From monopsonistic insurgent groups to oligopolistic cocaine traffickers: the market of cocaine in Colombia

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1 MPRA Muich Persoal RePEc Archive From moopsoistic isurget groups to oligopolistic cocaie traffickers: the market of cocaie i Colombia Omar Fdo. Arias-R. ad Alfoso Aza-Jacome Uiversidad de la Sabaa, Uiversidad de la Sabaa 17. November 2014 Olie at MPRA Paper No , posted 19. November :32 UTC

2 From moopsoistic isurget groups to oligopolistic cocaie traffickers: the market of cocaie i Colombia Omar Fdo. Arias-R. omararre@uisabaa.edu.co Alfoso Aza-Jácome alfoso.aza@uisabaa.edu.co November 17, 2014 Abstract The mai purpose of this ote is to model a imperfect competitive ad vertically itegrated market structure of productio ad traffickig of cocaie. We cosider the particular case of colombia cocaie market, but the results could be geeralized to differet scearios. We model three mai participats: farmers, producig the coca-leaf ad beig price-takers i its market; isurget groups, producig paste of cocaie ad beig a local moopsoy i the coca-leaf market; ad cocaie traffickers, beig a oligopoly competig a la Courot. We fid out a explicit relatioship betwee the price of coca-leaf ad paste of cocaie, with the cocaleaf elasticity of supply. A ielastic coca-leaf supply allows the isurget groups to icrease the gap betwee the price of coca-leaf ad the price of the paste of cocaie. Additioally, the isurget groups obtai importat profits from the oligopolistic market structure of cocaie market, because the icrease i the price of cocaie also icreases the price of paste of cocaie, through the icrease i its demad. These profits feed every step i the pyramid of cocaie productio exacerbatig the problem ad makig more difficult its solutio. These remarks offers importat iformatio to explai the reasos behid the ieffectiveess of some atioal ad iteratioal policies i the war agaist illegal drugs. Key words: Colombia, coca-leaf, paste-of-cocaie, cocaie, isurget-groups, moopsoy, oligopoly. JEL classificatio: D43, J42, K42. EICEA, Ecoomía y Fiazas Iteracioales, Uiversidad de la Sabaa Colombia). Facultad de Derecho y Ciecias Políticas, Políticas Públicas, Uiversidad de la Sabaa Colombia). 1

3 1 Itroductio It is well kow that Colombia is a very importat participat i the market of cocaie. The critical cosequeces from this market i the social ad political developmet of the coutry has bee subject of itese debate, ito the academic work ad outside. Differet atioal ad iteratioal policies have tried to solve the problem. I particular, the Pla Colombia was desiged with two mai purposes, o oe had, reducig the productio ad traffickig of cocaie ad, o the other had, reducig the violet power of isurget groups. Accordig to DNP 2006), the Natioal Departmet of Plaig of Colombia, its results are ambiguous, especially i the war agaist cocaie. Becker, Murphy ad Grossma 2006) suggest a aswer for this sort of puzzle by cosiderig the price i-elasticity of demad. Decreases i the supply of cocaie icrease its price ad, give a i-elastic demad fuctio, it icreases the profits, so we ed up with a very profitable busiess. This paradox motivates the research o the policies agaist the supply of illegal drugs, its fuctioality ad results. For the particular case of Colombia, the existig literature models the cocaie market as a perfect competitive ad vertically itegrated oe. Accordig to Mejía ad Posada 2008) there are producers of coca-leaf, base or paste of cocaie, ad fially cocaie. The farmers ad isurget groups participate i the productio of coca-leaf ad paste of cocaie, ad the drug traffickers operate i the fial market. The coca-leaf is a ecessary iput for producig base or paste of cocaie ad, i tur, this is a ecessary iput for producig cocaie. Toward a policy aalysis, Grossma ad Mejía 2008) models the war agaist drugs by cosiderig some supply policies such as eradicatio ad iterdictio. With eradicatio the govermet cotrol the crop of coca-leaf; ad, with iterdictio, it decreases the amout of traded illegal drug. Withi a competitive partial equilibrium model, they discuss the work of isurget groups i the coflict o productive factors, i particular, arable lad for producig coca-leaf. Mejía ad Restrepo 2013) exteds the later result by cosiderig a competitive vertical itegratio of the market. There is also coflict o the cotrol of arable lad for producig coca-leaf. They foud that iterdictio is a more efficiet policy tha eradicatio. I the preset ote, we also model the market as vertically itegrated, but we explicitly icorporate some imperfect competitio factors i the market. However, we do ot model the coflictive problem o the arable lad. We assume the presece of isurget groups i a regio ad study their market power. The geeral idea of our model is as follows. There are some farmers producig the crop of coca-leaf i the moutais. They are price-takers facig a trade-off betwee producig coca-leaf, with importat profits but risky, ad producig other commodities, with low profits without risk. There are some isurget groups with cotrol o the atioal territory. They are a local moopsoy i its territory by fixig the price of coca-leaf to iduce the farmers to produce the crop 1. Its fuctio i the market is of producig paste of cocaie i laboratories with stadardized techiques. They obtai importat profits i tradig it to cocaie traffickers. Cocaie traffickers are the fial group of the pyramid. The cocaie traffickers buy the paste of cocaie to isurget groups, ad produce the cocaie for cosumptio. 1 This market structure is remarked i the UNODC ad Gobiero de Colombia 2013) report, ad it is aalyzed i Mejía ad Rico 2010) with empirical data about the productio of illegal drugs i Colombia. 2

4 They are a oligopoly competig a la Courot with homogeeous margial costs. The importat profits from tradig cocaie hold importat profits from producig paste of cocaie which, i tur, hold importat profits from producig coca-leaf, ad it works by feedig the circle. Cosiderig imperfect competitive factors i the colombia cocaie market offers importat elemets i the discussio. First, the price of coca-leaf ad paste of cocaie is related with the coca-leaf elasticity of supply. The i-elasticity of this supply eables isurget groups to acquire importat profits by puttig relatively low prices to coca-leaf, ad obtaiig relatively high prices to the paste of cocaie. This elasticity is related with the scale returs of the coca-leaf productio fuctio ad the eradicatio or iterdictio programs from the atioal govermet. Secod, the price of the cocaie is ot oly determied by margial costs ad risks, but also the umber of the traffickers. I a oligopoly we have some traffickers producig ad tradig a higher quatity tha a moopolistic market, but a lower quatity tha a perfect competitive market. This limitatio i the productio eables the traffickers to obtai importat profits from the i-elasticity of the demad of cocaie, ad it determies the prices from the market demad fuctio. This ote is orgaized as follows. After this itroductio, we study the productio of coca-leaf. The, we model the participatio of isurget groups as a local moopsoy by fixig the price of the coca-leaf. The, we study the market of cocaie as a oligopoly competig a la Courot. Fially, we preset a brief discussio o the elasticity of substitutio i the coca-leaf productio fuctio, ad the refereces. 2 Productio of coca-leaf Let us start with the farmers. They are the base of the pyramid of the cocaie productio. They produce coca-leaf cl) by usig lad l) ad other factors f cl ), which may be capital or labour. Let a, b R ++ be the techological factors of l ad f cl respectively, 0 ρ < 1 the elasticity of substitutio betwee l ad f cl, ad 0 < β < 1 the returs to scale of the productio fuctio. Let us write the productio fuctio of cl as a CES-productio fuctio: cl = [al ρ + bf ρ cl ] β ρ 1) The govermetal policies may have importat effects o this productio fuctio. I particular, eradicatio ad iterdictio may decrease a ad b by iducig the cl-producers to produce the crop usig both o-covetioal labour techiques ad o-productive portios of lad. I geeral, the productio may be iefficiet. These policies may also have a log-ru egative effect o β. The govermet aims to elimiate the productio of cl by goig to the jugle. I oe case, it could fid ad destroy the crop with probability σ p cl, ad puts a pealty of χ cl to the producers. I the other case, it could iterdict a proportio τ cl of traded cl with probability σcl c. Let p cl be the price of cl, ad r, w the prices of l ad f cl respectively. Let us defie the expected profits from cl: Defiitio 1 A cl-producer maximizes the followig expected profit fuctio: E [π cl ] = p cl [al ρ + bf ρcl ] β ρ 1 τcl σ ccl) ) rl wf cl 1 σ p cl ) χ clσ p cl 3

5 Notice that 1 τ cl σcl c ) is the portio of cl that could effectively survive the iterdictio of the govermet. Also, if σ p cl = 1 the the farmer loses its profits, ad gets a pealty of χ cl. The farmer decides to produce cl if E [π cl ] > 0, so cl icreases with the icreases of p cl ad the decreases of σ p cl, σc cl, χ cl ad the costs. Propositio 1 The supply fuctio of clp cl ) is give by: clp cl ) = βp cl 1 τ cl σcl c [abr) )ab ρ ρ + baw) ] ρ β 1 β Proof : Maximize the expected profit fuctio of Defiitio 1. The decremet i the factor productivity, decrease the optimal supply of cl but, agai, the effect is eutralized by p cl. If p cl is highly eough to give E [π cl ] > 0 the the farmer becomes a cl-producer eve with a iefficiet system of productio. The p cl eds up beig a fudametal variable i the productio of cl ad it depeds crucially o the price-elasticity of the supply as we show i the ext sectio. The price elasticity of the supply of cl is give by β/1 β). The more decreasig returs to scale i the productio fuctio, the more i-elastic supply of cl. I the short-ru, the elasticity depeds o the techology of producig cl; i the log-ru, it may also deped o the result of govermetal policies such as crop substitutio, eradicatio ad iterdictio. Propositio 2 The optimal expected profit fuctio of a cl-producer is give by: E [π cl ] = p cl 1 τ cl σcl c )βab)β [abr) ρ ρ + baw) ] β) ρ 1 1 β 1 β)1 σ p cl ) χ clσ p cl Proof : Use Propositio 1 i the expected profit fuctio of Defiitio 1. As we will see i the ext sectio, the isurget groups are able to cotrol p cl. They use it as a istrumet for iducig the farmers to produce the coca-leaf crop. The farmers face a trade-off betwee, from oe had, a risky activity pealized by the govermet, ad o the other had, a very profitable activity assisted by the isurget groups. The market power ad the efficiecy of the govermetal policies defie the dyamic of this structure. 3 Productio of paste of cocaie Let us cotiue with the isurget groups. They are the secod stage of the pyramid, with the mai purpose of coectig the cl-producers with the cocaie traffickers. They produce past of cocaie pc) by usig coca-leaf cl) ad other factors f pc ), which may also be capital or labour. Let d R ++ be the Hicks-eutral techological factor of producig pc, ad α 0, 1) the elasticity of pc to cl. 4

6 Let us write the productio fuctio of pc as a Cobb-Douglas-productio fuctio: pc = df pc cl α 2) The govermet is also i coflict with the isurget groups. I particular, it looks for the producers of paste of cocaie, which is a ecessary iput for producig cocaie. Let us suppose it could iterdict a proportio τ pc of pc with probability σ c pc. The pc is usually produced i the jugle, ear to the cl-crop so σ c pc σ c cl. Defiitio 2 The profits of producig pc are give by: π pc = p pc df pc cl α 1 τ pc σ c pc) wf pc p cl cl)cl Where p pc is the price of paste of cocaie, ad p cl cl), w are the prices of coca-leaf ad other factors, respectively. The p cl depeds o cl because the isurget groups have local moopsoistic power. They are the uique pc-producer i the regio, so they are the oly oe cl-buyer. They use this market power i fixig p cl. Theorem 1 The isurget groups fix p cl accordig to the followig rule: p cl = ) 1 β αppc df pc 1 τ pc σpc) c Proof : Takig dπpc dcl Let = dcl p cl dp cl cl = 0 we have: ] [abr) ρ ρ ρ + baw) β1 τ cl σ c cl )ab αp pc df pc cl α 1 1 τ pc σ c pc) = p cl cl) + cl dp clcl) dcl β1 α) be the price elasticity of the supply of cl. The we have, αp pc df pc cl α 1 1 τ pc σpc) c = p cl ) 1 Replace Propositio 2 ad, after some calculatios, we have the required result. There are some isights behid this equatio. First, icremets i the margial icome of pc-producers iduce icremets i the margial icome of cl-producers. The profits i the busiess beefit every step of the pyramid. Secod, the p cl must cover both the margial costs of productio ad the associated risk. Third, a elastic supply of cl iduces isurget groups to icrease p cl for sustaiig the productio of cl. Fourth, icremets i the techology of pc icreases its productio, ad its demad of cl, so p cl also icrease. Fially, the effect of σ c pc o p cl is ambivalet because it also affect p pc so we will aalyse it i the ext sectio. We could calculate the supply of cl with the previous iformatio. Propositio 3 The supply of cl is give by cl = αβabdp pcf pc 1 τ pc σpc)1 c τ cl σcl c ) ] [abr) ρ ρ ρ + baw) ) β 5

7 Proof : Replace Theorem 1 i Propositio 1. There is a positive relatioship betwee cl ad p pc. A possible reaso from the model is because the icremet i p pc icrease the productio of pc, ad i tur it icreases the demad of cl, icreasig p cl. It is a possible way to trasfer profits from a step of the pyramid to aother. Now, we are able to estimate the supply fuctio of pc: Propositio 4 The supply fuctio of pc is give by: pc = αβabp pcdf pc ) 1 αβ 1 τpc σpc)1 c τ cl σcl c ) ] [abr) ρ ) ρ ρ + baw) Proof : Replace Propositio 3 i the equatio 2. αβ The isurget groups have local moopsoistic power i the cl market. However, there are some isurget groups i the coutry, so we assume they do ot have ay market power i the pc market. I this case, the p pc is determied through the iteractio betwee isurget groups ad cocaie traffickers. We study this iteractio i the followig sectio. 4 Cocaie traffickers Let us fiish the vertical structure of the market with the cocaie traffickers. They are o the top of the pyramid of cocaie busiess, obtaiig importat profits ad also assumig importat risks. They produce cocaie, ad trade it i a coutry differet where it was produced. The reaso of that is the importat differece i the willigess-to-pay for cocaie of the cosumers i both coutries. There are cocaie traffickers, ad let i I = {1, 2,..., } be their couter. Let c = Σ i=1c i be the total quatity of cocaie, where c i is the portio of the market correspodig to trafficker i I. The productio fuctio is c i = 1/)pc where 1/) is the amout of pc used by trafficker i i producig c i. As buyers, cocaie traffickers have o importat power i the market of paste of cocaie. However, as sellers, they operate i a oligopolistic market competig each other a la Courot. They try to icrease the quatity of c for obtaiig a importat participatio i the market, evertheless, it is costraied to the margial cost of productio. Suppose the margial cost is homogeeous amog them. Let us assume that each cocaie trafficker has a margial cost of µ. The govermet wats to elimiate the productio of c by seekig cocaie traffickers. It could elimiate the productio of c i with probability σ p c, ad puts a pealty of χ c to the trafficker. It could also iterdict a proportio τ c of c i with probability σ c c. The expected profits are give by: Defiitio 3 The profits from producig c i are give by: E [π ci ] = p c c i 1 τσ c c) µc i ) 1 σ p c ) χ c σ p c 6

8 Where p c is the price of cocaie i the cosumer coutry. It is clear p pc is part of µ but, give the huge differece p c p pc, we cosider p pc is ot relevat i the maximizatio process of the cocaie trafficker. We prefer to cosider p pc as a osigificatly part of µ, ad add it to the trasportatio cost, ad the efforts of passig the iterdictio, or tradig the cocaie i the market. As it is usual, the term 1 τ c σc) c is the portio of c i passig the iterdictio of the govermet i the producer coutry. Also, If σc p = 1 the the drug trafficker loses its profits ad gets a pealty of χ c. The govermet of the cosumer coutry puts a pealty of κ for beig caught cosumig c with probability of σc d. Let η be a parameter of persistece i the cosumptio of c. Defiitio 4 The cocaie market demad fuctio is give by: p c = ηc θ κσ d c Where θ R ++ is a parameter affectig the elasticity of the demad of c. With this demad fuctio we use the followig expected profit fuctio: Defiitio 5 The profits of the cocaie trafficker i I are give by: E [π ci ] = ηc θ κσ d c )c i 1 τ c σ c c) µc i ) 1 σ p c ) χ c σ p c The cocaie trafficker maximizes its profit fuctio i terms of c i. The solutio of this problem gives us the optimal idividual quatity produced for each trafficker, the total quatity traded i the market ad its price. With this iformatio we are able to solve the problem for the market of pc. Theorem 2 The total quatity of cocaie traded i the market is give by: c = [µ + κσ d c 1 τ c σ c c)] ) 1 θ θ The price of the cocaie traded i the market is give by: p c = µ + θ1 τ cσ c c)κσ d c θ)1 τ c σ c c) Proof : We proceed i two steps. First, we prove that each cocaie trafficker has the same participatio i the market. Let i j I be two cocaie traffickers with the followig optimal coditios: [ ] ηc θ θc i c θ 1 ) κσc d 1 τc σc) c = µ [ ] ηc θ θc j c θ 1 ) κσc d 1 τc σc) c = µ From these coditios, we have c θ θc i c θ 1 = µ + κσd c 1 τ c σ c c) c θ θc j c θ 1 = µ + κσd c 1 τ c σ c c) 7

9 The, we have each cocaie trafficker has the same participatio i the market because c i = c j. Write c 1 = c 2 =... = c. We are able to write c as c i i the i s optimality coditio. After some calculatios we have: c i = 1 [µ + κσ d c 1 τ c σ c c)] From this, we derive directly the claimed result. ) 1 θ θ The risk associated to the traffic ad cosumptio of c icrease its price. Because the risk is so importat, the margial icome must be so importat. If the demad is ielastic, the more price the more total icome of cocaie traffickers, so it icreases the dispositio to produce c. However, the more umber of cocaie traffickers, the less price of cocaie because it also icreases the total amout of cocaie. Let us estimate the demad of paste of cocaie: Propositio 5 The demad of pc is give by: Proof : Because c = pc. pc = [µ + κσ d c 1 τ c σ c c)] ) 1 θ θ Oe idea behid this equatio is that the more persistece η i the cosumptio of c, the more productio of c, ad pc ad cl. We the have a raifall effect, through the prices ad quatities, from the top to the base of the pyramid. The more profitable cocaie market, the more profitable paste of cocaie ad coca-leaf markets. Fially, we are able to estimate the p pc previously cosidered. Propositio 6 The p pc is give by: p pc = ] [abr) ρ ) ρ ρ + baw) αβabdf pc ) 1 αβ 1 τpc σ c pc)1 τ cl σ c cl ) Proof : Equal Propositios 4 ad 5. [µ + κσ d c 1 τ c σ c c)] ) θ αθβ This equatio relates isurget groups, simultaeously, with cl-producers ad cocaie traffickers. First, the more i-elastic supply of cl, the higher p pc. With a i-elastic supply curve of cl the isurget groups are able ot oly to decrease p cl but icrease p pc. It icreases the gap p pc p cl edig up with a very profitable busiess for them. Secod, the icremet of c-productio icreases p pc through its demad. There is a perfect positive relatio i the productio of c ad pc so they move i the same way. Third, the risk may also modify p pc. The riskier cl productio, the higher p cl ad the higher p pc to compesate the differece. Also, the riskier c productio, the higher p c ad, give a i-elastic demad of c, that icreases c, so it also icreases pc ad p pc. 8

10 5 Appedix I this appedix we are goig to estimate p cl, cl, pc ad p pc whe ρ chages. I particular, we cosider two scearios. First, we could have ρ = 0, with o substitutio betwee l ad f cl. The eradicatio policy may have importat effects i reducig cl by reducig the proportios of l ad f cl. I this case, the factors are perfect complemets ad we are able to write the productio fuctio as cl = mi β {al, bf cl }. Secod, we could have ρ, with perfect substitutio betwee l ad f cl. The policies of eradicatio or lad substitutio may have o importat effects, because the producer is able to alter the usage of oe factor to aother. I this case, the factors are perfect substitutes ad the productio fuctio may be writte as a liear fuctio cl = al + bf cl ) β. Corollary 1 The isurget groups fix p cl accordig to the followig rule: a) If ρ 0: ) 1 1 β αppc df p cl = pc 1 τ pc σpc) c ) β1 α) br + aw β1 τ cl σcl c )ab b) If ρ : ) 1 β αppc df p cl = pc 1 τ pc σpc) c mi{ r ; w} ) β1 α) a b β1 τ cl σcl c ) Corollary 2 The supply of cl is give by: a) If ρ 0: cl = αβabdp pcf pc 1 τ pc σpc)1 c τ cl σcl c ) br + aw) b) If ρ : cl = ) αβdp pcf pc 1 τ pc σ c pc)1 τ cl σ c cl ) mi{ r a ; w b } ) β β Corollary 3 The supply of pc is give by: a) If ρ 0: pc = αβabp pcdf pc ) 1 αβ 1 τpc σpc)1 c τ cl σcl c ) ) br + aw) b) If ρ : pc = αβp pcdf pc ) 1 αβ 1 τpc σpc)1 c τ cl σcl c ) ) mi{ 1 r ; w} + 1 a b αβ αβ 1 9

11 Corollary 4 The p pc is give by: a) If ρ 0: p pc = ) br + aw) αβabdf pc ) 1 αβ 1 τpc σ c pc)1 τ cl σ c cl ) [µ + κσ d c 1 τ c σ c c)] ) θ αθβ b) If ρ : p pc = mi{ r a ; w b } ) αβdf pc ) 1 αβ 1 τpc σ c pc)1 τ cl σ c cl ) [µ + κσ d c 1 τ c σ c c)] ) θ αθβ I each case, there are differeces i the impact of the techological factors ad factorial costs o each estimated variable. With perfect complemets, both techological factors ad factorial costs have a sigificat impact o the estimated variables, however, with perfect substitutes, there is oly oe techological factor or oly oe factorial cost with a sigificat impact. With them, we have the same sort of previously cosidered relatios but with differet proportios. Refereces [1] Becker, G., Murphy, K. ad Grossma, M. 2006). The market for illegal goods: the case of drugs. The Joural of Political Ecoomy 1141), [2] DNP 2006). Balace Pla Colombia: Reporte, Departameto Nacioal de Plaeació, Colombia. [3] Grossma, H. ad Mejía, D. 2008). The war agaist drug producers. Ecoomics of Goverace 91), [4] Mejía, D. ad Posada, C. 2008). Cocaie productio ad traffickig: what do we kow?. Policy Research Workig Paper Series 4618, The World Bak. [5] Mejía, D. ad Restrepo, P. 2013). The Ecoomics of the War o Illegal Drug Productio ad Traffickig. Documetos CEDE 54, Uiversidad de los Ades. [6] Mejía, D. ad Rico, D. 2010). La microecoomía del tráfico y la producció de drogas e Colombia. Libro Blaco de Drogas, Uiversidad de los Ades. [7] UNODC y Gobiero de Colombia 2013). Colombia: moitoreo de cultivos de coca Ceso de cultivos de coca. 10