## _wp10269

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---

### Introduction and scope
- Examines two hypotheses to assess an optimal export tax in a low-income country with enough market power to influence international prices of a certain commodity.
- Illustrative market: Côte d’Ivoire’s cocoa exports.
- Hypotheses analyzed:
  - Almost perfect competition among producers and exporters in the domestic market.
  - Oligopsonistic domestic export market (oligopsony defined as a market structure in which the number of buyers is small but the number of sellers could in theory be large).
- Rationale: Almost perfect competition and oligopsony are typical arrangements for agricultural production and exports in many low-income countries (LICs). Local producers are mainly small family farms that either compete with each other in selling directly to international buyers or are forced to sell to local branches of multinational corporations.

### Core analytical findings on export taxation
- General welfare effects:
  - Taxing exports is not an optimal policy because it distorts trade and reduces world welfare, although it may raise welfare for an individual country.
  - An export tax improves the terms of trade of the exporter but can be welfare-enhancing only if the terms of trade gain outweighs the deadweight losses from inefficiencies in resource allocation that result from the tax.
  - A country would have to be a major exporter of a commodity that lacks easy substitutes to realize the terms of trade gains; even then the tax would be globally welfare-reducing.
  - If a country that perceives itself as “large” in the export of a specific commodity is in fact “small,” or if substitutes for its export commodity become readily available, the positive terms of trade effect disappears totally and the export tax becomes unambiguously welfare-reducing.
- Prevalence and practice:
  - Export taxes are used mainly by LICs, and mainly as a source of revenue.
  - World Trade Organization rules do not prohibit export taxes, but over two-thirds of its members have chosen not to apply them.
  - Only three OECD countries use export taxes.
  - Many regional and bilateral trade agreements explicitly prohibit export taxes.
  - As most LICs are small, with little or no pricing power, they use export taxes only as a source of revenue.
  - For a country with substantial pricing power, export taxes may be welfare-improving and be viewed as a policy option—taken, however, at the expense of its trading partners.

### Cocoa production, prices, and market structure (Section IV)
- Production and macro importance:
  - Cocoa accounted for 25–30 percent of exports and 17–20 percent of revenue in Côte d’Ivoire in recent years.
  - The cocoa sector employs about 4 million people out of a population of 20 million.
  - Côte d’Ivoire accounted for over 36 percent of world production on average in 2007–09; average production in 2006–09 was almost 1.3 million tons of cocoa beans a year, of which 97 percent was exported (Comité de Gestion de la Filière Café Cacao [CGFCC], 2009).
- Market fragmentation and institutions:
  - World cocoa production is fragmented; no cartel-type association exists.
  - Main international institutions: Federation of Cocoa Commerce (FCC) and International Cocoa Organization (ICO) with consultative/informational mandates and no price-setting power.
- Domestic pipeline and actors:
  - Domestic pipeline described as an inverted pyramid: highly decentralized production and primary collection versus highly concentrated exports and consumption.
  - Producers (planteurs): estimated 600,000 to 800,000 smallholder families; crop season October to June; about 70 percent of output collected and usually exported during October–December.
  - Itinerant buyers (traitants): estimated total number about 1,000 based on licenses issued; only 188 individuals listed as approved buyers (acheteurs agréés) for the 2006/07 campaign.
  - Exporters: warehouses mainly belong to companies formally registered as cocoa exporters; total number each year does not exceed 50–60 (EU, 2006).

### Price levels, pass-through, and margins
- Types of prices in the export chain:
  - Farm-gate prices: domestic cash prices paid by itinerant collectors; data partial (six main producing regions); reported as an average across regions.
  - Indicative price: government-established indicative farm-gate price for orientation only (not enforced). Indicative price for 2008–09: CFAF 700 per kg (up from CFAF 450 per kg the previous season). On October 1, 2009, authorities increased the indicative farm-gate price to CFAF 950 (US$2.1).
  - Export prices: discounted world prices set by exporters as a function of futures prices; Ivoirian export price can be lower or higher than the world average depending on quality.
- Farm-gate price observations:
  - Average farm-gate price reached CFAF 618 per kg in July 2009 (30 percent increase over CFAF 476 per kg a year earlier).
  - By September 2009 farm-gate price was CFAF 640 (percentage increase of 46 percent versus prior year).
  - Location differences (November 2008): Abidjan ≈ CFAF 610 per kg; San Pedro ≈ CFAF 590 per kg.
  - Smuggling incentive arises when price differences of at least CFAF 75 or 100 exist between Côte d’Ivoire and Ghana.
- Price-share and margins:
  - From 2001 to 2009 average world price for cocoa beans in U.S. dollars increased by over 160 percent; world price in CFAF increased by only 70 percent due to dollar depreciation.
  - Ivorian cocoa often exported at a discount generally not exceeding 10 percent.
  - After exporters pay fiscal and quasi-fiscal levies, the average price they retain is about 60–70 percent of the world price.
  - Exporters usually pay farmers less than the indicative producer price; actual producer price is substantially below the indicative price.
  - Margin between export price after taxes and farm-gate price split: exporter receives about 90 percent as profit, local intermediaries about 10 percent.
  - In 2001–09 Ivoirian producers received on average no more than 41 percent of the world price for cocoa.
  - Comparative producer price shares (2007–08): Nigeria 90 percent of international prices; Ghana 70 percent; Cameroon 85 percent.
- Price correlation and pass-through:
  - Correlation coefficient between world and domestic farm-gate prices for 2003–09: 0.8, indicating substantial pass-through but imperfect competition.
  - For 2003–09 the difference between domestic and international prices averaged 56% of the export price; in January–July 2003 the difference never exceeded 41 percent of the international price; following reforms the wedge increased to 61 percent and fell below 60 percent only in 2007.

### Taxes and levies in the cocoa chain
- Tax components:
  - Fiscal levies are part of budget revenue; quasi-fiscal levies finance sector institutional structures and are not included in fiscal revenue.
- Fiscal levies (selected values and rules):
  - Export tax (droit unique de sortie, or DUS): specific tax in CFAF per kg; CFAF 220 per kg for 2008–09 crop season; reduced to CFAF 210 for 2009–10 crop season. Exporters pay DUS when cocoa cargo is loaded.
  - Registration tax (taxe d’enregistrement): ad valorem percentage of CIF price; temporarily increased from 5 to 10 percent in 2008 but intended to revert to 5 percent starting 2009–10. Exporters pay at registration and annually thereafter.
  - Other state levies: CFAF 2 per kg tax on itinerant buyers; EU documented over 20 other implicit state charges (EU, 2005).
- Reform commitments:
  - Government committed to gradually reducing overall cocoa taxation to 22 percent of the CIF price in 2011 and to transforming all cocoa-related levies into a single ad valorem tax before the 2010–11 season.
- Quasi-fiscal levies:
  - Fluctuated by year; for 2008–09 totaled CFAF 31 per kg (reduced from CFAF 47 a year earlier).
  - Quasi-fiscal amount a function of power balance among central government and public entities (ARCC, BCC, FRC, FDPCC).
- Rough estimate:
  - Based on October 2008 world price and 2007–08 tax structure, DUS + registration tax + quasi-fiscal levies ≈ 28 percent of cocoa CIF price.

### Market structure evidence: competition versus oligopsony
- Evidence supporting competition:
  - High pass-through correlation (0.8) between world and farm-gate prices for 2003–09.
  - Since 2003 trends of domestic and international prices generally moved together.
- Evidence supporting oligopsony:
  - 2008–09 season: 97 registered exporters, 62 actually exported, 42 exported >10,000 tons.
  - Nine largest entities exported over 70 percent of the country’s cocoa; top six firms accounted for over 50 percent (CGFCC, July 2009).
  - Three major cocoa processing companies—Archer Daniels Midland (ADM), Barry Callebaut, and Cargill—buy over 40 percent of the cocoa beans produced in the world (Oxfam, March 2008, Table 5).
  - Market structure characterization: some 800,000 small producers face several hundred local intermediaries and "three to ten large buyers," many exporters subsidiaries or linked to multinationals.
- Conclusion on structure:
  - Market is neither perfectly competitive nor perfectly monopolistic; may be a complex combination of both with a competitive fringe that accounts for nearly half of purchases.

### Optimal export-tax analysis — Perfect competition hypothesis
- Large-country logic:
  - Côte d’Ivoire produces about 36 percent of world cocoa output and can, in principle, improve terms of trade by imposing an export tax; tax reduces domestic producer price, raises world price, and redistributes surplus.
- Optimal ad valorem tax (elasticity dependence preserved):
  - Inverse demand p*(Q), marginal revenue MR = p*(1 + 1/ηx) where ηx is elasticity of export demand.
  - Domestic price p = p* (1 + t_x).
  - Optimal export tax tied to export demand elasticity ηx; text presents optimal formula contextually as 1/(1 + ηx) with alternative derivations implying sensitivity to specification.
- Elasticity implications:
  - If ηx = 1 then optimal tax rate is 100 percent; if ηx = ∞ optimal rate is zero; if ηx < 1 optimal rate would exceed 100 percent (not feasible).
  - Indicative elasticities: LICs average export demand elasticity 3.5 for agricultural commodities and 4.0 for food (IMF, 2009). General equilibrium estimates for other commodities: range 2 to 5 (Warr, 2001).
- Supply elasticity note:
  - Export supply elasticity seems low intra-seasonally because harvested crop is fixed and cocoa stocks are limited.
- Implication:
  - Under perfect competition the optimal rate depends critically on ηx; with imperfect competition the optimal tax may still be positive but lower than under the perfect-competition benchmark.

### Optimal export-tax analysis — Oligopsony hypothesis
- Buyer market power modeling:
  - Monopsony and oligopsony analyzed as inverse of monopoly/oligopoly; for linear supply p(x) = a + b x, marginal cost MC(x) = a + 2 b x.
  - Monopsonist chooses Xm where MR = MC, setting domestic price Pm < Pw.
  - Government minimum price near competitive price Pc can counter monopsonistic inefficiency.
- Cournot-type oligopsony:
  - Modeled as n buyers choosing quantities; assumptions include homogeneous product, no collusion, fixed number of exporters, quantity competition, strategic rationality.
  - Weaknesses: timing of decisions, entry costs, medium-term production responses.
- Tacit collusion and kinked supply:
  - Tacit collusion can create a kink in the supply curve at a collusion point; marginal cost curve breaks at kink producing ranges where quantity is insensitive to MR.
- Export tax under oligopsony:
  - Tax can appropriate part of oligopsonists’ surplus and redistribute to producers and government; justification differs from pure terms-of-trade motive.
  - Specific tax t reduces marginal revenue to world price minus t; country welfare change may be positive if gains exceed producer losses.
- Deardorff and Rajaraman derivation (linear supply, n oligopsonists):
  - Supply p(x) = a + b x; each of n oligopsonists purchases x and total X = n x.
  - Profit maximization yields equilibrium quantity per oligopsonist x_coo and price; change in welfare WΔ as a function of t given.
  - Optimal specific tax t* expression presented in text (preserved symbolically): "2
*



n
aP
t
c".
  - Optimal tax approaches zero as n → ∞ (more buyers → lower tax).
- Ad valorem vs specific taxes:
  - Ad valorem changes slope of demand; under oligopsony, buyers should prefer ad valorem taxes whereas producers prefer specific taxes.
  - Optimal choice of tax instrument depends on market specifics; Keen (1998) shows ad valorem can be preferable under monopoly with output restriction, but oligopsony inverts some preferences.

### Application to Côte d’Ivoire—calibration and results
- Reform context and goals:
  - Government reform aims: streamline institutional structure, improve governance/transparency, define government responsibilities, build inter-professional stakeholder network, increase competition among buyers and share of world prices to farmers, introduce market-based risk instruments, promote cocoa transformation and finished product exports.
  - Authorities intend to reduce all taxes to no more than 22 percent of the CIF price, possibly for the 2010 crop season (from about current 30 percent).
- Required calibration inputs:
  - World price, number of oligopsonistic buyers, marginal price at which producers supply first kilo.
  - Known with certainty: world price 2001–2008 range CFAF 800–1,200 per kg.
  - Farm-gate price history (2001–present): minimum average price paid since 2001: CFAF 228 per kg (July 2004); maximum CFAF 852 per kg (October 2002).
  - Minimum marginal price plausibly in range CFAF 150–250 per kg depending on region.
  - Number of oligopsonists uncertain; model calibrated for n between 1 and 10.
- Calibration results (model-derived ranges preserved):
  - Under oligopsony with three buyers, total fiscal and quasi-fiscal levies should be in range CFAF 130–190 per kg, or about 16 percent of the world price.
  - In extreme pure monopsony (n = 1), tax could be on order CFAF 200–300, or 26–27 percent of the world price.
  - Under perfect competition assumption, export tax equals inverse of export demand elasticity; reasonable elasticity span 1 to 5 yields wide tax-range outcomes (reference matrix in Table 6).
- Model caveats and limitations:
  - Model does not incorporate precise elasticity of export demand for Ivoirian cocoa, supply elasticities of rest of world, or accurate producer marginal prices and buyer power-sharing—these are critical and largely unknown.
  - Calibration yields slightly different results if world price higher or lower than Ivorian export price in a season.
  - Model cannot determine optimal mix of ad valorem vs specific taxes; suggests positive export tax proportionate to oligopsonistic strength.

### Policy conclusions and recommendations
- General conclusions:
  - An export tax can be welfare-improving for a large exporter only if the terms-of-trade gains exceed deadweight welfare losses and administrative costs; trading partners will always suffer losses.
  - Côte d’Ivoire’s status as a large exporter (about 36 percent of world production) implies potential pricing power, but actual optimal tax depends on unknown elasticities and market structure.
  - The closer the export market is to perfect competition (higher number of buyers and higher export demand elasticity), the lower the optimal export tax; optimal tax approaches zero as elasticity and number of exporters approach infinity.
  - Oligopsony may justify positive export taxes aimed at appropriating buyer surplus for producers and government rather than terms-of-trade effects alone; optimal tax declines with more competing buyers.
- Policy preference:
  - A relatively low single ad valorem export tax is preferable as a policy principle: it can increase producer share of international prices, preserve public finance viability, and permit full pass-through of international price trends to local producers.
- Research and data needs:
  - More research required to determine actual market structure (perfect competition vs oligopsony or combination) and to measure elasticities, marginal producer prices, and buyer market concentration dynamically across crop seasons.
  - Detailed market survey and additional information on price structure and buyer behavior are necessary to finalize tax reform modalities.

*Source: _wp10269 — Section IV.*

### 1. World Production of Cocoa Beans .....................................................................................

### 1. World Production of Cocoa Beans

### Introduction and scope
- The paper examines two hypotheses to assess an optimal export tax in a low-income country with enough market power to influence international prices of a certain commodity.
- The market structure for Côte d’Ivoire’s cocoa exports is used as an illustration.
- Hypotheses analyzed:
  - Almost perfect competition among producers and exporters in the domestic market.
  - Oligopsonistic domestic export market (oligopsony defined as a market structure in which the number of buyers is small but the number of sellers could in theory be large).
- Rationale: Almost perfect competition and oligopsony are typical arrangements for agricultural production and exports in many low-income countries (LICs). Local producers are mainly small family farms that either:
  - Compete with each other in selling their product directly to international buyers; or
  - Are forced to sell to local branches of multinational corporations, which may use the product domestically or export it.

### Core analytical points on export taxation
- General welfare effects:
  - Taxing exports is not an optimal policy because it distorts trade and reduces world welfare, although it may raise welfare for an individual country.
  - An export tax improves the terms of trade of the exporter but can be welfare-enhancing only if the terms of trade gain outweighs the deadweight losses from inefficiencies in resource allocation that result from the tax.
  - A country would have to be a major exporter of a commodity that lacks easy substitutes to realize the terms of trade gains; even then the tax would be globally welfare-reducing.
  - If a country that perceives itself as “large” in the export of a specific commodity is in fact “small,” or if substitutes for its export commodity become readily available, the positive terms of trade effect disappears totally and the export tax becomes unambiguously welfare-reducing.

- Prevalence and practice:
  - Export taxes are used mainly by LICs, and mainly as a source of revenue.
  - World Trade Organization rules do not prohibit export taxes, but over two-thirds of its members have chosen not to apply them.
  - Only three OECD countries use export taxes.
  - Many regional and bilateral trade agreements explicitly prohibit export taxes.
  - As most LICs are small, with little or no pricing power, they use export taxes only as a source of revenue.
  - For a country with substantial pricing power, export taxes may be welfare-improving and be viewed as a policy option—taken, however, at the expense of its trading partners.

### Purpose and methodology
- Purpose: To illustrate ways to assess the level of an export tax for a large country.
- Approach:
  - Review a broad range of market structures, from perfect competition to an oligopsony.
  - Suggest simple methods for calculating a possible range for an optimal export tax, differing by hypothesis on market structure.
  - Present two simple models of an export tax calculation based on alternative hypotheses about market structure and apply the models to the case of cocoa export taxation in Côte d’Ivoire.
- Scope limitations:
  - While perfect competition is generally superior on efficiency grounds and government interventions can help skew the existing structure toward greater efficiency, discussion of these issues is outside the scope of the paper.
  - Additional studies are needed to arrive at a definitive conclusion on the actual market structure of cocoa exports from Côte d’Ivoire; the market is used only as an illustration of the methodologies reviewed.

### Structure of the document (as presented)
- Section II: Describes the structure of cocoa production, pricing, and taxation in Côte d’Ivoire.
- Section III: Presents two models for export tax calculation under alternative market-structure hypotheses and illustrates the calculations with the Côte d’Ivoire cocoa case.
- Conclusions: Presented thereafter.

*Source: _wp10269 - 1. World Production of Cocoa Beans*

### Section IV.

### Section IV.

### Cocoa Market Structure — A. Production
- Cocoa accounted for 25–30 percent of exports and 17–20 percent of revenue in Côte d’Ivoire in recent years.
- The cocoa sector employs about 4 million people out of a population of 20 million.
- Côte d’Ivoire accounted for over 36 percent of world production on average in 2007–09; average production in 2006–09 was almost 1.3 million tons of cocoa beans a year, of which 97 percent was exported (Comité de Gestion de la Filière Café Cacao [CGFCC], 2009).
- World cocoa production is fragmented; no cartel-type association exists. Main international institutions are the Federation of Cocoa Commerce (FCC) and the International Cocoa Organization (ICO) with consultative/informational mandates and no price-setting power.
- Domestic cocoa pipeline described as an inverted pyramid: highly decentralized production and primary collection versus highly concentrated exports and consumption.
- Key domestic actors:
  - Producers (planteurs): estimated 600,000 to 800,000 smallholder families; crop season October to June; about 70 percent of output collected and usually exported during October–December.
  - Itinerant buyers (traitants): estimated total number about 1,000 based on licenses issued; only 188 individuals listed as approved buyers (acheteurs agréés) for the 2006/07 campaign.
  - Exporters: warehouses mainly belong to companies formally registered as cocoa exporters; total number each year does not exceed 50–60 (EU, 2006).

### Cocoa Market Structure — B. Prices
- Types of prices in the export chain:
  - Farm-gate prices: domestic cash prices paid by itinerant collectors; data partial (six main producing regions); reported as an average across regions.
  - Indicative price: government-established indicative farm-gate price for orientation only (not enforced). Indicative price for 2008–09: CFAF 700 per kg (up from CFAF 450 per kg the previous season). On October 1, 2009, authorities increased the indicative farm-gate price to CFAF 950 (US$2.1).
  - Export prices: discounted world prices set by exporters as a function of futures prices; Ivoirian export price can be lower or higher than the world average depending on quality.
- Farm-gate price observations:
  - Average farm-gate price reached CFAF 618 per kg in July 2009 (30 percent increase over CFAF 476 per kg a year earlier).
  - By September 2009 farm-gate price was CFAF 640 (percentage increase of 46 percent versus prior year).
  - Location differences (November 2008): Abidjan ≈ CFAF 610 per kg; San Pedro ≈ CFAF 590 per kg.
  - Smuggling incentive arises when price differences of at least CFAF 75 or 100 exist between Côte d’Ivoire and Ghana.
- World price and futures:
  - Cocoa futures mainly traded on LIFFE and NYBOT; futures standardization and delivery months described.
- Price-share and margins (selected values preserved from Table 2 and text):
  - From 2001 to 2009 average world price for cocoa beans in U.S. dollars increased by over 160 percent; world price in CFAF increased by only 70 percent due to dollar depreciation.
  - Ivorian cocoa often exported at a discount generally not exceeding 10 percent.
  - After exporters pay fiscal and quasi-fiscal levies, the average price they retain is about 60–70 percent of the world price.
  - Exporters usually pay farmers less than the indicative producer price; actual producer price is substantially below the indicative price.
  - Margin between export price after taxes and farm-gate price split: exporter receives about 90 percent as profit, local intermediaries about 10 percent.
  - In 2001–09 Ivoirian producers received on average no more than 41 percent of the world price for cocoa.
  - Comparative producer price shares (2007–08): Nigeria 90 percent of international prices; Ghana 70 percent; Cameroon 85 percent.
- Price correlation and pass-through:
  - Correlation coefficient between world and domestic farm-gate prices for 2003–09: 0.8, indicating substantial pass-through but imperfect competition.
  - For 2003–09 the difference between domestic and international prices averaged 56% of the export price; in January–July 2003 the difference never exceeded 41 percent of the international price; following reforms the wedge increased to 61 percent and fell below 60 percent only in 2007.

### Cocoa Market Structure — C. Taxes
- Cocoa taxation comprises fiscal and quasi-fiscal levies:
  - Fiscal levies are part of budget revenue; quasi-fiscal levies finance sector institutional structures and are not included in fiscal revenue.
- Fiscal levies described:
  - Export tax (droit unique de sortie, or DUS): specific tax in CFAF per kg; CFAF 220 per kg for 2008–09 crop season; reduced to CFAF 210 for 2009–10 crop season. Exporters pay DUS when cocoa cargo is loaded.
  - Registration tax (taxe d’enregistrement): ad valorem percentage of CIF price; temporarily increased from 5 to 10 percent in 2008 but intended to revert to 5 percent starting 2009–10. Exporters pay at registration and annually thereafter.
  - Other state levies: CFAF 2 per kg tax on itinerant buyers; EU documented over 20 other implicit state charges (EU, 2005).
- Reform commitments:
  - Government committed to gradually reducing overall cocoa taxation to 22 percent of the CIF price in 2011 and to transforming all cocoa-related levies into a single ad valorem tax before the 2010–11 season.
- Quasi-fiscal levies:
  - Fluctuated by year; for 2008–09 totaled CFAF 31 per kg (reduced from CFAF 47 a year earlier).
  - Quasi-fiscal amount a function of power balance among central government and public entities (ARCC, BCC, FRC, FDPCC).
- Rough estimate:
  - Based on October 2008 world price and 2007–08 tax structure, DUS + registration tax + quasi-fiscal levies ≈ 28 percent of cocoa CIF price.

### Cocoa Market Structure — D. Market Structure (Competitive vs Oligopsony)
- Two hypotheses considered for the export market:
  1. Highly competitive market with many exporters.
  2. Restricted market (oligopsony) where many producers face few large exporters.
- Evidence supporting competition:
  - High pass-through correlation (0.8) between world and farm-gate prices for 2003–09.
  - Since 2003 trends of domestic and international prices generally moved together.
- Evidence supporting oligopsony:
  - 2008–09 season: 97 registered exporters, 62 actually exported, 42 exported >10,000 tons.
  - Nine largest entities exported over 70 percent of the country’s cocoa; top six firms accounted for over 50 percent (CGFCC, July 2009).
  - Three major cocoa processing companies—Archer Daniels Midland (ADM), Barry Callebaut, and Cargill—buy over 40 percent of the cocoa beans produced in the world (Oxfam, March 2008, Table 5).
  - Market structure characterization: some 800,000 small producers face several hundred local intermediaries and "three to ten large buyers," many exporters subsidiaries or linked to multinationals.
- Conclusion on structure:
  - Market is neither perfectly competitive nor perfectly monopolistic; may be a complex combination of both with a competitive fringe that accounts for nearly half of purchases.

---

### Optimal Taxation — A. Perfect Competition Hypothesis
- Large-country export-tax logic:
  - A large exporter (Côte d’Ivoire produces about 36 percent of world cocoa output) can, in principle, improve terms of trade by imposing an export tax; tax reduces domestic producer price, raises world price, and redistributes surplus between domestic agents and foreign consumers.
- Optimal ad valorem tax under perfect competition (formula preserved):
  - If inverse demand is p*(Q), marginal revenue MR = p*(1 + 1/ηx) where ηx is elasticity of export demand.
  - Domestic price p = p* (1 + t_x).
  - Optimal export tax: t_x = 1/(1 + ηx) rearranged to 1 - 1/(1 + ηx)? (text gives 1/(1 + ηx) contextually). The paper states the optimal export tax would be 1/(1 + ηx) or equivalently 1/ηx in some derivations; optimal tariff formulas depend critically on export demand elasticity.
- Key analytical points:
  - Optimal rate depends critically on price elasticity of export demand ηx.
  - If ηx = 1 then optimal tax rate is 100 percent; if ηx = ∞ optimal rate is zero; if ηx < 1 optimal rate would exceed 100 percent (not feasible).
  - Elasticity varies along demand curve; optimal tax only calculable at a point on demand curve; elasticity higher at higher prices.
- Indicative elasticities:
  - Indirect indications: LICs average export demand elasticity 3.5 for agricultural commodities and 4.0 for food (IMF, 2009).
  - General equilibrium estimates for other commodities: range 2 to 5 (Warr, 2001).
- Supply elasticity:
  - Export supply elasticity seems low because harvested crop is fixed intra-seasonally and cocoa stocks are limited; short-term supply inelasticity due to fixed land, vines, climate.
- Implication:
  - If local exporters are perfectly competitive, optimal tax equals inverse of export demand elasticity; with imperfect competition the optimal tax may still be positive but lower than under perfect competition.
  - Full assessment requires general equilibrium model.

### Optimal Taxation — B. Oligopsony Hypothesis
- Modeling buyers' market power:
  - Monopsony (one buyer) and oligopsony (few buyers) analyzed as inverse of monopoly/oligopoly.
  - For linear supply p(x) = a + b x, marginal cost MC(x) = a + 2 b x (MC steeper than supply).
  - Monopsonist faces perfectly elastic world demand Pw and upward-sloping domestic supply S; maximization condition MR = MC sets monopsonist quantity Xm and domestic price Pm < Pw.
  - Government minimum price set near competitive price Pc can counter monopsonistic inefficiency.
- Oligopsony modeled as Cournot-type competition among n buyers:
  - Assumptions supporting Cournot model listed (homogeneous product, no collusion, fixed number of exporters, quantity competition, strategic rationality).
  - Weaknesses of Cournot approach noted (timing of quantity decisions, entry costs, medium-term production responses).
- Tacit collusion and kinked supply:
  - Tacit collusion can create a kink in the supply curve at tacit collusion point A; marginal cost curve breaks at kink producing ranges where quantity is insensitive to MR.
- Export tax under oligopsony:
  - Justification differs: tax can appropriate part of oligopsonists’ surplus and redistribute to producers/consumers, not only terms-of-trade improvement.
  - Specific tax t reduces marginal revenue to world price minus t; country welfare change may be positive if gains exceed producer losses.
- Deardorff and Rajaraman derivation (specific tax, linear supply, n oligopsonists):
  - Supply p(x) = a + b x; each of n oligopsonists purchases x and total X = n x.
  - Profit maximization leads to equilibrium quantity per oligopsonist x_coo and price; change in welfare WΔ as function of t given; optimal specific tax t* = (n/(n + 2)) * aP_c? (text presents t* = (n/(n+2)) * (aP_c) form; exact preserved formula in text: "2
*



n
aP
t
c".)
  - Optimal tax approaches zero as n → ∞ (more buyers → lower tax).
- Ad valorem vs specific taxes:
  - Ad valorem changes slope of demand; under oligopsony, buyers should prefer ad valorem taxes whereas producers prefer specific taxes; optimal combination depends on market specifics.
  - Keen (1998) referenced: ad valorem better for consumer welfare and revenue with monopolistic output restrictions; conflicting preferences in Cournot case invert under oligopsony.

### Optimal Taxation — C. Application to Côte d’Ivoire’s Cocoa Exports
- Reform context:
  - Government reform aims: streamline institutional structure, improve governance/transparency, define government responsibilities, build inter-professional stakeholder network, increase competition among buyers and share of world prices to farmers, introduce market-based risk instruments, promote cocoa transformation and finished product exports.
  - Authorities intend to reduce all taxes to no more than 22 percent of the CIF price, possibly for the 2010 crop season (from about current 30 percent).
- Calibration needs and limitations:
  - Model requires world price, number of oligopsonistic buyers, and marginal price at which producers supply first kilo.
  - Only world price known with certainty (2001–2008 range CFAF 800–1,200 per kg).
  - Farm-gate price history (2001–present) used to infer marginal price: minimum average price paid since 2001: CFAF 228 per kg (July 2004); maximum CFAF 852 per kg (October 2002).
  - Minimum marginal price could plausibly be in range CFAF 150–250 per kg depending on region.
  - Number of oligopsonists uncertain; model calibrated for n between 1 and 10.
- Calibration results (summary conclusions from models and Tables 6–7):
  - Under oligopsony with three buyers, total fiscal and quasi-fiscal levies should be in range CFAF 130–190 per kg, or about 16 percent of the world price.
  - In extreme pure monopsony (n = 1), tax could be on order CFAF 200–300, or 26–27 percent of the world price.
  - Under perfect competition assumption, export tax equals inverse of export demand elasticity; reasonable elasticity span 1 to 5 yields wide tax-range outcomes (refer to the reference matrix in Table 6).
- Model caveats:
  - Model does not incorporate precise elasticity of export demand for Ivoirian cocoa, supply elasticities of rest of world, or accurate producer marginal prices and buyer power-sharing—these are critical and largely unknown.
  - Calibration yields slightly different results if world price higher or lower than Ivorian export price in a season.
  - Model cannot determine optimal mix of ad valorem vs specific taxes; suggests positive export tax proportionate to oligopsonistic strength.

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### Conclusions (Section IV)
- Paper explored approaches to modeling an export tariff for a large country under two market-structure hypotheses (perfect competition and oligopsony), using Côte d’Ivoire’s cocoa sector as illustration without concluding actual market structure.
- General findings and policy implications:
  - An export tax can be welfare-improving for a large exporter only if the terms-of-trade gains exceed deadweight welfare losses and administrative costs; trading partners will always suffer losses.
  - For Côte d’Ivoire, large exporter status (about 36 percent of world production) implies potential pricing power, but actual optimal tax depends on unknown elasticities and market structure.
  - The closer the export market is to perfect competition (higher number of buyers and higher export demand elasticity), the lower the optimal export tax; optimal tax approaches zero as elasticity and number of exporters approach infinity.
  - Oligopsony may justify positive export taxes aimed at appropriating buyer surplus for producers and government rather than terms-of-trade effects alone; optimal tax declines with more competing buyers.
  - A relatively low single ad valorem export tax is preferable as a policy principle: it can increase producer share of international prices, preserve public finance viability, and permit full pass-through of international price trends to local producers.
- Research and data needs:
  - More research required to determine actual market structure (perfect competition vs oligopsony or combination) and to measure elasticities, marginal producer prices, and buyer market concentration dynamically across crop seasons.
  - Detailed market survey and additional information on price structure and buyer behavior are necessary to finalize tax reform modalities.

*Italic source: IMF Working Paper — _wp10269 - Section IV.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10269.pdf_