Managing animal health status information in the cattle market

Transcription

1 Managing animal health tatu information in the cattle market Rat-Apert O., Weldegeriel HT. 2, Stott AW. 2, Fourichon. National Veterinary School of Nante, INRA, UMR300 Biology, Epidemiology and Rik Analyi, Nante, France 2 Scottih Agricultural ollege, Animal Health Economic, Edinurgh, Scotland Atract The paper analye the prolem of information in the cattle market, particularly a it relate to the tatu of animal health, and dicue way to limit it with the view to improving ocial urplu. Againt thi ackground, it aim to achieve three major ojective. Firtly, it decrie the way of improving the level of information through uch cheme a onventional Warrantie and Third arty ertification and the different choice made y eller and uyer in the preence of thee cheme. Secondly, it tudie the variou way y which thee cheme make an impact on equiliria in different market (i.e., the pooling market and the premium market), and, conequently, on the ocial urplu. Thirdly, it identifie the neceary condition for a third party/pulic deciion-maker to increae ocial urplu and reduce the negative externality caued y dieae y managing and upporting Third arty ertification. The paper how that product certification and product warranty cannot coexit ecaue product warranty i uoptimal. It alo how that certification, and a poile upporting of certification or animal teting doe not necearily improve the afety of the trade. Keyword Aymmetric information Third-party certification Dieae Externalitie I. INTRODUTION Since Akerlof (970) introduced the world to hi market for lemon, there ha een a wide recognition of the importance of incomplete information in different market. A a reult of thi recognition, a numer of paper have een written which purport to dicu incomplete information, particularly information aymmetry, and point out poile way of limiting it. Notale paper in thi repect include Spence (973), Rothchild and Stiglitz (976), Stiglitz and Wei (98) and Allen (993), to name jut a few. In the cattle market, which form the focu of our paper, the prolem of information i quite prominent; even though the health tatu of the animal i important information for the uyer, thi information i rarely directly oervale. A numer of paper have invetigated the nature of the prolem in thi market from different angle. Allen (993) look at the phenomenon of Holtein veal calve dominating live eef auction in Britih olumia a a reflection of the prolem of aymmetric information in the market. arriquiry and Bacock (2004), however, argue that the information prolem prevalent in the market hould not necearily e one of aymmetry. In fact, they argue that given that delivered quality can only e imperfectly learned and affected tochatically y producer, the prolem of information can e oth ymmetric and aymmetric. For contagiou dieae, farm infection often arie either through contact with the environment or through contact with neighouring farm and with wild animal. However, uch an infection can alo ometime arie through trade involving infected animal. If they know that the environment i the ource of infection, farmer can take ioecurity meaure to eparate their herd from the environment. However, if the ource of infection i known to e trade involving infected animal, it i not eay for them to take any particular meaure a the ource of uch an infection are varied and difficult to identify. To protect their herd from the impact of dieae introduced to their farm ome farmer decide not to uy any animal and work a cloed herd (Ezanno et al, 2006). Other farmer ometime revaccinate their cattle after purchae, ut cannot e efficient for all pathogen (hymi et al., 2007). In the face of uncertainty regarding the ource of infection in the market place it i not urpriing that they reort to thee meaure. Infection through purchae of an infected animal i known to reduce the productivity and increae the mortality rate among herd. Furthermore, dieae pread triggered y the purchae of infected animal can at time have direct impact on human health or on the farm ytem. In order to promote ocial welfare, dieae that have nationwide implication are often 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

2 2 regulated with the community auming the rik. But dieae whoe impact i limited to the farm are not o regulated and, conequently, farmer are left to ear the cot of containing dieae pread. In practice thi ditinction i not clear cut. In Great Britain, policy maker are often concerned that takeholder pay for improvement in animal health in proportion to their enefit (Defra et al, 2004). Thi make it particularly important to undertand the market mechanim involved. For ome uch dieae a BVDV, the tatu of the animal purchaed i not well known at the time of trading ecaue there i no apparent dieae ymptom. In thi particular intance, uyer have two choice: either to take a major rik of infection y not teting the animal purchaed or to tet the animal after purchae. There are different tet for verifying the dieae-free tatu of the animal. However, reult are not alway perfect. Even though teting of the animal after purchae might limit the pread of the dieae, contact of purchaed animal with the herd often occur efore the tet reult i received y the farmer. Given the limited effectivene of teting in dealing with the prolem of infection through trade, therefore, the uyer ettle for acquiring information regarding the health tatu of the animal traded. Knowledge of an attriute reflecting the health tatu of an animal allow the uyer to reduce the rik of introducing the dieae to their own farm. Seller can provide thi knowledge y upplying animal whoe dieae tatu i known at a premium price. They can make thi attriute known to the uyer via, among other, onventional Warranty () and Third arty ertification (), contractual term, repeat purchae, rand name and hare contract (entner and Wetztein., 987). If the uyer know the eller, he can place trut in the latter 2. But when the uyer doe not know the eller, it i often the cae that he i ignorant of the tatu of the farm from which the animal purchaed originated. There are a numer of intance which give rie to and. Taking the French cattle market a an. ovine viral diarrhea viru 2. With imperfect information for the eller, the extent of repeat purchae or trut i limited. But it can e poile ecaue even if the information i incomplete for the eller, there i aymmetric information. intance, for regulated dieae, uyer are protected y latent defect warrantie, and the introduction of teting of animal i oligatory for dieae like rucelloi, tuerculoi and IBR 3. For BVDV, a not o regulated dieae, there i, in Brittany, a plan of certification of the animal managed y the GDS (Groupement de Défene Sanitaire). Thee are voluntary producer' aociation working on managing farm animal dieae. Indirect method, uch a teting ulk tank milk, allow the identification of farm tatu without teting all the animal, and deductive method identify the tatu of animal. In the cae of BVDV, the "Référentiel non II" (FNGDS, 2005), which i a protocol of certification of farm and animal, i ued. Herd certification i alo ued in the cae of paratuerculoi a the quality of the tet i not ufficient to certify animal dieae-free individually. When there i no latent defect warranty in place for dieae that are not o regulated, the eller and the uyer can alo vote for a onventional Warranty. Such a warranty give uyer a cahack guarantee when they return the animal to the original eller if the animal i found to e infected within a hort period after purchae. Thi warranty applie to dieae like paratuerculoi and BVDV ut i limited y the quality of the tet. By enuring the afety of the tranaction, thi kind of market can have an impact on the level of dieae prevalence. The prevalence of the dieae can, in turn, have an impact on the potential upply and demand for animal with a known dieae tatu. Againt thi ackground, thi paper et out to analye the prolem of information in the cattle market, particularly a it relate to animal health tatu, and dicue way of limiting it with the view to improving ocial urplu. In thi repect, it aim to achieve three major ojective. Firtly, it decrie the way of improving the level of information through uch cheme a and and the different choice made y eller and uyer in the preence of thee cheme. Secondly, it tudie the variou way y which thee cheme make an impact on the market equilirium, and, conequently, on the ocial urplu. Thirdly, it identifie the neceary condition for a third party/pulic deciion-maker to increae ocial 3. Infectiou Bovine Rhinotracheiti 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

3 3 urplu and reduce the negative externality caued y dieae y managing and upporting. II. MODELING ATORS DEISION The information prolem analyed i characteried y () the availaility of limited information regarding the tatu of the animal for the uyer and for the eller and (2) an aymmetry of information wherey the eller ha full information aout the health tatu of their cattle, ut the uyer ha imperfect information regarding the health tatu of animal traded (i.e., he/he ha a perception of the average level of the health tatu of animal in the market). In thi context, we decrie three type of tranaction; one without either warrantie or third party certification (), another one with and a third one with punctual contract, (). Following hymi et al. (2007), we define for each type of tranaction the enefit B for eller and the cot for the uyer. Thee cot and enefit are a function of the level of dieae incidence (or level of prevalence), for the uyer farm and for the eller farm 4. The average value of the prevalence,, i alo the average rik to uy an infected animal. Regardle of the type of exchange that prevail in the market, we aume that farmer are rik neutral and honet in their dealing and that either they maximie expected enefit or minimie expected cot once involved in trade. Given thee aumption, the eller maximie the expected enefit B of elling an animal coniting of the price of the animal minu expected cot due to dieae rik wherea the uyer minimie, the expected cot of uying an animal coniting of the price of the animal plu expected cot due to dieae rik. A. Trade without dieae information () Firtly, conider trade without dieae information, where there i only one price which rule in the market, i.e., the price in the pooling market. In the aence of full information regarding the health tatu of the animal purchaed, the uyer ha two deciion option; either to uy the animal without teting or tet 4. ecaue of lack of information and can e a perceived prevalence of the dieae. the animal after purchae. If the deciion i to uy the animal without teting, then the uyer' expected cot of purchae i: = + c, () where i the price in the pooling market, and c i the cot of infection when the uyer purchae an infected animal, with a proaility. We aume that c i a continuou function of, c( ), which atifie c( ) 0 and c, the firt derivative of c atifie c ( ) 0. Thi tate that the impact of the introduction of an infected animal i more important in the naive farm than in an infected farm ecaue the rik of infection on uch a farm i higher than on one whoe herd are more reitant to infection. Beyond the individual cot of the introduction of an infected animal, purchae without teting caue a negative externality a it increae infection rik for the neighourhood and the uyer y raiing the level of dieae prevalence. Thi effect, in eence, i not conidered y the uyer. If the deciion i to uy an animal and tet it after purchae, then the uyer keep on purchaing to the extent that the animal i not infected and that animal infected are culled. Thu the cot to the uyer i: + t ( c o) W = (2) where t i the cot of the tet, c i the enefit of culling the animal, and o i the opportunity cot of keeping the animal on farm. To implify the model, we aume that the tet i perfect (i.e., there i neither a fale poitive nor a fale negative cae), and that there i no longer any rik of infection once the infected animal i culled. See Annex for the derivation of thi equation. When animal are not differentiated y their health tatu, then, in the aence of full information regarding their health tatu, there i an apparent homogeneity of the rate of prevalence among different farm. In thi context, the eller ha no choice ut to ell at the pooling price with an expected enefit, B = (3) 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

4 4 B. Trade with Third arty ertification () Now conider the choice of the uyer and of the eller when the market involve. In uch a market, the cot of uying an animal i pecified a: = (4) where denote the premium price paid for a certified animal. To implify the model, we aume that the i o perfect a a tet that all animal old under the cheme are uninfected. The enefit to the eller of elling a certified animal i given y B ( ) + c c = (5) where c i a predetermined cot of certification 5. We aume that the animal i culled once it i infected (i.e., once it fail the certification tage); o eller ell at price with a proaility and cull the animal with a proaility.. Trade with onventional Warranty Finally, conider the choice of the uyer and of the eller when the market involve. Aume that, given thi exchange regime, the uyer tet every traded animal and keep on purchaing to the extent that uch an animal i not infected 6. The expected cot to the uyer can then e repreented a: = + t ( r o ) (6) The derivation of (6) i the ame a of (2), except that c o i replaced y r o'. r denote the cahack whoe component are the price of the animal ought with,, and a part of o' 7, the 5. We could alo aume that c depend on the level of prevalence in the eller farm. 6. Therefore we ignore the cae where the uyer doe not tet the animal ecaue he aume that animal old with are le likely to e infected. But even thi cae can e tudied uing the theory of game. 7. Note that the poiility to tet the animal on the eller' farm can reduce o, ut here, we aume that the uyer trade cot of purchae and of return plu the opportunity cot of doing o. Here, i the perceived average rik to uy an animal infected in the cae of the onventional Warranty, thi average rik mut e le than, ecaue farm with a high level of dieae do not trade with onventional Warranty. When r = + o' + t, we have a perfect warranty for the uyer with = + t. The expected enefit to the eller of elling an animal with i given y: B ( r c) = (7) The aumption here i that the eller cull the animal if returned y the uyer. In thi cae, the enefit of the eller i compoed of the price of the animal minu the cot when the animal i returned, compoed of the cahack r minu the enefit of culling the animal c, alanced y. D. oexitence of onventional Warranty and Third arty ertification To thi tage, the implicit aumption ha een that and coexit. We can aume that r, the cah ack for the uyer when he return an animal with onventional Warranty i greater than the direct cot of the trade, compoed of the cot of the animal and the cot of the tet on farm, and lower than the total cot of the trade, compoed of the direct cot and the opportunity cot. So, r atifie: + t r + t + o' (8) Given thi aumption, eller trading in a market with require that : ( + t r) > t c (9) For proof, ee Annex 2. The logic goe a follow. Since the tet guarantee no infection (thi i in accordance with the hypothei of perfect tet and perfect certification), we have c < t. So, when the cahack r i greater than the cot of uying,, in a pooled market where there i no poiility for teting the animal efore trade. 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

5 5 plu the cot of teting t, drive out from the market. Thu, in the following, we dicu market equilirium with only. III. DERIVATION OF SULY AND DEMAND FUNTIONS OF ANIMAL HEALTH STATUS In thi ection, we identify the condition under which equilirium exit in a cattle market where operate. To help identify thee condition, conider a hypothetical market where the price of animal trade without warranty and the rik of uying an infected animal without certification are given. Thi aumption hold when the market for cattle operate at a gloal level wherea the market for certified animal operate at the local level, ecaue in uch a market, animal without certification are ought on the gloal market and local actor do not impact the gloal market and the gloal epidemiology. onider alo that the numer of animal traded i given, ecaue the urplu given to uyer and eller y the do not impact their upply or demand. In thi market, the following aumption hold: firtly, the uyer doe not chooe the eller; econdly, he uy at an equilirium price ecaue the product (i.e., cattle) eing traded in the two market i homogeneou; and, thirdly, neither the eller nor the uyer ha market power. Aume that eller and uyer are characteried only y the level of dieae prevalence among their cattle, which i linearly ditriuted in the population, and that they have perfect knowledge of market price, of cot and of rik. Furthermore, aume that all uyer (repectively eller) uy (repectively ell) the ame numer of animal. Since for each uyer (repectively eller), the maximum (repectively minimum) price premium at which he uy (repectively ell) an animal with i a function of (repectively ), we can derive partial upply and demand function for the certified animal and, define the reulting equilirium in the market. Let θ (repectively θ ) e the proportion of eller (repectively uyer) who verify θ (repectively θ ). With the ame uniform ditriution for uyer and eller, the following hold: θ θ θ = ; θ = (0) 2 2 We ued here a uniform ditriution and the ame ditriution for eller and uyer, ut the ame reult follow any other continuou ditriution. A mentioned earlier, the eller chooe if and only if B > B wherea the uyer chooe if and only if <. Given thee choice, we can derive the price pref and pref at which θ eller and θ uyer chooe to trade with a: pref( θ ) pref( θ ) = min + c 2θ c = (a) with pref ( θ ) = 2θ ( pref ( θ ), pref ( θ )) + ( 2 θ ); ( o c) + and pref2 ( θ ) = 2 + t () For pref (θ 0 ) = pref 2, θ 0 repreent the proportion of uyer who uy and tet in a market where there i no. onider Φ to e the proportion of animal traded with. Aume that all the uyer and eller trade the ame numer of animal, then we have Φ = θ. Due to culling of infected animal prior to trade, we have Φ = θ ( θ ). We can derive the equilirium condition a: = pref( Φ) (2a) and pref 4 Φ = 2 + c c = + c 4 Φ (2) 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

6 6 Equation (2a) repreent the upply condition S wherea (2) repreent the demand condition D. They are ued to derive equilirium in Figure & 2 elow yielding the proportion, Ф*, of certified animal traded at the premium price, *. We repreent alo the preference curve pref. The area etween the pref curve and * repreent the urplu to eller offered y wherea the area etween the Demand curve D (ie the pref curve) and *, repreent the urplu to uyer offered y. The maximum value etween Ф* and θ 0 give the proportion of afe trade, o the proportion of animal exchanged are either certified or teted after purchae. In the following, we conider three cenario under which we determine the gain from trade with certification. The firt applie for Ф* > θ 0, the econd when Ф* < θ 0 hold and the third when the upply curve doe not cro the demand curve. rice * Buyer urplu Seller urplu θ 0 Ф* roportion Figure. Improvement of trade afety (Scenario ) 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

7 7 A. Scénario : Improvement of trade afety When Ф* > θ 0, oth the eller and the uyer gain a poitive economic urplu. The tet after purchae i uoptimal and i driven out y certification. The upply and demand in uch a cenario are repreented in Figure. Under thi cenario, a proportion, Ф*, of uyer uy with certification wherea a proportion, - Ф*, of uyer uy without certification and do not tet their purchaed animal. With the introduction of, the proportion of animal exchanged with the maximum level of afety increae y θ 0 Ф*. onequently, the negative externality caued y the trade of infected animal i reduced. rice * Seller urplu Ф* θ 0 roportion Figure 2. :Tranfer of reponiility from uyer to eller (Scenario 2) 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

8 8 B. Scenario 2: Tranfer of reponiility from uyer to eller When Ф* < θ 0, the eller gain economic urplu from trading in the certified market ut the uyer doe not. The upply and demand in uch a cenario are repreented in Figure 2. In the certified market, the price i given y pref 2. There i a proportion θ 0 of uyer who do not chooe etween teting the animal and uying a certified animal. Thi leave a proportion Ф* of uyer who uy with certification. The outcome of thi cenario i that a proportion, θ 0 Ф*, tet the animal after purchae and a proportion, ( θ 0 ), do not. Here, certification erve a a way for the eller to ignal the "dieae free" tatu of hi animal. In thi particular cae, certification doe not reduce the negative externality that arie due to trade involving infected animal. What take place in practice here i, therefore, a tranfer of reponiility for animal teting from the uyer to the eller with the reult that there i a proportion of uyer, who, rather than teting, uy with certification.. Scenario 3. The Inefficacy of ertification When pref i uperior to pref 2, Ф* = 0 and the upply curve doe not cro the demand curve. In thi cae, certification i inefficient, and, conequently, neither the uyer nor the eller gain a urplu, and the proportion of afe trade doe not increae. IV. A OSSIBLE OTIMISATION BY THE DEISION-MAKER In the preceding ection, we decried market equilirium and identified the different cenario under which certification enhance the level of farmer' urplu and the level of poitive externality which arie therein. In thi ection, we conider the poile intervention availale to the deciionmaker, i.e., the pulic-choice maker or uch producer' aociation a GDS intereted in reducing negative externality and increaing farmer' urplu. In the context of our model, it i ocially eneficial to introduce when the um of uyer' and eller' urplue derived from certification i greater than the cot of management of the upported y the deciion-maker. However, conidering Scenario, even if the cot of management i higher than the um of uyer' and eller' urplue, the deciion-maker might find the introduction of certification in the interet of ociety ince doing o reduce the negative externality reulting from infection. Our model alo allow the deciion-maker to upport the teting on farm of traded animal and ear the cot of certification in order to reduce negative externality. In oth cae, upport lead to a u-optimum equilirium wherey the net ocial urplu, compoed of farmer' urplu minu deciion-maker' cot, i reduced. But uch a upport can improve the level of trade afety a it improve farmer' welfare y reducing the rik of infection and, conequently, the level of dieae prevalence among farm. onidering Scenario again, the proviion of upport for certification increae the value of Φ*, o decreae externality due to the trade y increaing the proportion of afe trade. But proviion of upport for teting of animal after purchae i of no value ecaue no farmer tet hi animal. In Scenario 2 and Scenario 3, upport for the tet at the point of purchae i alway efficient and decreae the externality due to the trade. But upport for certification increae the eller' urplu at the expene of the ocial urplu. Given our aumption, we how that it i never efficient for the deciion-maker to upport oth the certification and the tet at introduction, the choice to upport either one mut e made taking account of the cenario oerved. V. DISUSSION The theoretical framework developed in thi paper hould e een a a firt attempt toward analying the full impact of animal health tatu on equilirium in the cattle market. It erve a a tarting point for a rigorou tudy of the negative externality reulting from the exchange of infected 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

9 9 animal and a a guide for the management of information regarding animal dieae. By determining the choice of actor in the market in the face of incomplete information, we have hown that Third arty ertification and onventional Warranty cannot coexit ecaue all actor in the market find the former more efficient than the latter. Thi eem to e conitent with finding from other market (Dewally and Ederington, 2006). Furthermore, we have hown that, with Third arty ertification, eller' urplu increae and that for uch a cheme to increae uyer' urplu and reduce the negative externality aociated with infection, it mut firt drive out the practice of teting after purchae from the market. In thi repect, we offer a rough guide for deciion-maker to reduce the negative externality y upporting either the "teting after purchae" or "certification" cheme. We find that the deciion-maker ha to elect to upport either mechanim ut never oth of them. Given the implified aumption ued in the model, however, the reult hould e treated with caution. We aume in our model that the price of an animal without certification and the numer of animal old are given. However, in practice, the enefit to the eller and to the uyer, which are higher with certification, might modify the gloal upply and demand condition. Furthermore, we aume that the gloal demand and upply are fixed and, a uch, we do not decrie upply and demand curve for animal. Neverthele, the aforementioned theoretical framework can e further extended to how how the gloal quantity upplied and demanded and the price can change over time. Alo, price without certification can change ecaue premium price ha a direct impact on the dieae prevalence of uncertified animal. In effect, animal free of the dieae are preferentially old with the premium price. So there are more infected animal old without certification. In our model, the dieae prevalence and the rik in the market without certification are aumed to e known y farmer. But in practice, farmer have jut a limited perception of the rik and it evolution. The tudy of thi perceived rik, and of how producer cope with thi rik can provide an avenue for a ueful collaoration with ociologit. In our conceptual framework, limited perception can e modelled y auming a perceived prevalence and a perceived rik different from the actual rik. The exitence of a gap etween perceived rik and actual rik reult in a uoptimal equilirium. A principalagent approach can e developed to determine the maximum uch enefit a done in a previou work on food laelling (See, for intance, Marette, 2005). By decriing the principal a the deciion-maker and uyer and eller a agent, we can decrie the rationale for teting, for certification and for advertiing the rik through different ignal. Our modelling framework can alo decrie regulatory mean uch a the warranty of latent defect and the teting after purchae. We aume in our model that dieae prevalence i given exogenouly. But we have hown that, following certification, dieae prevalence can change ecaue of the leening of the effect of externality. Furthermore, the model conider the choice of certification jut a a trade choice. But the proce of certification can alo e motivated with the view to protecting farm ojective a the farmer control hi animal to manage the dieae in hi herd. A an extenion of thi framework, we enviage to undertake a dynamic model that ha economic and epidemiological component with a particular focu on a dieae like BVDV or paratuerculoi and that i empirically tetale. AKNOWLEDGMENT Thi work wa carried out with the financial upport of the «ANR- Agence Nationale de la Recherche - The French National Reearch Agency» under the «rogramme Agriculture et Développement Durale», project «ANR-05- ADD-04, Action collective pour une maîtrie durale de la anté animale : qualification anitaire en élevage de ruminant». REFERENES. Akerlof, G. A., 970. The market for lemon : quality uncertainty and the market mechanim. Q. J. Econ. 84 (3) : Allen, D. W., 993. ot-bellie, attle Breed and Revealing Signal. Economic Inquiry, 3(3) :48. 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

10 0 3. arriquiry, M., Bacock, Bruce A., 2007 Reputation, Market Structure, and the hoice of Quality Aurance Sytem in the Food Indutry. American Journal of Agricultural Economic, 89(): entner, TJ., Wetztein, Michael E., 987. Reducing Moral Hazard Aociated with Implied Warrantie of Animal Health. American Journal of Agricultural Economic, 69(): hymi, A.G., Jame, H.S, Konduru, S, ierce, V.L.,2007. Aymmetric Information in attle Auction: the rolem of Revaccination. Agricultural Economic, 36(): Defra, Scottih Executive and Welh Aemly Government, Animal Health and Welfare Strategy for Great Britain. Defra, London. 7. Dewally, M., and Ederington, L., Reputation, ertification, Warrantie, and Information a Remedie for Seller-Buyer Information Aymmetrie: Leon from the On-line omic Book Market. Journal of Buine, 79(2): Ezanno., Fourichon., Beaudeau F., Seeger H Between-herd movement of cattle in Bretagne and rik of introducing infected animal. Animal Reearch: 55(3) : FNGDS, Referentiel Technique De Garantie D un Animal Non-II, Réf/BVD/0. 0. Marette S., The Regulatory hoice Between a Lael and a Minimum-Quality Standard. enter for Agricultural and Rural Development, Iowa State Univerity, Working aper Numer 05-W 46.. Rothchild, M., Stiglitz, J., 976. Equilirium in ompetitive Inurance Market: An Eay on the Economic of Imperfect Information. The Quarterly Journal of Economic, 90(4 ) Spence, M., 973. Jo Market Signalling. Quarterly Journal of Economic, 87(3) : Stiglitz, J. E., Wei, A., 98. redit Rationing in Market with Imperfect Information. The American Economic Review, 7(3): Annex : Derivation of equation 2 Let α=+t, the cot of uying an animal, and β=(+t-c+o), the cot of culling and of uying another animal when the firt one i infected. Becaue the proaility of uying an infected animal i, the proaility of uying an infected animal n time i n. So, = lim α + β + n + = lim α + β n + n a= a 2 β n β (Aa) Since for all [ 0, [ lim n a =, (A) n + a= We have = α + β = + t ( Ac o) (Ac) 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008

11 - Annex 2: The incompatiility of onventional Warranty and Third arty ertification We aume that r, the cah ack for the uyer when he return an animal with onventional Warranty atifie: + t r + t + o'. (A2a) So, the cot for the uyer i higher than or equal to the cot with a perfect warranty, and t (A2) + A uyer who trade in a market with onventional Warranty require that > > ( + t + t) (A2c) A eller who trade in a market with onventional Warranty require that B > B r > ( ) c ( ) ( r ) > ( ) c ( t) ( ) ( r ) > ( ) ( + t r) > t c c Becaue of (A2c) (A2d) 2 th ongre of the European Aociation of Agricultural Economit EAAE 2008