area is defined according to one of these two polar cases: (i) a competitive model where the GI area is delineated a priori and producers within it freely decide to produce the GI according to their comparative advantage, and (ii) a collective model where the area of production is delineated to maximize aggregate profits of the GI industry so that it excludes some producers. In the case of the EU GI labeling scheme, the Protected Designation of Origin (PDO) label is closer to the collective model as producers define the exclusive area of production. However, the certification mark protection system, such as that implemented in the US, is closer to a free-entry setting because all producers in the designated region—defined according to pre-existing boundaries—are free to use the regional name.

First, the model shows that the direction of the relocation, when the GI industry delineates the area collectively, depends on the variation of quantity and quality with changes in the production area. Specifically, if a marginal modification of the production area leads to a large GI quality variation relative to the quantity variation, a climate-induced increase in opportunity cost leads to a further restriction in the production area. In this configuration, shrinking the area of production maintains the optimum profits under climate change, because the supply becomes concentrated on the most suitable producers. This leads to a further increase in price that compensates for the quantity losses from the area restriction.
Then, when the GI industry delineates the area collectively, but if quality varies moderately with changes in the production area, and also when the delineation is competitive, the GI production area can expand and include parcels at the border that are less suitable for the production of GI. The climate-induced supply shortage generates an increase in the GI price, which makes including more producers highly valuable, despite the resulting deterioration in quality. This extension of the area of GI production occurs for a moderate range of climate change effects and is more likely to happen if consumers have strong preferences for the GI and the opportunity cost in GI specialization is low. Ultimately, as climate change effects become more extreme, the supply of GI declines and disappears, as expected in the absence of technological adaptation.

Finally, the results show the interest for agricultural producers under GI labels in considering the extension or shrinkage of their GI areas of production as a strategy to adapt to climate change. In 2013, the Cítricos Valencianos GI enlarged its production area as a reaction to climate change, because neighboring lands had become suitable to produce the required citrus quality (Marescotti et al., 2020).<fnref n="2" />,<fnref n="3" /> Other GIs in the wine sector are currently considering the redefinition of their production area to introduce parcels that were long neglected but are now suitable (Thermes et al., 2020). These cases show configurations of adaptation to climate change through relocation, which this stylized model allows us to consider in part. For instance, some wine GIs in the Loire Valley may expand their production areas, as there are land reserves nearby with low opportunity cost but whose quality provided must be assessed upstream. However, the Burgundy *Premier Cru* and *Grand Cru* GIs are likely not to have an extensive margin of adaptation and to shrink their area, given the risk of a major quality downgrade from expanding their borders (Ay, 2021).

Climate change ultimately challenges the historical balance of the GI political economy. The modification of the GI production area generates heterogeneous individual outcomes, with some producers benefiting while others lose. In this regard, past adaptations of GIs to major changes have not happened without tension (Meloni & Swinnen, 2018). This suggests potential barriers to future relocations. To adapt to climate change, GI industries must then design compensation mechanisms so that producers adhere to the relocation.

## 2 | MODELING THE MARKET OF THE GI PRODUCT

In this section, I detail the modeling framework. First, I present the assumptions made regarding the heterogeneous geographic characteristics that confer a comparative advantage in the production of a vertically differentiated product and influence its quality. Then, I define the demand for the GI product. Finally, I model the GI legal protection system that frames the delineation of the GI production area.

### 2.1 | Assumption on land characteristics and comparative advantage

Consider a continuum of producers, with a mass normalized to 1. Each producer is endowed with a land parcel of identical surface area. Producers are heterogeneous concerning the characteristics of their land. Assume that the heterogeneity can be summarized into a one-dimensional measure denoted by $y$; in this analysis, $y$ is assumed to be non-manipulable by the producers and is distributed

<footnote n="2">²Although not in the farming context, the EU PGI label for Cornish sardines also extended its geographical area in 2017. The temperature of water in the catching area increases with climate change, which shifts the shoals of sardines and is required to include Plymouth Port to land fresh sardines. See https://eur-lex.europa.eu/legal-content/EN/TXT/?qid=1511421882537&uri=CELEX:32017R0910.</footnote>

<footnote n="3">³Note that the equivalent quality of the citrus production on the neighboring parcels motivates this expansion. To be more precise, “Climate change in the production area has led to the development of ecosystems which are suitable for citrus production using the same growing methods and producing fruit of the same organoleptic quality.” See https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:52013XC0614(02).</footnote>
according to a CDF $F(y)$, defined for all $y$ in $\mathcal{Y} = [y, \bar{y}]$ with $y \ge 0$. The associated PDF, denoted $f(y)$, is such that $f(y) > 0$ for all $y \in \mathcal{Y} = 0$ everywhere else. The land characteristics $y$ form what we call the terroir, that is, biophysical attributes specific to a place that to some extent contribute to the actual (or perceived) quality and to the comparative advantage in the regional product. $f(y)$ reflects the variety of production conditions within the GI region. The range $\mathcal{Y}$ is the extent of the region-specific land characteristics at the basis of the reputation of its production (before receiving the GI label). Thus, producers endowed with $y \in \mathcal{Y}$ can reasonably claim the use of the region's name to label their product with a GI.

The producers can allocate their land to the production of two goods: the regional product labeled with the GI and the commodity, respectively subscripted with $k = \{G, C\}$. The regional product is produced according to the production standards that are assumed as given and are mandatory to be granted the GI label. Each producer can alternatively produce a commodity, which is an undifferentiated product as in Lence et al. (2007); $\alpha_G(y)$ ($\alpha_C(y)$) denotes the quantity of the GI (commodity) that a producer with land characteristics $y$ produces. Functions $\alpha_G$ and $\alpha_C$ are assumed to be continuous. However, no further assumption on their monotonicity or shape is made.

Denote with $\alpha(y)$ the quantity of GI produced for one unit of the commodity by the producer with land characteristics $y$, that is:

$$ \alpha(y) = \frac{\alpha_G(y)}{\alpha_C(y)}, \qquad (1) $$

The following assumption states precisely the comparative advantage provided by the land characteristics in the production of the GI:

**Assumption 1.** (Comparative advantage and terroir). The greater $y$, the larger is the comparative advantage of the GI product over the commodity, that is, $\alpha'(y) > 0$.

Thus, producers with high $y$ are relatively more efficient in the production of a high quality product (Menapace & Moschini, 2012). It means that land characteristics have an increasing effect on the relative productivity for the GI, without specifying the direction of their effect on absolute GI productivity. This assumption is partly motivated by the fact that existing GIs for wine and cheese have appeared on difficult arable land—in mountainous areas or on hillsides—where it is difficult to produce the main agricultural commodities.<fnref n="4" /> Under Assumption 1, land uses are ordered by land characteristics, and land share is a function of the land characteristics distribution, in a similar approach to the Ricardian models (Dornbusch et al., 1977).

## 2.2 | Assumption on the technology

The producer decides to allocate his land to the production of the GI or the commodity by comparing the net revenues associated with each alternative. The following assumption specifies the technology to derive and compare net revenues according to the land characteristics:

**Assumption 2.** (GI and commodity technology). When combining a fraction $l_k$ of land for the production of good $k = \{G, C\}$, with a quantity $n_k$ of labor, the producer with land characteristics $y$ can produce $q_k$ quantity with the following relationship:

<footnote n="4">⁴For instance, this pattern is hypothesized in Huysmans and Swinnen (2019), who suggest the specialization for GI production in regions with a low productivity for agricultural commodities. In our case, it translates in $\alpha_C(\cdot)$ decreasing more rapidly in $y$ than $\alpha_G(\cdot)$. There is, however, no empirical evidence to our knowledge for an increasing or a decreasing effect of terroir attributes on productivity. Then, Assumption 1 is general by not requiring a monotonic effect of $y$ on $\alpha_G(\cdot)$ and $\alpha_C(\cdot)$, solely needing the rate of variation for the GI productivity being higher than that for the commodity.</footnote>
$$q_k(y) = \min \left\{ \alpha_k(y) l_k, \frac{n_k}{\nu_k} \right\} \qquad (2)$$

where $\nu_k$ measures the unit labor requirement with $\nu_C = 1$ and $\nu_G > 1$.

First, Assumption 2 implies that output uses labor and land in fixed proportions. However, this holds for given climatic conditions. We will indeed later assume that climate change reduces the GI productivity per unit of land. Second, the perfect complementarity assumption is the one used in modern Ricardian models (Costinot et al., 2016; Gouel & Laborde, 2021), as it has the advantages of simplifying the expression of revenue and keeping the model tractable. Third, even if returns to scale of land are constant at the individual level, they are determined by the shape of $\alpha_k(y)$ at the aggregate level. Fourth, the labor unit requirement for the GI is greater than that for the commodity ($\nu_G > 1$). This captures the labor requirements constraining the implementation of the production practices and the certification efforts required when producing the GI, as underlined in the literature (Lence et al., 2007; Moschini et al., 2008).

I can now describe the land allocation decision as a function of the land characteristics $y$. The producers are assumed to be price takers. In addition, land is bought and sold in a competitive market, and thus its price (that is, the land rent) corresponds to the net revenue (that is, the difference between the revenue and the labor cost). Perfect competition in the land market ensures that producers choose the land use that maximizes their net revenue. Given Assumption 2, the net revenue for product $k$ that a producer with land characteristics $y$ would earn is

$$r_k(y) = \alpha_k(y) (p_k - \nu_k w). \qquad (3)$$

This net revenue is the land rent. The producers compare their land rent between the GI and the commodity, and they exit the GI market when $r_G(y) < r_C(y)$. That is when the net land rent for the GI is non-positive. Note that the GI land rent depends on the GI price, which, in turn, depends on the GI preferences and the supply conditions induced by the GI label protection.

## 2.3 | Assumptions on the demand for the GI

I assume that consumers' preferences for the GI product are valued in a vertical differentiation framework similar to the one of Mussa and Rosen (1978), specified in the following assumption:

**Assumption 3.** (Inverse demand function for the GI). There is a mass of $N$ consumers heterogeneous in their preferences for quality $\theta$ who are uniformly distributed along $\Theta \equiv [\underline{\theta}, \bar{\theta}]$, and each buy at most one unit of the GI good. The inverse demand for the GI good denoted with $p_G(Q_G, s_G)$, where $Q_G$ and $s_G$ denote respectively the quantity and the actual (or perceived) quality of the GI product, is the following:

$$p_G(Q_G, s_G) = s_G \left[ \bar{\theta} - \frac{Q_G}{N} (\bar{\theta} - \theta) \right] \qquad (4)$$

for given $Q_G$ in $[0, N \frac{\bar{\theta}}{\bar{\theta}-\theta}]$.
First, the construction of the inverse demand function relies on consumers with heterogeneous preferences for quality and buying one or zero units of the GI.<fnref n="5" /> Second, the uniform distribution assumption for the preferences parameter $\theta$ is made to conveniently model the demand for a differentiated product (see among others Roe & Sheldon, 2007; Moschini et al., 2008). Third, I assume that the GI product has no substitute at other levels of quality.<fnref n="6" /> Finally, under Assumption 3 the GI consumers' surplus, denoted with CS, reduces to:

$$CS(Q_G, s_G) = s_G \frac{Q_G^2}{2N} (\bar{\theta} - \underline{\theta}). \qquad (5)$$

The commodity's price, denoted as $p$, is fixed on a world market and is unaffected by changes in the GI market.<fnref n="7" />

## 2.4 | Definitions of the GI labels and the types of delineation of the production area

The GI label informs the consumers of the place of production, to indicate quality and protect producers from the misuse of their region's name. I consider two sets of assumptions, respectively, regarding (i) the dependence of the quality of the GI product on land characteristics and (ii) the definition of the GI production area. The definitions below represent polar cases considering whether the land characteristics determine the GI product's quality.

**Independent GI quality.** The quality of the GI product is said to be independent of the terroir when $s_G$ is a given exogenous parameter.

**GI quality dependent on the terroir.** The quality of the GI product is said to be dependent on the terroir, when $s_G$ depends on the producers' land characteristics and corresponds to the mean of the producers' land characteristics who effectively produce the GI, that is:

$$s_G = \mathbb{E}[y|q_G(y) > 0] \qquad (6)$$

These two definitions represent the existing GI labels and their distinct perceptions of the links between the products' quality and the characteristics of their place of production (Josling, 2006). First, some GIs are akin to brands where the product's quality is independent of the land characteristics but related to the success of marketing the regional name (Moschini et al, 2008). For instance, the certification mark system, implemented in the US, is based on this principle (Josling, 2006). According to this definition, the quality of the GI product remains at its historical level when climate-induced changes in the GI production area occur. The alternative definition represents GI labels, which consider that the level of quality of the GI product cannot be reached everywhere as it is linked to land characteristics. This is a principle at the heart of the *sui generis* protection scheme, which is implemented in the EU (Josling, 2006). In this perspective, *terroir* attributes, which are specific to a place and heterogeneously distributed, contribute to the actual (or perceived) quality of the product. As a result, the product's quality reacts to a climate-induced change in the location of the production area. In fact, the effect of land characteristics on quality remains an empirical question,

<footnote n="5">⁵The online supplementary Appendix S1 presents more detailed construction of Equation (4). See page 8.</footnote>

<footnote n="6">⁶I consider an alternative situation in the online supplementary Appendix S1, page 9, where the commodity is the lower quality substitute for the GI product in a standard two possible quality demand structure (Moschini et al., 2008).</footnote>

<footnote n="7">⁷This simplifying assumption affirms that the potential commodity supply of producers in the GI region is small relative to the world supply of the commodity, so that they face a perfectly elastic demand at price $p$.</footnote>
and the literature shows mixed evidence.<fnref n="8" /> Note that both assumptions suggest that quality is non-manipulable by the producers albeit they may in practice modify quality by changing their production practices (Mérel & Sexton, 2012). Also, the GI label is assumed to be credible, with producers effectively following the specifications and consumers effectively observing the quality.<fnref n="9" />

Then, how the GI production areas are delineated vary widely from one jurisdiction to another (Gangjee, 2017).<fnref n="10" /> The following definitions introduce two polar systems to define the GI production area:

**Competitive delineation.** *The competitive delineation gives the right to produce the GI to any producers within the a priori denominated region.*

**Collective delineation.** *The collective delineation corresponds to the allocation of the production rights that maximizes the aggregate GI producers' net land rents.*

According to the competitive delineation, all producers within the *ex-ante* specified region have the option to produce the corresponding GI product. Under this competitive entry model, the distribution of the comparative advantage for the GI determines the effective GI area of production. Under the collective delineation, the parcels entitled to GI production are the ones that maximize aggregate net land rent. The industrial organization literature on GIs has studied similar GI industry structures, alternating from perfect competition (see e.g., Moschini et al, 2008; Menapace & Moschini, 2014) to monopoly (see e.g., Marette et al., 1999; Marette & Crespi, 2003; Mérel & Sexton, 2012) and also including mixed situations with limited supply control (Lence et al., 2007).

In practice, the delineation of the GI production area depends both on the importance of the link between the good's quality and land characteristics, as considered by the labeling authority, along with the lobbying power of producers. When considering a quasi-deterministic dependence, such as for the PDO label, the area is delineated based on the evidence of a causal link between land characteristics and the product's quality (Josling, 2006). These are based on microbiological or biophysical aspects but also interfere with eminently political negotiations (Deconinck & Swinnen, 2021). In the case of some GIs, interest groups lobbied their respective government to include or exclude neighboring producers.<fnref n="11" /> The certification mark protection system aims at protecting the reputation of the name of the region rather than the specific regional characteristics. The delineated areas correspond to pre-existing boundaries such as administrative districts or easily demarcating patterns derived from hydrological networks, roads, or railways. As an illustration, the GI delineations for Idaho potatoes, Florida citrus, or Washington apples correspond to the respective state borders, within which all producers can produce the GI.

If for the competitive definition the area results from the aggregation of private decisions, the collective delineation requires that the producers coordinate to maximize their surplus. Virtually, an organization representative of the producers, that is, the producers' organization (PO), manages to impose its parcel selection. In the model, we implicitly assume that the decision emanates from a

<footnote n="8">⁸The wine economics literature has widely debated the factors affecting wine quality. Some results underline the potential for replicating wine quality independently of land characteristics, because the production technologies (Gergaud and Ginsburgh, 2008) and the reputation building of specific brand names (Costanigro, McCluskey, and Goemans, 2010) influence quality more than regional land characteristics. In contrast, Ay (2021) shows that the heterogeneous soil and climate combinations between wine GI areas in Burgundy allow one to recover the historical ranking of wine quality. This implies that the combination of some physical attributes directly affects GI quality. Finally, the nested structures observed for many GIs may also be the result of some places being more suitable than others to produce a high-quality good (Yu et al., 2018; Costanigro et al., 2019).</footnote>

<footnote n="9">⁹As underlined by Moschini et al. (2008), the credibility of the GI label rests on the presence of a control and deterrence system that annihilates opportunistic behaviors of producers. This requires us to consider a monitoring policy that sets a fine and a probability of inspection to deter GI producers from failing to comply with specifications. Also, the certification costs must be shared among members, to verify coalition stability constraints.</footnote>

<footnote n="10">¹⁰Note that the Trade-Related Aspects of Intellectual Property Rights (1994) agreement protects from the misuse of a GI name. However, it does not include provisions regarding the implementation and enforcement of labels.</footnote>

<footnote n="11">¹¹For instance, such lobbying pressures happened during the delineations of Morbier cheese in France in the 90 s, of Melton Mowbray pork pies in the United Kingdom in the 2000 s, and of the "Lardo di Colonnata" in the 2000 s, which is a high-quality lard produced in Italy (Rippon, 2013; Landi & Stefani, 2015). The resulting delineations were determined after an administrative process that balanced not only evidence on the quality provided by inside producers and neighboring producers but also the regional economic interests.</footnote>
unified collective of producers who share the same interests and benefits from their label. If this assumption simplifies understanding by reasoning at the industry level, it omits the need for a binding and stable agreement between the producers to effectively implement the decision in a cartel fashion (Marette & Crespi, 2003). This assumption is discussed later to reveal the importance of the GI label governance in the area relocation.

The latter definitions close the model, as they determine the producers who are allowed to supply the GI. For the competitive delineation, high-y producers produce relatively more units of GI and allocate their land to the GI (Assumption 1). An arbitrarily chosen producer indifferent between producing the GI and the commodity is defined by:

$$ \alpha(y_S) = \frac{p-w}{p_G - \nu_G w}, \qquad (7) $$

where $y_S$ is an implicit function of the GI price and the commodity price. By individual optimization and monotonicity of the $\alpha(\cdot)$-function, all producers with $y > y_S$ allocate their land to the GI, and conversely for the commodity. For this arbitrary producer, the GI aggregate supply $Q_G(y_S)$ is

$$ Q_G(y_S) = \int_{y_S}^{\bar{y}} \alpha_G(u)f(u)du. \qquad (8) $$

When the GI quality is dependent on the land characteristics, it corresponds to the left-truncated mean of the land characteristics:

$$ s_G(y_S) = \frac{\int_{y_S}^{\bar{y}} uf(u)du}{1 - F(y_S)}. \qquad (9) $$

For the collective delineation, the selection of eligible parcels is made using an exclusion threshold for land characteristics denoted as $y_E$. Only producers with land characteristics $y$ above $y_E$ are entitled to produce the GI, whereas producers with $y$ below $y_E$ are excluded from the GI production area. The GI supply and quality correspond to the expressions in Equations (8) and (9), now expressed as a function of $y_E$. The GI industry objective function is expressed as follows:

$$ \max_{y_E} \Pi_G(y_E) = \int_{y_E}^{\bar{y}} \{\alpha_G(u)[p_G(Q_G(y_E), s_G(y_E)) - \nu_G w] - \alpha_C(u)(p - w)\} f(u)du. \qquad (10) $$

Because the GI industry maximizes *net* land rents, or the difference between the GI and the commodity land rent, it internalizes the costs and benefits of excluding producers (Deconinck & Swinnen, 2021). Thus, the collective delineation of the GI area is similar to the one resulting under the maximization of the sum of commodity and GI producers' absolute land rents.

## 3 | THE HISTORICAL DELINEATION OF THE GI PRODUCTION AREA

For the competitive delineation, the producers at the margin determine the GI area. These producers are indifferent between producing the GI and the commodity under market-clearing conditions in the GI market. $y^*$, the land characteristics of the indifferent producers when the GI market is at equilibrium, are defined as follows:
$$ \alpha_G(y^*) \{p_G[Q_G(y^*), s_G(y^*)] - \nu_G w\} = \alpha_C(y^*)(p-w) \quad (11) $$

Equation (11) specifies the producers at the margin under the competitive delineation and for a GI quality that depends on the *terroir*.

Under the collective delineation model, the optimal delineation is directly determined from the first order condition of the program in Equation (10). The land characteristics at the border that maximize $\Pi_G(y_E)$, denoted as $\tilde{y}$, are defined as follows:

$$ \underbrace{Q_G(\tilde{y}) \left[ \frac{\partial p_G}{\partial Q_G} Q_G'(\tilde{y}) + \frac{\partial p_G}{\partial s_G} s_G'(\tilde{y}) \right]}_{\text{Marginal benefits from exclusion}} = \underbrace{f(\tilde{y}) \{ \alpha_G(\tilde{y}) [p_G(Q_G(\tilde{y}), s_G(\tilde{y})) - \nu_G w] - \alpha_C(\tilde{y})(p-w) \}}_{\text{Marginal costs of exclusion}} \quad (12) $$

From Equation (12), the collective delineation is optimal when the marginal benefits correspond to the marginal costs induced by the exclusion of the producers at the border. When marginally increasing $y_E$, the GI supply decreases, which in turn increases the price and the revenue of the included producers. If quality depends on land characteristics, the GI price further increases, because the marginal exclusions concentrate the GI supply on producers with high-y and increase quality. In contrast, the marginal costs of exclusion correspond to the foregone profits for the GI industry as measured by the net land rent of the excluded producers at the border.

In practice, the regulator delegates the design of GIs' specifications to the producers, given the heavy administrative burden of collecting information regarding consumers' preferences and comparative advantage. However, consider now, as a first-best outcome, the situation where the regulator has perfect knowledge of the consumers' preferences and producers' comparative advantage. This delineates the GI production area by selecting an exclusion threshold on land characteristics to maximize total surplus, that is, the sum of consumers' surplus and producers' land rent:

$$ \max_{y_E} W(y_E) = \int_0^{Q_G(y_E)} p_G(v, s_G(y_E)) \, dv - \nu_G w \int_{y_E}^{\bar{y}} \alpha_G(u) f(u) \, du + (p-w) \int_{\bar{y}}^{y_E} \alpha_C(u) f(u) \, du \quad (13) $$

The solution to the regulator's program in (13), denoted with $\hat{y}$, is characterized as follows:

$$ \underbrace{\dot{s}_G(\hat{y}) \int_0^{Q_G(\hat{y})} \frac{\partial p_G(v, s_G(\hat{y}))}{\partial s_G} dv}_{\text{Total marginal valuation of a quality increase}} = \underbrace{f(\hat{y}) \{ \alpha_G(\hat{y}) [p_G(Q_G(\hat{y}), s_G(\hat{y})) - \nu_G w] - \alpha_C(\hat{y})(p-w) \}}_{\text{Marginal costs of exclusion}} \quad (14) $$

While delineating the GI production area, the PO and the regulator consider the quantity and the quality variations when marginally changing the border. In this respect, the elasticity of quantity with the border, $\varepsilon_{Q_G/y_E}$, and the elasticity of quality with the border, $\varepsilon_{s_G/y_E}$, determine these variations. They are defined as follows:

$$ \varepsilon_{Q_G/y_E} = \frac{Q_G'(y_E)}{Q_G(y_E)} y_E \quad \varepsilon_{s_G/y_E} = \frac{\dot{s}_G(y_E)}{s_G(y_E)} y_E \quad (15) $$

The following propositions compare the GI production area under competitive delineation and collective delineation with that under first best, for any climatic conditions:
**Proposition 1.A.** When the GI quality is independent, the GI production area under competitive delineation corresponds to that under first-best, and that under collective delineation is smaller:

$$y^* = \hat{y} < \tilde{y}. \qquad (16)$$

**Proposition 1.B.** When the GI quality depends on the terroir, the GI production area under competitive delineation is always larger than that under first-best. In addition, the GI production area under collective delineation is smaller or larger than that under first-best depending on how quality and quantity vary at the border of the exclusive area. That is to say:

$$y^* < \hat{y} < \tilde{y} \quad \text{when at } \tilde{y}, \quad \varepsilon_{SG}/y_E < -2\varepsilon_{QG}/y_E \qquad (17)$$

$$y^* < \tilde{y} \le \hat{y} \quad \text{when at } \tilde{y}, \quad \varepsilon_{SG}/y_E \ge -2\varepsilon_{QG}/y_E, \qquad (18)$$

*Proof.* See the Appendix A. □

<figure><img src="image_2.png" /></figure>

Propositions 1.A and 1.B partly recover well-known results from the industrial organization literature on GI labels (Marette et al., 1999; Lence et al., 2007; Moschini et al., 2008). The two polar perceptions regarding the influence of terroir on quality raise opposite conclusions regarding whether further entry into the GI industry should be controlled (Josling, 2006). If quality is independent of land characteristics, there is no need to restrict the area of production, and the competitive delineation corresponds to the first-best outcome.<fnref n="12" /> Indeed, there would be a social loss in circumscribing the GI area to some locations, as it would unnecessarily keep out competitors—for instance, who could reproduce GI quality elsewhere—without providing supplemental information. In contrast, when quality depends on land characteristics, Proposition 1.B underlines the social interest in further controlling the GI area of production. Similar to Menapace and Moschini (2014), the design of the GI area here results from a trade-off between enabling more competition and enhancing the quality of the GI product. Under competitive delineation, producers enter the GI market and do not internalize the quality decrease. This pushes down the GI price at the expense of producers with high land characteristics. By reducing the production area, it is possible to increase quality and consumers' willingness to pay for quality, to the profit of producers with high-y.

In addition, Proposition 1.B sheds new insights on how the heterogeneity of the quantity and quality supplied between producers shape the provision of a differentiated product. The socially optimal production area is smaller than the one for the collective model, when quality increases at least twice more rapidly than the decrease of quantity when marginally shrinking the border of the exclusive area. In this situation, the marginal revenue is lower than the average valuation of the demand for a marginal increase in quality at the collective outcome. In other words, it is socially optimal in these conditions to further restrict the supply, so that the increase in quality will substantially compensate the quantity decrease and, in turn, increase total consumer surplus. The industrial organization literature on quality provision under monopoly and its application to GI labels have already underlined conditions of quality over-(under)provision relative to the social optimum (Spence 1975; Mérel & Sexton, 2012). Proposition 1.B complements these results by adding conditions on the flexibility of quality and quantity provision at the borders of the GI production area.

<footnote n="12">¹²By contrast with Moschini et al. (2008), where the competitive GI industry falls short of delivering the socially optimal outcome, they are reconciled here. The GI product is not underprovided under competitive delineation, as producers do not bear any fixed costs in the model that can deter entry or limit the supply of GI.</footnote>
# 4 | RELOCATING THE GI PRODUCTION AREA UNDER CLIMATE CHANGE

Given the historical GI production area depicted in Propositions 1.A and 1.B, I now analyze the effects of climate change. I first introduce the modeling of the effects of climate change on GI production and then study their implications for the GI supply.

## 4.1 | Introducing the effect of climate change on the supply of GI

Climate change, here, is understood as a deterioration of GI production conditions. Climate change is assumed to only decrease the potential GI quantity produced, that is, $q_G(y)$ is multiplied by a scalar $1 - \delta$, with $0 \le \delta \le \bar{\delta} < 1$. $\bar{\delta}$ is a climate-induced parameter that measures the GI quantity that is lost under climate change relative to the historical conditions. $\bar{\delta}$ is the most extreme climate scenario, that is, the one under which the regional land characteristics no longer provide a comparative advantage in the GI and the GI production area disappears. As in the modern Ricardian framework, climate change corresponds to a shift in land productivity (Costinot et al., 2016; Gouel & Laborde, 2021), which is homogeneous here. A producer with land characteristics $y$ now supplies a potential GI quantity $q_G(y) = (1 - \delta)\alpha_G(y)$, and the aggregate supply is $Q_G = (1 - \delta)\int \alpha_G(u)f(u)du$. For now, we assume that climate change does not affect the potential quantity of the commodity produced.

## 4.2 | Adaptation of the delineation of the GI production area

The outcome for the GI market can be expressed as a function of the climate-induced parameter $\delta$; that is $y^*$ and $\tilde{y}$ in Equations (11) and (12) depend on $\delta$. The historical production areas under competitive and under collective delineations, denoted by $y^{*H}$ and $\tilde{y}^H$ respectively, are defined by $y^{*H} \equiv y^*(\delta|\delta=0)$ and $\tilde{y}^H \equiv \tilde{y}(\delta|\delta=0)$. Climate change decreases the potential supply of GI homogeneously, and $\delta$ progressively increases starting from $\delta=0$. This marginal increase in $\delta$ is a stylized modeling of the gradual effects of climate change on the potential production of GI. The comparative statics on $y^*$ and $\tilde{y}$, for marginal increase in $\delta$, give the adaptation of the GI production area to climate change.

Under competitive delineation, the comparison between the climate-induced changes in the net revenues of the GI and the commodity (Equation (3), adjusted for $\delta$) drives the decision to reallocate land in reaction to climate change. For a given producer, and $y^*$ remaining fixed, a marginal increase in $\delta$ affects the GI net revenue in two opposite directions: (i) it reduces its revenue by decreasing the quantity produced, and (ii) it increases its revenue as climate change reduces aggregate supply and then increases the GI price. The latter effect, denoted $b(y)$ for a producer with land characteristics $y$, derives as follows:

$$b(y) = -\alpha_G(y) \frac{\partial p_G[Q_G(y^*), s_G(y^*)]}{\partial Q_G} Q_G(y^*). \quad (19)$$

The following proposition depicts the adaptation of the GI production area when it is defined under competitive delineation:

**Proposition 2.** (Adaptation of the GI production area under competitive delineation). If the effects of climate change imply $(r_C(y^{*H}) < b(y^{*H}))$ then there exists a parameter $\delta^*$ with $0 < \delta^* < \bar{\delta}$ such that for $\delta \le (>) \delta^*$, $\frac{dy^*}{d\bar{\delta}} \le (>) 0$; otherwise, if $(r_C(y^{*H}) \ge b(y^{*H}))$, then $y^*$ monotonically increases with $\delta$.
*Proof.* See the Appendix A.

<figure><img src="image_3.png" /></figure>

**Proposition 2** gives the schedule of adaptation of the GI production area under competitive delineation following a climate-induced decrease in supply. If the effects of climate change imply lower opportunity costs than the increase in revenue for the GI producers at the historical border (condition in parentheses), then there are moderate climate change scenarios where the GI production area increases. Otherwise, the GI production area always shrinks with a climate-induced deterioration in the conditions of production. $\delta^*$ is the climate change scenario where the GI production area, under competitive delineation, is inert to climate change.

In addition to depending on the intensity of direct climate change effects, the direction of the adaptation results from the comparison between the price effect and the opportunity cost effect induced by climate change at the border (See Equation (A.8) in the Appendix A). Climate change decreases GI supply, GI price increases, and the outside producers at the border receive a marginally higher revenue for the GI. Thus, the scarcity of the GI supply, strengthened under climate change, produces an interest in extending the border of the area. Although climate change reinforces and further decreases GI land productivity, comparative advantages are progressively reversed in the commodity's favor. Then, this increase in the opportunity cost of producing the GI dominates the increase in GI price, and inside producers progressively stop the production of the GI. Figure 2 illustrates the adaptation schedules under competitive delineation (dotted line).

**Proposition 2** underlines that the adaptation of the GI supply under open delineation is characterized by (i) the extent of the extensive margin (when it exists) measured with $\delta^*$, and (ii) the extent of the adaptation margin measured with $\bar{\delta}$. The former shows the maximum percentage of climate-induced reduction of GI supply that an extension of the GI area can compensate. The latter gives the maximum percentage of climate-induced reduction of GI supply until there is no more comparative advantage in the GI. The technology, the costs of the supply, and the preference parameters for the GI that determine the price-to-quantity variations $(-Q_G \frac{\partial P_G}{\partial \delta} \frac{\partial P_G}{\partial \delta Q_G})$ shape both margins. In particular, the higher the comparative advantage for the GI in the historical situation, the greater the range of moderate climate scenarios leading to the extension of the GI production area (high $\delta^*$, see Equation [A.13] in 17) and the more the supply can endure climate change (high $\bar{\delta}$, see Equation [A.12] in 17). The higher the opportunity cost $r_C(\cdot)$, the lower is climate change's endurability for the GI supply (low $\bar{\delta}$) and the lower the extensive margin of adaptation (low $\delta^*$). This is because producers at the border have an increased interest in allocating their land to the commodity. By contrast, when the opportunity cost is zero, the GI area always adapts by integrating outside producers until it reaches the boundaries of the finite set of producers, as depicted in the online supplementary Appendix S1, Figure B.1.

The following proposition illustrates the GI production area's adaptation to climate change under collective delineation and when quality depends on land characteristics:

**Proposition 3.** (Adaptation of the GI production area under collective delineation). If $(-2\varepsilon_{Q_G/y_E} > \varepsilon_{s_G/y_E})$ and if the effects of climate change imply $(\frac{\partial^2 \Pi_G}{\partial \delta \partial y_E} |_{y_E=y} \stackrel{\sim}{H} < 0)$, then there exists a parameter $\tilde{\delta}$ with $0 < \tilde{\delta} < \bar{\delta}$ such that for $\delta \le (> ) \tilde{\delta}$, $\frac{\partial \tilde{y}}{\partial \delta} \le (> ) 0$; otherwise if $(-2\varepsilon_{Q_G/y_E} \le \varepsilon_{s_G/y_E})$ or $(\frac{\partial^2 \Pi_G}{\partial \delta \partial y_E} |_{y_E=y} \stackrel{\sim}{H} \ge 0)$, then $\tilde{y}$ monotonically increases with $\delta$.

*Proof.* See the Appendix A.

<figure><img src="image_4.png" /></figure>

$\tilde{\delta}$ is the climate change scenario where the GI production area under collective delineation is inert to climate change. Proposition 3 gives the schedule of the adaptation of the GI production area under collective delineation following climate-induced decrease in the GI potential supply. The
<figure><img src="image_5.png" /><figcaption>(a) Adaptation schedule in Prop. 2 and 3 including GI area expansion</figcaption></figure>

Delineation of the GI area
- Competitive
- Collective

<figure><img src="image_6.png" /><figcaption>(b) Adaptation schedule in Prop. 2 and 3 where the GI area monotonically shrinks</figcaption></figure>

Share of GI production lost under climate change: [8]

Delineation of the GI area
- Competitive
- Collective

FIGURE 2 Illustrations of Proposition 2 and 3. The y-axis shows the land characteristics at the border, with the set of GI producers being those with land characteristics above $\tilde{y}$ or $y^*$. The x-axis represents the percentage of GI production that is lost under climate change relative to the historical situation, where $\delta=0$. The adaptation schedule depicted in Proposition (2) under competitive delineation and Proposition (3) under collective delineation must be understood starting from the historical situation ($\delta=0$), from which climate change occurs progressively until reaching the most extreme potential scenario ($\delta=\bar{\delta}$). As climatic conditions deteriorate the GI production, the GI production area adapts by expanding to include outside producers (decreasing $\tilde{y}$ or $y^*$) or by restricting to exclude inside producers (increasing $\tilde{y}$ or $y^*$). The illustrations are obtained from simulations when the GI quality depends on the *terroir* and using a uniform distribution of land characteristics with $Y=[1, 3]$. Column A is obtained for a linear relationship between land characteristics and GI production where $\alpha_G(y) = 0.5y$, a constant commodity production where $\alpha_C(y) = 1$, and the other parameters are $p=1$, $w=0.75$, $\nu_G = 1.25$, $\Theta = [0, 1]$, and $N=1.5$. Column B is obtained with a concave relationship between GI production where $\alpha_G(y) = 0.25y^{1/2}$, with a constant commodity production where $\alpha_C(y) = 2$, and the other parameters are $p=1$, $w=0.75$, $\nu_G = 1.25$, $\Theta = [0, 1]$, and $N=1$.

direction of the adaptation ultimately depends on the comparison between quantity and quality variation at the border (first condition in parentheses). Indeed, this comparison determines the direction of variations in marginal revenue through marginal willingness to pay for quality and in marginal revenue with quantity changes. In a situation where the increase in quality is more than twice the decrease in quantity when shrinking the border $(-2\epsilon_{QG}/y_E \le \epsilon_{SG}/y_E)$, the GI industry is always interested in further diminishing the production area in the face of climate change. In other words, the maximum aggregate profit is sustained when the industry increases quality to compensate for revenue loss induced by the reduction in quantity under climate change. Thus, the production area concentrates on top-quality producers, whereas the industry does not forego much of the quantity supplied, as quantity varies slowly. Conversely, if the quantity decrease is more than half the quality increase when shrinking the border *and* if, at the historical delineation, climate change decreases the marginal profitability of exclusion ($\frac{\partial^2 \Pi_G}{\partial \delta \partial \delta'}|_{y=y} \sim_H 0$), the GI industry has an interest in adapting by expanding the production area. This second condition means that the climate-induced diminution in the marginal costs of exclusion is smaller than the diminution in the marginal benefits of exclusion at the historical collective delineation (see Equation [A.23] in the proof of Proposition 3), which furnishes an incentive to expand the production area. When these conditions on the elasticities and the marginal profitability of exclusion are met, the GI industry profits increase under climate change by integrating more producers and quality does not substantially diminish. The adaptation under collective delineation is also represented in Figure 2 (solid line).

The extensive margin ($\bar{\delta}$) and the adaptation margin ($\delta$) are determined by the technical characteristics of the GI supply and also the preference parameters for GI quantity and quality. Note that the adaptation margin is similar under collective as that of competitive delineations. Considering fixed costs of certification and marketing in the model would introduce a gap, as they could be more
easily borne by an industry in monopoly than by a competitive industry. This would increase the adaptation margin under collective delineation relative to competitive delineation. Concerning the extensive margin of adaptation, higher price elasticity for GI quantity notably increase $\delta$, as climate-induced supply shortage leads to responsive price variations and increases the interest in integrating outside producers.

## 4.3 | When climate change simultaneously affects the supply of the GI and the commodity

Propositions 2 and 3 assume that climate change does not alter the potential supply of the commodity. However, this is not likely to be the actual case. $\delta_C$ is denoted as the share of the historical potential supply of the commodity that would be lost under climate change. Two situations can be considered, according to the level of $\delta_C$: (i) $\delta_C \ge \delta$, and (ii) $\delta_C < \delta$. In the configuration (i), both the competitive and the collective production areas enlarge (as long as $-2e_{Q_G}/y_E > e_{S_G}/y_E$, see the online supplementary Appendix S1, Equations (B.17) and (B.18), for detailed derivations). In this configuration, the incentive in producing the GI product is further increased as the opportunity cost in producing the GI decreases with climate change. However, the outcome under situation (ii) is not clear and gets closer to those illustrated in Propositions 2 and 3.

## 4.4 | The influence of land characteristic heterogeneity on adaptation response

The adaptation of GI supply might benefit from heterogeneous production conditions across parcels to adjust land allocation flexibly. In other words, when land characteristics are more homogeneous, the supply overreacts, as more producers have similar land characteristics, and simultaneously enter or exit the GI area. I implement numerical simulations to showcase the results of Proposition 2 and 3 under different heterogeneity levels in the land characteristics distribution. The results, summarized in the online supplementary Appendix S1 in Figure B.2, suggest a higher adaptation potential for GIs with stronger heterogeneity in the land characteristics distribution.

# 5 | ECONOMIC AND POLICY IMPLICATIONS FOR EXISTING GEOGRAPHICAL INDICATIONS

The model's results have practical implications for agricultural production under geographical indication labels. This section examines which adaptation patterns may arise for some GIs, considering the circumstances underlined in Propositions 2 and 3. Also, this section discusses barriers that limit GI relocations to adapt climate change in practice.

## 5.1 | The extensive margin of adaptation for existing GIs

To date, some GIs have temporarily modified their specifications to face extreme weather events.<fnref n="13" /> Our model highlights the conditions under which existing GIs might consider expanding their production area to adapt to persistent climate change. Identifying opportunities to relocate requires the

<footnote n="13">¹³As an illustration, between 2018 and 2020, the INAO, the French government body in charge of GIs, reported 35 temporary modifications for the PDO cheeses specifications—out of the 50 PDO cheeses registered in France—to cope with exceptionally dry years. The increased risk of drought calls into question the fodder and grazing self-sufficiency of the exclusive area of production, imposed in most PDO specifications for cheese.</footnote>
consideration of biophysical impacts of climate change on the agriculture. For instance, the works from Hannah et al. (2013) and Moriondo et al. (2013) determine shifts in agronomic suitability of wine production and shed light on areas sustaining similar conditions of production in the future. Our model incorporates heterogeneity in the potential quality and productivity of land, as well as other determinants of adaptation such as the GI industrial structure and key economic tradeoffs. The results of this model can then be transferred to the cases of existing GIs to suggest potential patterns of adaptation. However, note that our model is stylized. Hence, more specific implications for relocation of GIs must consider instances for heterogeneous effects of climate change within the GI region, changes in consumer preferences, or even the potential for other adaptation margins such as the implementation of innovative practices.

The adaptation mechanisms described in the model apply to the case of French wine GIs. These GIs are closed to a collective delineation model, as the PO defines the parcels eligible for production under the GI name (Mérel et al., 2021). However, local circumstances vary between GIs, affecting the determinants of the quality-quantity tradeoff described in the model and thus the potential of the extensive adaptation margin. On one hand, *Grand cru* and *Premier cru* GIs in Burgundy region, such as Chevalier-Montrachet or Les Chaumes from Vosne-Romanée, have a narrow room for extensive adaptation, and climate change will imply that these GIs shrink their production areas. Indeed, the delineation of these GIs accurately matches the mapping of the specific characteristics in their vineyards (Ay, 2021). As a consequence, the variation in *terroir* conditions at their borders is such that an enlargement could greatly downgrade the quality signal conveyed, that is, $ε_{SG}/y_E$ is large enough to be greater than $2ε_{QG}/y_E$.

Contrastingly, some GI wines in the Loire Valley will perhaps benefit from an extensive margin of adaptation. For instance, Chinon GI, one of the main wine GIs in the Loire Valley, has a large land reserve available, with nearly 4000 hectares, besides the 2000 hectares already in cultivation. This land is technically suitable for viticulture, with a low opportunity cost of producing the GI. However, as underlined by Thermes et al. (2020), the adequacy of these bordering parcels in providing the wine quality is questioned, and producers are further studying soil formation and phenological process at the parcel level. Thus, the consideration of the quality change on this neighboring *terroir* is again an essential feature of the extensive margin of adaptation for this GI under collective delineation.

Some wine GIs could also extend on neighboring parcels at higher altitude. In a warming context, such parcels, with a cooler climate, allow the production of wine with a standard alcohol level while keeping total acidity constant (van Leeuwen and Darriet, 2016). This is particularly relevant for Chianti or Mont Ventoux GIs in Italy and France, which consider relocating after such patterns (Thermes et al., 2020). Our model ignores heterogeneous climate change effects where outside parcels in high altitude gain in productivity and those historically inside in plains decrease. Nonetheless, it is likely that joint expansion on these more suitable parcels and exclusion of the less suitable ones might occur.<fnref n="14" />

## 5.2 Relocation and the political economy of GIs

The relocation has different implications on the political economy of GIs according to the GI industry structure. In a competitive delineation system, the producers are free to enter or exit the GI market in response to climate change according to what is privately optimal. In other words, the aggregation of private production decisions leads to the adaptation in Proposition 2. This situation is represented in Figure 3. It shows the individual net land rent in the historical delineation defined by

<footnote n="14">¹⁴A quantitative empirical analysis can accommodate the heterogeneous effects of climate change and would highlight the extent to which the rise in altitude of the GI area is relevant. The work of Zhu et al. (2016) employs this approach in the case of the GI wine Chianti. They determine the cost and benefit of the relocation of the vineyards uphill, using a spatially explicit model with heterogeneous impacts of climate change on grape yields.</footnote>
<figure><img src="image_7.png" /><figcaption>FIG URE 3 Individual net revenue for every producers in the historical situation and under climate change. Three situations are considered: the historical outcome (orange line), the outcome without adaptation of the GI production area (yellow line), and that with adaptation of the production area (green line) under climate change. Note that all three lines are superimposed to the left $y^{*C}$ and $\dot{y}^C$, because climate change does not affect commodity producers. The illustration is obtained from simulations when the GI quality depends on the *terroir* and using a uniform distribution of land characteristics with $Y = [1, 3]$. The relationship between land characteristics and GI production is linear with $\alpha_G(y) = 0.5y$, the commodity production is constant with $\alpha_C(y) = 1$, and the share of the GI historical production under climate change is $\delta = 0.5$. The other parameters are $p = 1$, $w = 0.75$, $v_G = 1.25$, $\Theta = [0, 1]$, and $N = 1.5$.</figcaption></figure>

$y^{*H}$ (orange line), and those under a discrete change in climatic conditions without (yellow line) and with relocation (green line), where the new area is defined by $y^{*C} = y^*(\delta|0 < \delta < \delta^*)$ and where $y^{*C} < y^{*H}$. As climate change occurs, the aggregate supply decreases, which generates a scarcity rent, materialized by the area *BDEF*, that is, the supplement of profit to historical producers if there was no entry. This rent is immediately captured by the entry of bordering producers, represented by the area *ACD*.

These entry and exit flows may not be as fluid as that represented in our model if the relocation has further economic consequences on GI industry. It might be realistic to consider a lag between the effects of climate change and the consequent entry of bordering producers. For example, the presence of conversion or adjustment costs to GI production could explain such latency. If climate change effects are progressive, then the entry will only be profitable beyond the degree of climate change that allows the bordering producers to absorb their conversion costs. Thus, under moderate climate change, bordering producers would not enter the GI market, and historical producers would enjoy a temporary monopoly rent (area *BDEF* on Figure 3).

To limit this perspective, the EU can direct its program to support EU quality labeling schemes for agricultural products towards the efforts of GI producers to adapt to climate change.<fnref n="15" /> This financial support could lower the fixed-cost burden associated with the infrastructural developments needed to integrate the entrants in the supply chain (transportation, storage location, processing plants). Also, the relocation of GIs affects consumers' willingness to pay (Saïdi et al., 2020). To maintain consumers' willingness to pay for quality, costly efforts to sustain the GI's collective reputation have to be undertaken (Lence et al., 2007). Hence, such financial support can limit the fixed costs of adaptation and the rent accruing to historical producers under climate change.

<footnote n="15">¹⁵The EU currently assists agricultural producers to promote their products. An aggregate amount of 200 million euros was granted in 2020 to help agricultural products gain market share, with a specific focus on the EU's major non-EU markets, such as China, Japan, South Korea, Canada, and the USA. This program dedicates 50 million euros to marketing actions that improve the awareness and recognition of EU quality labeling schemes (GI and organic food labels). Indeed, only 8% of European consumers recognize the PDO and PGI logos (Gangjee 2017).</footnote>
<figure><img src="image_8.png" /><figcaption>FIG URE 4 Aggregate benefits of adaptation under collective delineation. The solid line (dotted line) represents aggregate industry net revenues under the historical climatic conditions (under climate change) for every possible rule upon $y_E$ defining the border of the GI production area. Aggregate profits are “U-shaped” for land characteristics above $y^+$ and constant below. Indeed, when $y_E < y^+$, the GI exclusive area always corresponds to the competitive outcome, and the industry profits are constant. The maximum of profits is obtained for a GI production area defined by $\tilde{y}^H$ in the historical situation and $\tilde{y}^C$ under climate change. For the historical production area, climate change diminishes aggregate profits, as GI quantity produced diminishes, and the GI price increase following this rarefaction does not offset. The yellow arrow measures this direct loss induced by climate change. In this configuration, the industry as a collective adapts to climate change by integrating new producers and reducing $\tilde{y}^H$ to $\tilde{y}^C$. By expanding its production area, the industry can increase profits by selling more products. The green arrow measures the increase in profits when adapting to climate change. The illustration is obtained from simulations when the GI quality depends on the *terroir* and using a uniform distribution of land characteristics with $Y = [1, 3]$. The relationship between land characteristics and GI production is linear with $\alpha_G(y) = 0.5y$, the commodity production is constant with $\alpha_C(y) = 1$, and the share of the historical production of GI under climate change is $\delta = 0.5$. The other parameters are $p = 1$, $w = 0.75$, $v_G = 1.25$, $\Theta = [0, 1]$, and $N = 1.5$.</figcaption></figure>

For GIs under collective delineation, the model assumes that the decision to relocate emanates from the PO of the GI region which implicitly balances the consequent conflicting outcomes between producers. Figure 4 illustrates the collective benefits from adaptation in the case of an extension. The aggregate net gains from the relocation correspond to the green arrow on Figure 4. They break down into absolute individual losses (for the historical producers in the case of an expansion and for the excluded producers for a reduction) and individual absolute gains (for new entrants in the event of an expansion and for historical producers for a contraction). Figure 3 illustrates this conflicting outcome in the case a GI production area expansion following a discrete change in climatic conditions, from the historical allocation $\tilde{y}^H$ to $\tilde{y}^C \equiv \tilde{y}(\delta|0 < \delta < \tilde{\delta})$ and where $\tilde{y}^C < \tilde{y}^H$. The historical GI producers have a higher net revenue without relocation (yellow line) than with relocation (green line). However, the industry collectively prefers to adapt, because the aggregate loss for historical GI producers, or area DCEF, is smaller than the aggregate gain for the new GI producers, area ABGC.
For the relocation to occur, it must be accompanied by a compensation system that redistributes the collective gains among producers, so that the PO can seamlessly coordinate the producers of the region. However, if we avoid considering the conditions for such a compensation system to emerge, it leaves the acceptability of the relocation unclear.

Some past examples of changes in GI production area illustrate the conflicts associated with relocation.<fnref n="16" /> For instance, Meloni and Swinnen (2018) show that the combination of a trade liberalization period, which increased the demand for wine, and *Phylloxera* devastating vines in the Douro Valley by the end of the 19th century yielded Port wines in Portugal to be produced by new producers in a larger region. Historical Port wine producers lobbied the government to prevent new producers from labeling their wine as Port wines, though unsuccessful.

In the context of climate change, the French wine industry is currently building a national strategy for climate change adaptation, which includes the assessment of scenarios encompassing wine production relocations.<fnref n="17" /> This initiative launches regional discussion groups involving producers and experts. By debating whether to expand the production area or amend the specifications to include innovative practices while keeping the existing area, GI producers can develop shared perspectives on strategies for adapting (Aigrain et al. 2019). Thus, such a program can be construed as a public action to prevent potential coordination failure between GI producers that could arise in the face of climate change.

6 | CONCLUSION

In this paper, I have developed a stylized framework to understand the relocation of agricultural production under GI labels in the face of climate change. The model considers GIs to be a label that perfectly informs consumers about the quality of a product, whether the latter is or not influenced by the characteristics of the production area. In order to control quality, the GI supply is confined to an exclusive production area and comes from producers with varying productivity and quality in the GI product. This area can be defined competitively (such as for Idaho potato or Florida citrus) or so to maximize the regional producers’ welfare (such as for Champagne or Chianti wine). Then, climate change deteriorates the conditions of production in the region by gradually decreasing the land productivity in the GI. In line with the rules regarding the definition of the exclusive production area, producers within and bordering the GI region consequently adapt by reallocating their land between the GI and a commodity. Based on the model, climate change makes GI products scarce, so that the production area could possibly extend at the expense of product quality.

The main results from this approach can be summarized as follows. First, for competitive GI production areas, before climate change deteriorates the conditions of production and diminishes the GI production area, there can be private interests for bordering producers to enter and enlarge the area under moderate effects of climate change. Second, for GI production areas that have been collectively determined and are under moderate climate change scenarios, there is an interest for the GI industry to also enlarge the production area. They can do so when the quality gradually decreases relative to the quantity increase associated with the integration of the bordering producers. Third, if some GIs can exploit an extensive adaptation margin, such as southern European GIs for wine considering relocating uphill to limit the yield losses, some others are limited by the potential of their neighboring *terroir* to provide a consistent quality, such as Burgundy wine GIs. Fourth, the relocation of GI requires the consideration of their political economy and their governance, as included and excluded producers from relocation may oppose it.

<footnote n="16">¹⁶The first delineation of the designated production area during the creation of a GI label can also produce winners and losers and generate conflicts that are documented in the literature and summarized in Note 11.</footnote>

<footnote n="17">¹⁷The construction of this strategy is the result of a field research project involving stakeholders from the wine industry. This research project is called LACCAVE, standing for Long-term Adaptation to Climate Change in Viticulture and oEnology.</footnote>
Overall, this work aims to open avenues of research on the extent to which localism, authenticity, and constancy, as principles that have contributed to the success of GI labels, affect their adaptation to climate change. This work could be extended in several directions. First, the model only focuses on the effects of climate change that decrease the supply of GI homogeneously. It does so to ease the interpretation of the results. It is possible to consider a progressive inversion in comparative advantage along the land characteristic dimension to model the gradual relocation around a central point describing the optimal conditions to produce the GI. Second, the model studies the relocation of the GI product in isolation from the rest of the economy due to the unique specificities of its production area. It may be interesting to consider the competition of several GI products as close substitutes in the same jurisdictions or with different jurisdictions and facing different effects of climate change.

## ACKNOWLEDGMENTS

I thank editor Terry Hurley and two anonymous reviewers for their thoughtful suggestions. I also thank Stéphane De Cara for his constant support and for his countless comments when he supervised this work during my PhD. I thank Christophe Gouel, Aurélie Méjean, and Pierre Mérel for their helpful comments and suggestions. I thank Pierre-Alain Jayet and the Skiminaire participants; Lionel Ragot, Jean-Philippe Nicolaï, and EconomiX seminar participants; Jean-Sauveur Ay, Valentin Bellassen, and CESAER seminar participants; Sarah Parlane and UC Dublin School of Economics seminar participants; and Emmanuelle Taugourdeau and CEPS seminar participants for their insightful comments. Helpful comments have also been received from participants at EAAE PhD Workshop in Uppsala, FAERE Annual Conference in Rennes, AAEA Annual Conference (online), EAERE Annual Conference (online), EAERE Winter School in Ascona, EAAE Annual Conference (online), and friends of the Plouguerneau Spring School. I acknowledge the support of the funding from the Agence Nationale de la Recherche as part of the Cland Institut de convergence (ANR-16-CONV-0003).

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## SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.

**How to cite this article:** Henry, Loïc. 2023. “Adapting the Designated Area of Geographical Indications to Climate Change.” *American Journal of Agricultural Economics* 105(4): 1088–1115. https://doi.org/10.1111/ajae.12358

## APPENDIX A

### PROOFS

*Proof of Propositions 1.A and 1.B*

When quality is independent of the supply composition, $s'_G(y_E) = 0$, and from Equations (11) and (14), the socially optimal delineation corresponds to the competitive delineation, that is, $\hat{y} = y^*$. In these situations, the GI net land rent at the border satisfies

$$ \alpha_G(y^*) \{p_G[Q_G(y^*), s_G] - \nu_G w\} - \alpha_C(y^*)(p-w) = 0. \quad (A.1) $$

Taking Equation (12) and canceling the term in $s'_G$, the collective delineation is such that the GI net land rent of the producers at the border equals the marginal revenue, which is positive. This implies the following inequality for the producers at the border:

$$ \alpha_G(\tilde{y}) \{p_G[Q_G(\tilde{y}), s_G] - \nu_G w\} - \alpha_C(\tilde{y})(p-w) > 0. \quad (A.2) $$

Now, we need to show that the GI net land rent in the left-hand term in expressions (A.1) and (A.2) is monotonically increasing in $y_S$ and $y_E$. If this is the case, the collective delineation is reached for the optimal $y_E = \tilde{y}$ greater than $y^*$. For the competitive delineation to exist, the land rent at the GI border when the border corresponds to the boundaries of $\mathcal{Y}$, that is, when $y = \{\underline{y}, \bar{y}\}$, must satisfy:

$$ \alpha_G(\underline{y}) [p_G(Q_G(\underline{y}), s_G) - \nu_G w] \leq \alpha_C(\underline{y})(p-w) \quad (A.3) $$

$$ \alpha_G(\bar{y}) [p_G(Q_G(\bar{y}), s_G) - \nu_G w] > \alpha_C(\bar{y})(p-w). \quad (A.4) $$

The conditions in Equations (A.3) and (A.4) mean that the producers at the boundaries of land characteristics distribution must always have a comparative advantage in the commodity for $y^* = \underline{y}$ and in the GI for $y^* = \bar{y}$. Now, as $\alpha(\cdot)$ is a monotonic function, the land characteristics at the border with a GI net land rent that is zero $y^*$ are uniquely defined by:
$$y^* = \alpha^{-1} \left( \frac{p-w}{p_G(Q_G, s_G) - \nu_G w} \right) \qquad (A.5)$$

Therefore, for the GI net land rent to be strictly positive in $\tilde{y}$, it requires $\tilde{y} > y^*$. .

Now, we need to order the size of the GI area of production when quality depends on the terroir. It is clear that $\tilde{y}$ and $\hat{y}$ are greater then $y^*$. Following the reasoning above, characterizations in Equations (12) and (14) lead to a positive GI net land rent at the border and as a result greater land characteristics at the border than under competitive delineation. Comparison of the socially optimal delineation and the collective delineation is not straightforward. To get further insights, I study the slope of the welfare function in the neighborhood of $\tilde{y}$. Given the concavity of the welfare function $W(y_E)$, the sign of the slope of $W(\cdot)$ in the neighborhood of $\tilde{y}$ will determine whether the optimal collective delineation is above or below the socially optimal delineation $\hat{y}$. Note that sufficient conditions for the GI industry aggregate net revenue and the welfare function to be concave are presented in the online supplementary Appendix S1 in (B.3) and (B.15). The derivative of $W$ when evaluated at $\tilde{y}$ yields:

$$ \begin{aligned} \left. \frac{\partial W(y_E)}{\partial y_E} \right|_{y_E=\tilde{y}} &= \dot{s}_G(\tilde{y}) \int_0^{Q_G(\tilde{y})} \frac{\partial p_G(v, s_G)}{\partial s_G} dv - Q_G(\tilde{y}) \left[ \frac{\partial p_G(Q_G, s_G)}{\partial Q_G} \dot{Q}_G(\tilde{y}) + \frac{\partial p_G(Q_G, s_G)}{\partial s_G} \dot{s}_G(\tilde{y}) \right] \\ &= Q(\tilde{y}) \frac{(\theta - \theta_0)}{2N} \left[ \dot{s}_G(\tilde{y}) Q_G(\tilde{y}) + 2s_G(\tilde{y}) \dot{Q}_G(\tilde{y}) \right] \\ &= CS(\tilde{y}) \left[ \frac{\dot{s}_G(\tilde{y})}{s_G(\tilde{y})} + 2 \frac{\dot{Q}_G(\tilde{y})}{Q_G(\tilde{y})} \right]. \end{aligned} \qquad (A.6) $$

The variation in welfare induced by a marginal change in the collective area of production corresponds to the change in consumer's surplus induced by the changes in quantity and quality. According to our assumption regarding preferences for the GI, quantity variation weighs twice as much as quality variation in the change in welfare at the margin of the collective allocation. The sign of welfare variation when marginally changing the border of the collective area of production corresponds to the sign of $\frac{\dot{s}_G(\tilde{y})}{s_G(\tilde{y})} + 2\frac{\dot{Q}_G(\tilde{y})}{Q_G(\tilde{y})}$. Studying the sign of this expression is equivalent to comparing $\varepsilon_{s_G/y_E} + 2\varepsilon_{Q_G/y_E}$, where $\varepsilon_{s_G/y_E}$ and $\varepsilon_{Q_G/y_E}$ are defined in Equation (15) and are respectively the elasticity of GI quality and the elasticity of GI quantity with marginal changes in the area of production. As a result, the derivative in Equation (A.6) is positive when $\varepsilon_{s_G/y_E} \ge -2\varepsilon_{Q_G/y_E}$, implying that $\tilde{y}$ is lower than $\hat{y}$, and is strictly negative when $\varepsilon_{s_G/y_E} < -2\varepsilon_{Q_G/y_E}$ implying that $\tilde{y}$ is strictly greater than $\hat{y}$.

### Proof of Proposition 2

Note that this proof is obtained when quality depends on the terroir and can be recovered when quality is independent by replacing $s_G(y^*)$ with an exogenous and invariant parameter. Characterization of $y^*$ in Equation (11) can be rewritten as a function of $\delta$ (omitting for clarity the $y^*$ argument inside $p_G$ operating through the $Q_G(y^*)$ and $s_G(y^*)$ functions):

$$ (1 - \delta) \alpha_G(y^*) [p_G(Q_G, s_G) - \nu_G w] - \alpha_C(y^*) (p - w) = 0. \qquad (A.7) $$

Note that $Q_G$ is a linear function of $\delta$. By totally differentiating Equation (A.7) and canceling it so that the GI area of production is still determined from the competitive equilibrium on the GI market,
the variation in the GI area of production at the margin following an increase in $\delta$ is given by (omitting the $Q_G$ and $s_G$ arguments in the GI price function):

$$ \frac{dy^*}{d\delta} = \frac{\alpha_G(y^*)(p_G - \nu_G w) + \alpha_G(y^*) \frac{\partial p_G}{\partial Q_G} Q_G(y^*)}{(1 - \delta) \alpha'_G(y^*)(p_G - \nu_G w) - \alpha'_C(y^*)(p - w) + (1 - \delta) \alpha_G(y^*) \left[ \frac{\partial p_G}{\partial s_G} Q'_G(y^*) + \frac{\partial p_G}{\partial s_G} s'_G(y^*) \right]} \quad (A.8) $$

We have to determine the sign of Equation (A.8). Regarding the denominator, following Assumption 3 on preferences, we have $\frac{\partial p_G}{\partial Q_G} Q'_G(y^*) > 0$ and $\frac{\partial p_G}{\partial s_G} s'_G(y^*) > 0$. Following Assumption 1 regarding comparative advantage structure, we have that $\frac{\alpha'_G(y^*)}{\alpha_G(y^*)} \ge \frac{\alpha'_C(y^*)}{\alpha_C(y^*)}$ for all $y \in \mathcal{Y}$. For the producers at the border of the GI area under competitive delineation and for a given $\delta$, we know that marginal net land rent for the commodity and for the GI are equal (Equation (11)), hence multiplying the left-hand side of Equation (11) by $\frac{\alpha'_G(y^*)}{\alpha_G(y^*)}$ and right-hand side by $\frac{\alpha'_C(y^*)}{\alpha_C(y^*)}$ yields $(1 - \delta)\alpha'_G(y^*)(p_G - \nu_G w) \ge \alpha'_C(y^*)(p - w)$. So, the denominator is always positive.

The sign of the variation in $y^*$ with increase in $\delta$ is thus determined by:

$$ \left(\frac{dy^*}{d\delta}\right) = \left\{ \alpha_G(y^*)[p_G(Q_G, s_G) - \nu_G w] + \alpha_G(y^*) \frac{\partial p_G(Q_G, s_G)}{\partial Q_G} Q_G(y^*) \right\} \quad (A.9) $$

Now, we study the sign of the expression in Equation (A.9). As under competitive delineation, we have $\alpha_G(y^*)[p_G(Q_G, s_G) - \nu_G w] = \alpha_C(y^*)(p - w)$, it can be written as:

$$ \alpha_G(y^*)[p_G(Q_G, s_G) - \nu_G w] + \alpha_G(y^*) \frac{\partial p_G}{\partial Q_G} Q_G(y^*) = \alpha_C(y^*)(p - w) + \alpha_G(y^*) \frac{\partial p_G}{\partial Q_G} Q_G(y^*) \quad (A.10) $$

$$ = \alpha_C(y^*)(p - w) + (1 - \delta)\alpha_G(y^*) \frac{\partial p_G}{\partial Q_G} \int_{y^*}^{\bar{y}} \alpha_G(u)f(u)du. \quad (A.11) $$

First, note that expression in Equation (A.11) linearly increases with $\delta$ (because $\frac{\partial p_G}{\partial Q_G} < 0$). Second, consider the most extreme climate scenario, measured with parameter $\bar{\delta}$, where producers cannot any longer allocate their land to the GI, except the most efficient producers with land characteristics $\bar{y}$. Following characterization of $y^*$ in Equation (A.11), $\bar{\delta}$ is defined by the following expression:

$$ \bar{\delta} = 1 - \frac{\alpha_C(\bar{y})(p - w)}{\alpha_G(\bar{y})[\bar{y}\theta - \nu_G w]}, \quad (A.12) $$

because $p_G(Q_G(\bar{y}), s_G(\bar{y})) = \bar{y}\theta$. For $\delta = \bar{\delta}$, a marginal increase in $\delta$ implies that no producers are able anymore to sustain the production of the GI, because they now all have a comparative advantage in the commodity. Note that the aggregate quantity supplied when the marginal land characteristics are $\bar{y}$ is zero. The expression in Equation (A.11) reduces to $\alpha_C(y^*)(p - w)$, which is positive to ensure an interior equilibrium in the GI market. Therefore, in the neighborhood of $\bar{\delta}$, the numerator in Equation (A.8) is positive at $\bar{\delta}$, and $\frac{dy^*}{d\bar{\delta}} > 0$.

Thus, the expression in Equation (A.11) is linearly increasing and reaching a positive value at its upper boundary $\bar{\delta}$. Then, there is a parameter $\delta^*$, with $\delta^* < \bar{\delta}$ where the expression in Equation (A.11) is zero, which is the value of the climate parameter where there is no entry or exit with marginal deviations in climate conditions under competitive delineation. From Equation (A.11), $\delta^*$ is defined by:
$$ \delta^* = 1 + \frac{p-w}{\alpha(y^*) \int_{y^*}^{\bar{y}} \alpha_G(u)f(u) du \frac{\partial p_G}{\partial Q_G}}, \quad (A.13) $$

where the second term in Equation (A.13) is negative. As a result, following Equation (A.9), if in the historical GI market equilibrium, $y^{*H} \equiv y^*(\delta|\delta=0)$, the following condition is satisfied,

$$ \frac{p-w}{\alpha(y^{*H})} \geq -Q_G(y^{*H}) \frac{\partial p_G}{\partial Q_G}|_{y^*=y^{*H}}, \quad (A.14) $$

it implies that $\delta^* \le 0$ and that the numerator of Equation (A.8) is positive all along the interval of climate parameter $[0, \bar{\delta}]$. Thus, it results in the adaptation response where $\frac{dy}{d\delta} \ge 0$ for all $\delta$ in $[0, \bar{\delta}]$.

By contrast, if in the historical GI market equilibrium, the following condition is satisfied,

$$ \frac{p-w}{\alpha(y^{*H})} < -Q_G(y^{*H}) \frac{\partial p_G}{\partial Q_G}|_{y^*=y^{*H}}, \quad (A.15) $$

it implies that $\delta^* > 0$, and that the numerator of Equation (A.9) is negative for $\delta$ in $[0, \delta^*]$ and positive for $\delta$ in $[\delta^*, \bar{\delta}]$, resulting in the adaptation response where $\frac{dy^*}{d\delta} \le (>0)$ for $\delta \le \delta^*$.

### Proof of Proposition 3

Note that this proof is obtained when the quality is dependent on the terroir and can be recovered when quality is independent by replacing $s_G(\tilde{y})$ with an exogenous and invariant parameter. Characterization of $\tilde{y}$ in Equation (12) can be rewritten to account for the climate parameter $\delta$ (omitting the $\tilde{y}$ argument inside $p_G$ operating through the $Q_G(\tilde{y})$ and $s_G(\tilde{y})$ functions for clarity):

$$ Q_G(\tilde{y}) \left[ -f(\tilde{y})(1-\delta)\alpha_G(\tilde{y}) \frac{\partial p_G(Q_G, s_G)}{\partial Q_G} + \frac{\partial p_G(Q_G, s_G)}{\partial s_G} s_G'(\tilde{y}) \right] = f(\tilde{y}) \left\{ (1-\delta)\alpha_G(\tilde{y}) [p_G(Q_G, s_G) - \nu_G w] - \alpha_C(\tilde{y})(p-w) \right\}. \quad (A.16) $$

By totally differentiating Equation (A.16) and canceling it so that the GI production area is still defined collectively, we obtain the adaptation of the GI area of production at the margin following an increase in $\delta$ (omitting the $Q_G$ and $s_G$ arguments in the GI price function $p_G$, and the $\tilde{y}$ argument in $Q_G$ and $s_G$):

$$ \frac{d\tilde{y}}{d\delta} = \frac{\frac{1}{1-\delta} \left\{ 3Q'_G Q_G \frac{\partial p_G}{\partial Q_G} + Q'_G (p_G - \nu_G w) + Q_G s'_G \left( \frac{\partial p_G}{\partial s_G} + \frac{\partial^2 p_G}{\partial Q_G \partial s_G} Q_G \right) \right\}}{\frac{\partial^2 \Pi_G(\tilde{y}, \delta)}{\partial y_E^2}}. \quad (A.17) $$

where the denominator of Equation (A.17), namely $\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial y_E^2}|_{y_E=\tilde{y}}$ defined as in the online supplementary Appendix S1 in Equation (B.3), must be negative to ensure the concavity of profits. The numerator of Equation (A.17), which is $-\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=\tilde{y}}$, measures the variation in marginal profitability of exclusion with marginal variations in climate conditions. Its sign is ambiguous. You can refer to the online supplementary Appendix S1, Equation (B.16), for detailed interpretations of the
terms in the numerator of Equation (A.17) and their respective signs. Its sign ultimately depends on the strength of climate change $\delta$. Using the expression of inverse demand function in Equation (4), we simplify its expression, and we obtain:

$$-\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y} = (1-\delta) \left[ 4 \frac{Q_G Q_G'}{(1-\delta)^2} \frac{\partial p_G}{\partial Q_G} + 2 \frac{Q_G^2}{(1-\delta)^2} s_G' \frac{\partial^2 p_G}{\partial Q_G \partial s_G} \right] + \bar{\theta} \left( \frac{Q_G'}{1-\delta} s_G + \frac{Q_G}{1-\delta} s_G' \right) \\ - \nu_G w \frac{Q_G'}{1-\delta}. \qquad (A.18)$$

Because $Q_G(\tilde{y})/(1-\delta) = \int_{y}^{\tilde{y}} \alpha_G(y)f(y)dy$ and $Q_G'(\tilde{y})/(1-\delta) = -\alpha_G(\tilde{y})f(\tilde{y})$, the variations of the marginal profitability of exclusion with the climate-induced parameter in Equation (A.18) are a linear function of $\delta$, where $-\left[4 \frac{Q_G Q_G'}{(1-\delta)^2} \frac{\partial p_G}{\partial Q_G} + 2 \frac{Q_G^2}{(1-\delta)^2} s_G' \frac{\partial^2 p_G}{\partial Q_G \partial s_G}\right]$ is the slope and the rest of the terms forms the intercept.

Consider the most extreme climate scenario, measured with parameter $\bar{\delta}$, where producers cannot any longer allocate their land to the GI, except the most efficient producers with land characteristics $\bar{y}$. Further, $\bar{\delta}$ is defined equivalently as in the competitive delineation case by the expression in Equation (A.12). Note that for $\delta = \bar{\delta}$, the aggregate quantity of GI is zero and the variations of the marginal profitability of exclusion with the climate-induced parameter (numerator in Equation (A.17)) reduce to $Q_G'(p_G - \nu_G w)$, which is negative. Therefore, in the neighborhood of $\bar{\delta}$, $-\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y, \delta=\bar{\delta}}$ is always negative, that is, the marginal profitability of exclusion increases with $\delta \left( \frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E} \right)_{y_E=y, \delta=\bar{\delta}} > 0$ and $\frac{d\tilde{y}}{d\bar{\delta}} > 0$.

Next, the linear expression in Equation (A.18) increases with $\delta$ on $[0, \bar{\delta}]$ if the following condition is satisfied:

$$2Q_G' \frac{\partial p_G}{\partial Q_G} \le -Q_G s_G' \frac{\partial^2 p_G}{\partial Q_G \partial s_G} \Leftrightarrow -2\epsilon_{Q_G/y_E} \le \epsilon_{s_G/y_E}, \qquad (A.19)$$

and the expression decreases with $\delta$ on $[0, \bar{\delta}]$ if the following condition is satisfied:

$$2Q_G' \frac{\partial p_G}{\partial Q_G} > -Q_G s_G' \frac{\partial^2 p_G}{\partial Q_G \partial s_G} \Leftrightarrow -2\epsilon_{Q_G/y_E} > \epsilon_{s_G/y_E}. \qquad (A.20)$$

When $-2\epsilon_{Q_G/y_E} \le \epsilon_{s_G/y_E}$, the linear expression in Equation (A.18) always increases with $\delta$. As it is negative at $\delta = \bar{\delta}$; it is then always negative over the whole range of climate scenarios; in other words, $-\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y} \le 0$ for all $\delta$ in $[0, \bar{\delta}]$. As a result, $\frac{d\tilde{y}}{d\bar{\delta}} > 0$, and we obtain the second part of the adaptation response in Proposition 3.

Now, in the situation where $-2\epsilon_{Q_G/y_E} > \epsilon_{s_G/y_E}$, the linear expression in Equation (A.18) always decreases with $\delta$. Therefore, at $\delta = \bar{\delta}$ we have that $-\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y, \delta=\bar{\delta}} < 0$, and for a parameter $\tilde{\delta}$ with $\tilde{\delta} < \bar{\delta}$, we have $\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y, \delta=\tilde{\delta}} = 0$, which is the value of the climate parameter where there is
no adaptation in GI area with changes in climatic conditions under collective delineation. From Equation (A.17), $\tilde{\delta}$ is implicitly defined by:

$$3\dot{Q}_G Q_G \frac{\partial p_G}{\partial Q_G} + \dot{Q}_G (p_G - \nu_G w) + Q_G \dot{s}_G \left( \frac{\partial p_G}{\partial s_G} + \frac{\partial^2 p_G}{\partial Q_G \partial s_G} Q_G \right) = 0. \quad (A.21)$$

As we consider deviations from the optimum of the collective delineation, the term $\dot{Q}_G(p_G - \nu_G w)$ corresponds to the opposite of the marginal revenue of exclusion minus the land rent for the commodity at the border (see the FOC of the collective delineation program in Equation (12)), the implicit expression of $\tilde{\delta}$ in Equation (A.21) can be expressed as follows:

$$\tilde{\delta} = 1 - \left\{ \frac{f(\tilde{y}) \alpha_C(\tilde{y}) (p - w)}{\int_{y}^{\tilde{y}} \alpha_G(u) f(u) du \left[ \frac{\partial^2 p_G}{\partial Q_G \partial s_G} \dot{s}_G(\tilde{y}) \int_{y}^{\tilde{y}} \alpha_G(u) f(u) du - 2 \frac{\partial^2 p_G}{\partial Q_G} f(\tilde{y}) \alpha_G(\tilde{y}) \right]} \right\}^{1/2} \quad (A.22)$$

Finally, if in the historical collective delineation, $\tilde{y}^H = \tilde{y}(\delta|\delta=0)$, the marginal profitability of exclusion increases with climate-induced deterioration in the GI conditions of production, $\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y, \delta=0} \stackrel{\sim}{\le} 0$, then $\tilde{\delta} \le 0$. So, the numerator in Equation A.17 is always negative all along the interval of climate parameter, that is, $-\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y} \stackrel{\sim}{\le} 0$ for all $\delta$ in $[0, \bar{\delta}]$. Thus, it results in the second part of the adaptation response in Proposition (3), that is, $\frac{\tilde{y}}{\delta} \ge 0$ for all $\delta$ in $[0, \bar{\delta}]$.

By contrast, if in the historical situation, the marginal profitability of exclusion decreases with climate-induced deterioration in the GI conditions of production, $\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y, \delta=0} < 0$, then $\tilde{\delta}$ is such that $0 < \tilde{\delta} < \bar{\delta}$. In this case, there is an incentive to increase the area of production because the marginal profitability of exclusion decreases for some climate-induced deterioration in the conditions of GI production. Then, the numerator in Equation (A.17) is positive; that is, $-\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y} \ge 0$ for $\delta$ in $[0, \tilde{\delta}]$ and strictly negative for $\delta$ in $[\tilde{\delta}, \bar{\delta}]$, resulting in the adaptation response in the first part of Proposition (3).

Also, note that the variations of the marginal profitability of exclusion with climate-induced deterioration in the conditions of GI production when evaluated at the historical collective outcome derives as follows:

$$\frac{\partial^2 \Pi_G(y_E, \delta)}{\partial \delta \partial y_E}|_{y_E=y, \delta=0} = -Q_G(\tilde{y}^H) \left[ \frac{\partial^2 p_G}{\partial Q_G \partial s_G}|_{y=y} \stackrel{\sim}{\le} Q_G(\tilde{y}^H) \dot{s}_G(\tilde{y}^H) + 2 \frac{\partial^2 p_G}{\partial Q_G}|_{y=y} \stackrel{\sim}{\le} Q_G(\tilde{y}^H) \right] + f(\tilde{y}^H) \alpha_C(\tilde{y}^H) (p - w), \quad (A.23)$$

where the first term in Equation (A.23) measures the diminution in the marginal profitability of exclusion under a climate-induced deterioration in the GI conditions of production, which is associated with the diminution in the marginal benefits of exclusion. This diminution in the marginal benefits of exclusion results from the decrease of the GI production from the included producers under climate change, and this is not compensated for by the increase in willingness to pay for quality. The second term in Equation (A.23) measures the increase in the marginal profitability of exclusion
under a climate-induced deterioration in the GI conditions of production, which is associated with the diminution of the marginal costs of exclusion. This component also interpretes as the decrease of the foregone profits associated to the marginally excluded producers under climate change, because the producers at the border potentially produce less GI under climate change.