POLICY RESEARCH WORKING PAPER 1245 The Adding-Up Problem Poliies designedto address the regional a:n p, problem in Sut>-Sahaian ,rka Strategies for Primary Commodity such as a region-optia. Exports in Sub-Saharan Africa exportax.- generate unequal benefris among countries. Further. few' Takamasa Akiyama n Donald F. Larson urnsi,bSaa: Africa have sufficient market power to influence commodity prices in the ,ong run. Export taxes may prove beneficbi for' some countries but, at certain levels, transfer res:ources From smaliholders6' to government with limited welfare gains. The World Bank International Economics Department Intemanonal Trade Division January 1994 POLICY RESI.ARCII WORKING PAPER 1245 Summary findings Many countries in Sub-Saharan Africa remain dependent such a policy. Moreover, if an export tax is imposed on on a few primary commodities - coffee, cocoa, cotton, Sub-Saharan Africa as a whole, the greatest benefits may sugar, tea, and tobacco - for a large share of exrort go to producers in other regions such as Asia and Latin earnings. Because demand for these commodities is price- America. inelastic, production and export expansion can depress Individually, few countries in Sub-Saharan Africa have world prices and hence reduce net export revenuc. sufficient market power to influence commodity prices i Akiyama and Larson discuss the effects of this the long run. Possible exceptions include COte d'lvoire phenomenon - the adding-up problem - on policy and (in cocoa) and to a lesser extent Ghana (in cocoa), Kenya development strategies for major agricultural export (in tea), and Malawi (in burley tobacco). Export taxes commodities in Sub-Saharan Africa. may prove beneficial for these countries but, at certain They conclude that, as a practical matter, it is not levels, the primary effect of "optimal" taxes is to transfer feasible to design a regional commodity production and resources from smallholders to governments with limited trade policy for Sub-Saharan Africa as a whole because of marginal velfare gains. the difficulty of equitably distributing the benefits of This paper-a product of the International Trade Division, International Economics Department-.is part of a larger effort in the department to assess policy effects on international trade. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Anna Kim, room S7-038, extension 33715 (41 pages). January 1994. 7he Policy Research Working Paper Series disseminates the findings of work in progress to encourae the exchange of ideas aboNt development issues. An objective of the series is to get the findings out quickly, evn ifthe presentations are less than fully polished The papers carry the names of the authors and should be used and cited accordingly. The findings, interpretations, and conclusons are the authors' own and should not be attributed to the W-rld Bank, its Executive Board of Diretors, or any of its member countries. Produced by the Policy Research Dissemination Center Adding Up Problem - Strategies for Primary Ccmmodity Exports in Sub-Saharan Africa By Takamass Akiyama and Donald F. Larson Summary Sub-Saharan Africa remains dependent on a few primary commodities for a large shre of its export eamings-coffee, cocoa, cotton, sugar, tea and tobacco. Several countries are aLnost exclusively dependent on one or two of these commodities. Because these commodities face a relatively price-inelastic demand, production decisions by individual countries can affect world prices even when their market share is relatively low. This characteristic complicates investment decisions for producers and policy decisions for govenmnunts as follows. First, production expansion that would be profitable for price-taking fims may result in lower prices, lower revenues, and lower profitability. This phenomenon is known as the 'adding-up" problem and was first introduced to the eco omics literature by Harry Johnson and Jalhdish Bhagwati in the 1950s. Second, docisions to tax producers will also affect international pries, with a portion of the tax burden bome by international consumers. Deciding the correct level to tax producers is the "optimal tax' problem. Third, the extent of real exchange rate changes on the balance-of-trade may be small since changes in export revenue may offset export volume changes for commodities facing an "adding-up' problem. Finally, regionally optimal production levels and tax levels are different from country-specific levels. Imposing a tax which is optimal for the region across all countries within the region will not maxinize the welfare of the countries in the region unless traufrs are made among the countries. This paper systenatically examines the markets for the major agricultural commodities that are of primary importance to Sub-Saharan Afr.ca (SSA) for evidence of an "adding-up" problem. Few SSA countries individually face an 'adding-up' problemn. However, in the cases of cocoa in Cote d'lvoire and, to a lesser extent cocoa in Ghana, tea in Kenya, and burley tobacco in Malawi, new investments are likely to affect intemational prices. Where an "adding-up" problem does exist, export taxes rather than export quotu should be used Such taxes must be constantly evaluated as the unterlying d-termina:nts-exchange rates, production coss, prices, and market shares- change. Further, sLice agricutlure is frequently heavily taxed, implicit taxes - such as over-valued exchange rates- should be c.nsidered as well. The extent to which an "adding-up" problem does exists depends on marginal revenue effects relative to marginal cosu. As a result, i government programs which encouraging production tbrougii area expanion will have a different effect cn welfare than programs encouraging more efficient methods of production such as the development of improved varieties. At a practical level, the analysis suggests that often the export tax level does not need to be calculated preciscly, since the primary effect of setting the export tax anywhere in the neighborhood of the optimal tax is to transfer revenues from producers to the government, rather than to affect total welfare. As a result, the primary effect of setting export taxes at a less-than-optimal level is to provide more resources to farmers and the agricultural sector at the expense of government revenue. This characteristic is especially important when the crop is grown by low-income smaliholders. The coordination of tax policies and production levels regionally in Sub-Sahran Africa faces sevre problems, both in terms of implementation and equity. Policies that would reduce output levels regionally would benefit larger, often wealthier, African countries at the expense of smaller countries. Also, in rany instances, regions outside Sub-Saharan Africa, especially Latin America and Asia, would receive the primary bcnefits from such an arrangement. ii 1. Introduiction Sharp decUi es in world agricultural commodity prices and in teal revenues (income terms of trade) generated by the important export commodities from Sub-Saharan Africa (SSA) have led to concern over the export prospects for the region. A rcal price index for SSA's major agricultural export commodities shows a decline of 4.2% per annum (p.a.) since the late 1970s. SSA's income tern of trade for agricultural commodities declined at 4.2%, while, during the same period, the agricultural income tenn of trade for Asia increased at 1.7% (Table 1). Table 1: Growth rates of income terms of trade for selec:ed regions, 1975-90. Nine tnajor Total Relodo SSA commodliles Anrculur -%p.a. - -%p.a- :ia -1.7 1.7 Latin America -3.9 *1.S Sub-Sah rAica 4.2 4.2 Source: FAO and IECIT, WVorld Bank A feature of SSA's agricultural commodity exports is that a few commodities account for a large share of total agricultural comunodity exports - .he top five export crops account for about two-thirds of total agricultural comnmodity exports - and this share has been increasing over time. The decline in Sub- Sahamn Africa's agricultural income terms of trade and the increasing concentration of SSA's agri,:ultural commodity exports has raised anew the issue of the 'adding up" or fallacy of composition problem. The 'adding up" problem has been discussed widely, especially in the context of primnary commodity expc strategies for SSA countries. Since many SSA exports face price-inelastic demand, an increase in export quantities can potentially reduce overall export revenues from these commodities and lower the general economic welfare of the country. However, there seems to be confusion as tc the p,actical implications of an adding-up problem for commodity production and export policies. Because the formulation of strategies is of great importance for Sub-Saharan Africa, clarifization of the issues in teru of theoretical and empirical analysis is needed. Hence, the main focus of the paper is to identify the nature and extent of the adding-up problem in Sub-Saharan Africa and to sugge.c appropriate commnodity policies for the region. Following this introduction, Section 2 reviews the characteristics of SSA's agriculuWal commodity exports. Section 3 defines the adding-up problem and provides an empirical measure of the problem for pnmzwy commodity exports in Sub-Sahaaz Africa. Section 4 exaniis how the adding-up problem can complicate a number of standard policy-related problems. Section 5 concludes. 2 2. Agriculture Export Eamings in Sub-Saharan Africa Sub-Saharan Africa is dependent on a few prinary commodities for export eaming. For nmny countries, this dependence has not changed significantly over three decades. Since the 1960s when agriculture avraged over 20% of world trade, the inportance of agriculual trade world-wide has dinmnished such that, for the 1988 to 1990 period, agricultuic accounted for less than 10% of world trade. Yet agricultural pr ~.a.ts comprise more than 25% of export earninp in 29 African countries. Agricultural expoxti account for 50-75% of export camings in eight countries, and for more than 75% in eight countries (see Table 2). Further, many of those countries no longer dependent on ariculture ua instead dependent on a non-agricultural primar, commodity. For example, Angola and Nigeria rely almost exclusively on petroleum exports; Zaire and Zambia carn most of their export carings through copper exports; ani Botswana relies heavily on the export of diamonds. Table 2: SSA countries dependency on aBriculture fcr export earnings Agriculture's s iare of export earmings (1988-90 averge) Less thte 25% LI0% 50-75% a00% Angola B:nin Cote dlvoire Burundi Bouwana Cental Afnan Republic Cameroon Ethiopia Congo Cape Terde Gumea.Bissau Mali Gabon Gluna Kenya Malawi Guinea Gambia Madagcar Rwanda Equatorial Guinea Burkina Faso Sao Tome & Prinpe Sudan Mauritania Liberia Chad Somlia Malawi Lesotho Tanzana Uganda Niger Mozambique Nigeria Mauritius Senegal Swaziland Sitra Lcone Togo ScycheUes ZimbabAe Zairc ZAire Zambia Source: EAO One or more of a set of nine agricultural crops-banaars, cocoa, coffee, cotton, groundauts, rubber, sugar, tea, and tobacco-are of primary importance in at least one country in Africa and together these commodities account for about 70-76% of agricultural exports for the region. This statenent has been true for three decades as can be seen in Table 3. Table 4 provides the share of total expot earminp 3 derived from these nine z&6ncultural crops for each SSA country. The nost srildng depedencies are in Bunmdi, Ethiopia, Malawi, Rwanda, and Uganda. Table S shows each country's reliUnce on exports fom each of the nine commodities The exclusive dependence of Burundi and Uganda on rv 'e hat be a constant feature of tho,e -onomies across decades. In some cases, notably tobacco in Malawi, or tea in Kenya, the dependence bh been incrmasing rather than diminishing. Table 3: Share of Sub-Saharan Africa's agricultural export earnings by crop, 1961-90 au J6V2 127021979 198021989 19.i920 Bannas 0.3 0.7 05 0.7 Cocoa 1.1 20.6 21.9 19.5 Coffee 19.2 25.9 26.7 20.5 Cottou 10.0 9.1 8.5 12.0 Orounwjuts 10.9 5 s 2.1 2.S Rubba ;6 1.7 2.1 3.0 Sugp 4.0 4.7 5.1 7.0 Tea 2.1 2.6 3.7 4.2 Tobao 3.9 3.2 4.1 '.4 Nin major crop 70.0 74.1 76.0 75.9 Source: FAO While many SSA countries remain highly dependent on the export of a few agricultura commodities, the world has become less dependent on exports from Sub-Saharan Africa (Table 6). While banana exports may be vitally important to Somalia, banana exsports from all of SSA now constitute less than 3% of world trade in banwias whereas in the 1960s their share was 9%. Groundnut exports are important in that thinly traded market; however, groundnut exports are trivial in the larger market for oilseeds and oilseed products. Cocoa is the only major agricu!tural conunodity for which Sub-Saharan Africa produces more than one-half of world production. 4 Table 4: Share of total export earnings from nine major crops, by countr, 1961-90 Country .961-69 1970-79 1980-89 1963-90 Angola 48.5 27.0 3.9 0.5 Buunudi 74.9 90.9 90.3 31.9 Bcnin 2?.9 51.3 31.6 33.4 Botswana 1.8 0.2 0.0 0.0 CentAficau RepubUo 47.0 45.4 ;7.1 25.1 Cote dvoirm 62.5 57.7 56.5 S3.2 Cameoon 70.0 61.6 49.8 4S.3 Congo 14.3 1.3 1 0 0.9 Cape Vrde 25.9 11.5 18.4 28.4 Ethiopia 60.7 56.3 h6.1 61.7 Gabon 1.9 0.6 0.4 0.3 Ghan 70.4 69.3 49.4 44 9 Guinea 21.4 7.9 2.9 2.3 Gumbi; 92.9 89.1 45.3 39.6 Guinea-Bissau 59.8 56.9 20.5 6.2 Equatorial Guinea 17.0 44.2 21.4 Burkina Faso 13.8 37.5 43.3 35.0 Kenya 29.7 40.3 45.9 46.3 Liberia 22.3 17.6 25.2 26.3 Madagasca 44.5 40.2 42.3 27.2 Mali 21.9 39.4 35.2 47.3 Mozambique 40.1 34.1 21.1 11.2 Mauritius 92.7 79.4 45.8 32.2 Malawi 81.4 82.8 34.8 88.6 Niger 67.5 12.9 0.3 0.6 Nigeria 46.9 6.3 2.5 2.9 RPWaa a S4.3 74.9 31.6 80.7 Sudan 63.5 67.0 46.0 49.4 Senegal 75.4 45.2 18.3 19.5 SieraLeone 5.8 16.7 25.0 15.4 Somalia 39.9 16.5 12.7 28.1 Sao Tome & Principe 73.4 75.8 70.4 50.3 Swaziland 29.2 34.9 36.4 29.1 Seychelles 0.1 0.0 Chad 67.1 39.1 35.4 48.3 Togo 53.0 37.3 31.6 30.7 Tanzanis 33.5 44.1 52.2 49.2 Uganda 72.3 89.2 95.9 94.1 Zaire 11.3 13.5 17.0 11.4 Zambia 1.2 0.8 1.1 1.0 Zimbabwe 26.4 25.2 32.1 32.1 Sub-Sahara Africa(non-oil) 38.0 37.2 29.8 26.4 Sub-S aAfrica 39.S 25.4 18.8 18.3 World 5.9 3.4 2.1 1.5 Source: FAO and ECIT, World Bank S TabIt 5: Share of export dmrnings from impcnan. export crops in sel!-ted SSA countries, 1961-90 1961-69 1970-79 12s0Qs9 2890 Deftsas C"pV'uerde 17.6 11.3 18.2 27.9 Somalia 39.6 16.5 12.7 28.1 Cocoa Cotedlvowre 21.3 24.9 33.0 31.4 Camerao 30.3 27.4 19.5 17.8 Gh.iza 69.3 69.3 49.3 44.6 Equatob GOine 70.4 40.5 19.2 SoaTomeA&Principe 70.6 75.0 70.1 50.2 Coftee l3urundi 66.8 34.6 84.6 tO's Central AfricnRepubLc 19.8 '6.9 13.3 17.0 Cote dlvoiu 36.4 i9.2 17.8 13.0 Cameroon 25.2 27.2 23.9 20.0 Ethiopia 57.8 52.9 63.8 60.1 Kenya 17.t 26.2 25.6 21.6 Maguar 30.1 34.2 37.0 20.9 Rwanda 5;.S 66.5 71.2 65.1 '. &rvArj a 13.7 23.1 31.0 22.8 Uganda 43.6 72.4 93.3 90.6 Cotton 1iedn 1.8 24.8 20.8 31.6 Burkina Faw 9.9 29.1 42.6 34.7 Nhli 7.2 28.6 32.8 45.4 Sudan 53.3 53.3 38.0 43.2 Chad 66.8 39.0 35.3 47.7 Togo 3.9 1.6 10.4 16.9 T ai 15.2 13.2 12.1 15.9 Groundnuts Ganbia 92.9 89.1 44.4 36.9 S-negal 75.3 42.9 16.0 17.7 Rubber Liberia 19.8 13,6 19.1 24.5 Sugar Mauritius 90.7 77.3 44.3 36.9 SAvzzland 27.8 32.9 34.9 28.8 Tea Kenya 10.8 13.3 19.4 24.6 Malawi 27.0 19.0 16.7 11.7 Rwanda 2.5 8.5 10.4 15,6 Tobacco Malawi 37.3 47.3 51.6 64.4 Zimbabwe 22.3 13.9 18.8 20.2 Source: FAO 6 Table 6: Share of SSA exports in world trade, by selected commodities and aggreLates, 1961-90 Country 1961.69 1970-79 198049 13s.s90 Banan 9 0 5.9 2.9 2.3 Cocoa 67.4 59.6 47.4 44.5 Coffe 24.5 27.1 21.9 19.2 Cotton 12.1 12.8 10.9 12.9 Grundnutb 61.1 39.0 13.4 20.4 Rubb,t 6.9 5.6 5.1 6.1 BSUU 5.7 4.5 4.5 5 2 Tea 3.7 14.9 15.3 14.9 Tobaco 9.4 8.5 10.1 12.5 Nine Mjor crops 17.9 17.7 14.8 13.9 Total apicUltute 7.1 5.7 3.7 2.9 Total dadc 2.7 2,4 1.6 1.2 Source: FPAO Tle dependency on a few agicultural commodities for export earaings often reflects a dependency on agriculture in the country's ecrnomy. Table 7 prov'des the agriculture's share of GDP in countries with available data. In many countries agriculture generates such a large portion of the country's awnual income that polic.es and programs targeting commodity and agricultural sub-sectors become vitalIy important fir the economy as a whole. Table 7: Agriculture's share of GDP for selected countries in Sub-Saharan Africa Country 1970 1980 199s per cent - BCrin 37 34 33 Botuwan 25 14 6 Cameroon 37 28 27 Congo 21 15 13 ComOro= . 4 1 Cape Verde 14 13 Gabon 9 9 Ghana 54 56 47 Gunea . 26 Guinea-!3issau 66 39 46 Mali 55 50 47 Rwanda 42 47 37 Senegal 28 22 21 Seychelles . 6 4 Chad 46 54 38 Togo 30 s6 36 Zambia 10 10 11 Source: Ini.ational Econornics Deprtmnent, World Bank. 7 Price volatility is a chaacteristic of commodity prices and dependence on commodity exports generally translates into volatile export revenues. Figure I illustrates the effects of commodity price movements in trade data from SSA. The top line in the graph is the income terms of trade (the value of exports deflated by a price index of manufactured exports from G-5 countries-the Bank's MUV) for total trade. The high level and volatility of the index throughout much of the 1970s was notably due to the development of oil production in Nigeria combined with the two oil shocks of that decade. Excluding Nigeria from the aggregate data (the second line fr .r the top), the effect of the 'conunodity boom' of the 1970s is less pronounced. The third line from the top is an index based on the export value of the nine major agrcultural export crops in S SA, while the bottom line is an index for all agricultural exports. These indices are characterized by a sharp peak in 1977 and then a precipitous drop that was somewhat reversed in the mid-1980s and a continued decline thereafter. While the decline fromn 1977 to 1980 was sharp, it occurred from historically high price levels. The most recent decline from 1986 to the present is a decline from what might be considered, in a historic sense, average income terms of trade levels. Income terms of trade for Sub-Saharan Africa 450 400 50 2- 250 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 = Major crop index - Total agricu1lure -c- TOIal trade O B Trade (exc Nigerio) Figure 1: Income terms of trade for total tradc (including and excluding Nigeria), agriculture, and major SSA commodities. 8 Figure 2 compares indices of income terms of trade based on the nine major SSA commodities for the Latin American, Asian, and SSA regions. For the group of commodities important to Africa, the experience of SSA has not been radically different from the experience of Asia or Latin America-although large differences did occur in pecific crops and in specific countries. While the income terns of trade for Asia have been more stable than for Latin America and Africa, all three regions have experienced a substantial deterioration in the terms of trade for this group of crops since the mid 1970s. For agriculture as a whole, however, a diffcrent story emerges (see Figure 3). In SSA the nine commodities represent a large proportion of total agricultural exports so that an income terms of trade index for total agriculture follows fairly closely the path of the nrne-commodity index, falling sharply after 1977. In Asia and Latin America, the export performance of other crops resulted in improving income terms of trade in the case of Asia, and a less dramatic decline in the case of Latin America. Regional income terms of trade for major SSA commodities, 196 1-90 200 1 80 80 1200 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 62 64 66 68 70 7.' 74 76 78 80 82 84 86 88 90 | Sub-Sohara Africa - Latin America - Asia Figure 2: Regional income terms of trade for the nine commodities that are of major importance to Sub-Saharan Africa. 9 Regional income terms of trade for agricultural exports 220 1200 180 80 160 ... . . . . . . . . . . . . . . 61 63 65 67 69 71 735 75 77 79 81 a83 85 87 89 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 Suffb-Sohnra Africa - Lotin Arnerice Asia Figure 3:: Regional income torms of trade for agriculture. In both Asia and Latin Arnerica, non-traditional crops expanded while the composition of ex)ports from SSA rmaninedi fairly sta8nat (Figure 4). In Latin America (see Figure S) the dominiance of co fee in export ewnings gave way to expanding exports of ftuits, vegetables, and oilseed products-primsarily soybewu and soybean meal. In Asia (see Figure 6), productivity increases affected all sectors of rioculture with the largest gains co.rting from fruits and vegetables and the dramatic increase in palm oil exports from Mialaysia and Indonesia. U'hile we have focused on the more relevant measure, the income terms of trade which includes the effwc of production gains there mav be some interest in purely price terms of trade. Figure 7 plots the barter terms of trade (a nominal price index deflated by the Of UV for the nine rnajor export crops. Two sets of commodity prices were used to derive indices. I Tne index given in the top line in the graph is based on observed spot narket prices taken as indicative of world prices. I\oC second is an average of SSA export unit values based on FAO export quantity and value dtat. Ite advantage of the fonner is that the prices can be more readily observed without effor. Yet very little trade mnay be associated with such priceus I There nrc also choices in thec mechanics of constructing a price index. A Fishcr index, which is thie geometric avergte Of Laspeym and Pauchc. indices, is repottd hcre. However, the battcr terms of tmde tdW not prove *cnsitive to indexation and either a Laspeym or Psachec index would provide SiMilW M3sult 10 Composition of agricultural exports Sub-Sahara Africa, 1970 & 1990 tobacco f 119901 cereols so sugar fats and olhseed prodeuts frwit c veegotabls cottoni ______ coffee. ecooe & tea _ _ __5__ othe_____ of hw ŁG.XUNo i 4 0.0 1.0 2.0 3.0 4.0 5.0 1.0 7.0 billion (1990) $uS Fgure 4: Composition of agricultural exports form Sub-Saharan Africa for 1970 and 1990. Composition of agricultural exports Lotin America, 1970 & 1990 tobocco 119901 fats &ohtd products - - - - cofton_ cerls s meal & lOv enma ____ frult & veogetals es wgar ___ coffee, cocoa. & tea oo Q _ _ __ other__ _ _ 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 5.0 9.0 billion (1990) Sus Figure S: Composition of agricultural exports from Latin America for 1970 and 1990. ll Composition of agricultural exports Asia, 1970 & 1990 meat & Nve animals . 1 99 0 sugar 1 970 tobacco Cotton coffee, cocoa, & tea fats & oliseeds cereals fruit & avegelobles !___ § other ______ ___ 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 billion (1990) sUS Figure C: Composition of agricultural exports from Asia for 1970 and 1990 and unit valu,es could more accurately reflect actual earnings. There are some important differences between the two sets of indices. Conspicuous by their absence are price spikes in 1963, 1974, and 1980 for the barter terms of trade based on export unit values. Decomposition of the index revealed that these were the result of sharp peaks in the world price for sugar that failed to show up in SSA export earnings. Nonetheless, in both series, real commodity prices declined during the past decade. 12 Barter terms of trade for major agricultural exports from SSA, 1961-90 220' . 174 200 A 1 80t I,, 1 o160 I~ , 60 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 World prices - SSA unit values| Figure 7: Barter terms of trade for major Sub-Saharan African commodity exports, valued at international market prices mnd at averag export price 13 3. The Adding-up Problem in Sub-Saharan Africa lTe adding-up problem occurs because individuals can produce small amounts of a commodity without affecting world prices, although their additional collective supplies can drive down wo:ld prices. Individual producers will continue to produce to the point where marginal cost equals the world price, while the profit mximizing point, from the perspective of country-wide welfare, is where marginal cost equals marginal revenue. Stated another way, the adding-up problem arises when a country fails to fully exercise any maket power its producers collectively possess. The problem was first discussed in the context of imnuserizing growth by Jagdish Bhagwati (1958) and Harry Johnson (1955). Bhagwati proved that economic growth could be inmmiserizing in the presence of the adding-up problem. More recently, the paradox of immiserizing growth was proven to be more general and arises from a sub-optimal allocation of resources. (See for example, Bhagwati, Brecher and Hata, 1984; and Hata, 1984.) Still, issues relating to the adding-up problem, especially in the context of primary commodities, remain hotly debated because the: optimal policies prescriptions rest on hard-to- measure empirical parameters. The adding-up problem can be described mathematically by starting with the producer problem of maximizing profits over time: max EJ [ps' - C(sA)Jehdt s.t. d' = s + s' 1) p that is, the producer maximizes the expected discounted stream of profits, where p is price, sb are home- country sales, c is the cost of production, and r is the discount rate. The problem is constrained by the fact that the home-country sales and sales from tl. rest of the world (s') must equal world demand (dw). The solution to the problem is given by2: -J, = Max,E[p(dw - S5) - C(dw - st)] 2) 2Brock and Malliaris, 1989, pp.352-55, provide a good summary of dynamic optimization issues. 14 The first-order condition is given by: d ' -s`+p(d; -s `t)- C'(d;w- s,") =O. 3) p Noting that .hd s' , and rearranging (3) provides: =P_ ~~~~~~~~~~4) d; - sfJw Dividing both sides by p and by dividing the numerator and denominator of the LHS by dw provides the optimal tax condition: m n' - E) p where s < 0 is the elasticity of derand, c > 0 is the supply elasticity for the rest of the workld m' = d/d is the market shure o' :' home country and where mw - md is - themuet sareo f the rest of the world. T defines the optimal tax rate. Expressed in terms of (5), the adding-up problem occurs when the individual marginal producer produces to the point where price equais marginal cost. Generally this is sub-optimal and a non-zero export tax will increase over-all retums to the country. However, as a practical matter, the optimal tax is often zero because of small market share or because other producers can easily expand production. In terms of the optimal-tax condition, the optimal export tax approaches zero when the narket share of the home country (mA) shrinks, when the supply responsiveness of competitors (s ) increases, and when demand becomes more elastic (when - s, increases). To see how the various parameters of the model affect the choice of the optimal tax, a simple model was constructed of the type used to calculate optimal tax rates reported later in the paper. Constant- elasticity supply curves for the home country and the rest-of-the-world were specified along with a world- wide constant-elasticity demand curve. A world price and home-country price were solved via the adding- up constraint that total supply and demand must match. As a result, market share, which is a function of home-country and res-of-the-world supplies, is endogenous as well. As a staring point, the home country 15 was assumed to have about a 25% share of the world mnarket; the world demnand price elasticity was set at - 0.4; and the home country and the rest-of-the-world both supply elasticities were set at 0.9. Figure 8 show the effects of changing the assumed demnand elasticity on the optimal tax rate (left- hand axis) and the equilibriumn market share (right-hand axis). As the demand elasticity rises, the optimal tax rate declines. However, since the decline in the tax rate rises home-country prices and home-country supplies, the equilibrium market share for the home-country rises as well, partially off-setting the first- order effect on the tax rate. Effect of demand elasticity on optimal tax rote and market share 35% 27.5%7 l 30% 27.0% 25% 2 6.5% -5 0~~~~~~~~~~~~~~~~~~~~~ 15% _ 25.5% 10%- 2 5.0 I) L.I o 5% [ 24.5% % 0 % b2.7 0.2 0.4 0.6 0.8 0.3 0.5 0.7 Demand elasticity |] LJoptimal tax rote + market shore Figure 8: Effects of demand elasticity on the optimal tax rate and mnarket share. Figure 9 maps out the effects of changing the supply elasticity of the rest-of-the-world, while holding the home-country elasticity constant at 0.9. The net-effects are similar to increasing the demnand elasticity. The first and primary effect is to push down the optimal tax rate which increases domestic prices and increases the home country's market share. 16 Effect of supply elasticity on optimal tax rate and market shore 35% 27.5% c 30% - 2 7.0% E 25% 26.5% 0~~~~~~~~~~~~~~~~~~~~~ x 20%-260 0 1 5%.4 25.5% t 10%_ 25.0% x 5%7. 24.5% . 0 % 4. ~~~~~~~~~~~24.0% E 0.5 0.7 0.9 1.1 0.6 0.8 1.0 Supply elasticity for ROW optimal tax rote - market share Figure 9: Effect of the rest-of-the-world supply elasticity on the optimal tax rate and market share. Finally, Figure 10 maps the effect of changing the home country's supply elasticity while holding the supply elasticity constant at 0.9 for the rest-of-the-world. Unlike the other parameters, the optimal tax rate is not very sensitive to alternative home-country supply elasticities. Instead, the primary effect is on market sha- which declines as home-country supplies become increasingly inelastic. The adding-up problem can be stated in terrns of the elasticity of export revenue with respect to volume (ERV). This is a convenient concept, since it relates to the market power of the hor.nc country. Since the revenue generated by exports (sales) is R(sh ) = psI = p(d - .s), ERV = 1 + + so that: a, p ERV = 1+-=_- =I-/ e 6) J7 p where the entity 17 = (e;- mmw") / m' is the price elasticity of demand facing a country (see., fot example, Imnan and Duncan). Therefore the ERV is bound somewhere between 1 (when the market share of th: home country is nearly zero, and 0 (since the marginal cost of production cannot be negative). Although the adding-up problem usually centers on commodities (Martin, 1993 is one of the exceptions), there is no reason from theory that the adding-up problem be a comnmodity problem. Still, the 17 Effect of supply elosticity on optimal tax rate and market share 35%_ 27.5% °30% 27.0% 1 257.- 26.57. - 20% : 26.0% 157. 25.57. Cv 107%. 25.0% 57 24.5% 0.50 0.70 0.90 1.10 0.60 0.80 l.C0 Supply *elsticlty for horre courtry o=ptmrrcl iox roti-4- mtorlei shore Figure 10: The effect of changing the home-county supply elasticity on the optimal tax rate and market share. raw material cosu in the final-corLsunrption form for niany commodities is quite low. For example, the tax on a cigaret in most countries greatly exceeds the cost of the raw tobacco contained in the cigarett. As a result, a ve-y large decline in the price of a commodity like tobacco nay result in a very small decline in the price of the form in which the good is finally consumed such as cigarettes or cigars. Since very large price char. es result m very small changes in consumption, these goods tend to have low demand price elasticities. Additionally, several countries and regions have concentrated market shares. These features suggest that adding-up problems are likely to occur in commodity markets. Further, since several raw commodities ar especially important in several countries in Sub-Saharan Africa, opdmal pricing becomes an urgent policy and development issue. In much of the literature on the adding up problem, Sub-Saharan Africa is treated as a single region. As will be discussed in the next section, that approach leads directly to fumdamental difficulties in terms of policy inplementation. Still, that approach has been taken in initially calculating estimates of the regional adding-up problem for SSA, as reported in Table 8. The table shows esfimatea of the short- (2 to 18 3 years) and long-term (7 to 10 years) ERVs based on SSARs market share in world production, for agricultural commodities in which SSA holds a sizable share of the world market (soe Annex Tables 1-6 for greater detail). Since adjustments such as production expansion for perennial crops takes time, long. run strategies should be based on long-run ERVs. Basing the analysis on SSA as a single entity generates lower ERVs (and higher optimal tax rates) than does an analysis based on single country sares. Still, ignoring for the moment implementation issues, the adding-up problem for Sub-Saharan Africa appurs limited to cocoa, coffee, tea, and tobacco Cocoa faces the nost serious adding-up problem. In the short run, the ERV for cocoa is negative, implying that SSA export revenues will fall with an increase in exports. Even in the long run, it is not profitable for SSA to produce cocoa unless the production cost of the additioral output is less than 33% of the world price. Coffee, tea, and burley tobacco may face an adding-up problem in the short-run, but it is not nearly as serious as for cocoa. It is profitable to increase production for these commodities so long us the production cost of the additional output is less than about 80% of the world price. 19 Table 8: ExpOrt revenue elasticities and optimal export tax for selected commodities in Sub-Saharan Africa demand elasticity supp;y alasticity IRV estimate optimal CommoditV share short long short lOna Dhort loaf tme (/) Cocoa SSA 54.5 -0.30 -0.40 0.35 0.90 -0.19 0.33 67.3 Coae dlvorc 29.8 -0.30 -0.40 0.35 0.90 0.45 0.71 23.9 Ghana 11.2 -0.30 -0.40 0.35 0.90 0.82 0.91 9.3 Nigeria 6.5 -0.30 -0.40 0.35 0.90 0.90 0.95 5.2 Cwncr.o)n 5.1 -0.30 -0.40 0.35 0.90 0.92 0.96 4.0 Coffee SSA 20.7 .0.30 -0.40 0.35 0.80 0.64 0.80 20.0 CoW dlvore 4.3 -0.30 -0.40 0.35 0.80 0.93 0.96 3.7 Ethiopia 3.3 -0.30 -0.40 0.35 0.80 0.95 0.97 2.8 Uganda 3.0 -0.30 -0.40 0.35 0.80 0.95 0.97 2.6 Zaire 1.7 .0.30 -0.40 0.35 0.80 0.97 0.99 1.4 Tea SSA 16.3 -0.30 -0.40 0.25 0.70 0.68 0.83 16.6 Kenya 10.3 .0.30 -0.40 0.25 0.70 0.80 0.90 10,0 M1Aawi 2.1 .0.30 -0.40 0.25 0.70 0.96 0.98 2.0 Burley Tobacco SSA 10.6 -0.10 -0.50 0.50 0.80 0.79 0.87 12.6 ! lawi 9.0 -0.10 -0.50 0.50 0.80 0.84 0.93 7.3 Cotton SSA 5.4 .0.15 -0.30 0.30 0.90 0.88 0.95 4.7 Sudan 0.7 -1.15 -0.30 0.30 0.90 0.98 0.99 0.6 Cote dlvoire 0.7 .0.15 -0.30 0.30 0.90 0.99 0.99 0.6 Sugar SSA 3.7 -0.20 -0.30 0.45 0.80 0.94 0.97 0.5 MaUriti'is 0.7 -0.20 -0.30 0.45 0.80 0.99 0.99 0.4 20 4. The Effect of the Adding-Up Problem on Trade Policy Policies suggested for regions facing an adding-up problem include diversification (Godfrey, 1983; Stewart, 1991), taxaion (Stewart), and production quotas (Stewart). Usually, these policies imply reduc& incentives for tradiuonal export crops in SSA. However, an important consideration often ignored in the analysis is whether, in fact, SSA should be treated as a single econormic unit. It is clear that Cote d'lvoire faces a serious adding-up problem with regard to cocoa because of its large world :.aarket share (30%). But shoulu countries such as Togo or Benin which individually do not face an adding-up problem adopt j, licies aimeo at discouraging cocoa production? Further, it is not clear that it is necessary or even beneficial to encourage diversification by penalizing traditional exports. hi the past, policies explicitly or implicitly discouraging the production of prinary commodities have ofter. led to adverse and lasting consequences in SSA. Exarnples include Ghanas cocoa policy and Nigeria's pclicies affecting palm oil in the 1970s. Policies or events which constrain tditional exports often spur investmez in other countries. Should diversification prove unsuccessful, it leaves SSA with considerably less total exyert revenue than before. For cxample, in response to the decline in Ghana's cocoa production in thc .'v7 Os, Brazil, Cote d'lvoire, and Malaysia expanded their production substantially. Five issues pertinent to countries in which exports are concentrated or face an adding-up problen are discussed in detail below-export taxes, coordination of policies among SSA countries, diversification, the effect of extension services and production increases on welfare, and exchange rates policies. Export Tiaes As discussed earlier, export taxes can maximize welfare from exports of a commnodity for a country which has some measure of monopoly power. The optimal level of the export tax is that which, at a country level, equates marginal most with marginal revenue when the commodity is produced by a largc number of smallholder farmers who otherwise perceive the world price as their marginal revenue. The optimal tax level in a sttic frimework is the inverse of the price elasticity of demand facing the country. 21 Calculation of the optimal tax level dynamically becomes considerably more complicated especially in the case of perennials which require more than one year of investnent for production. Still a prominent characteristic of the relationship between the export tax and welfare fron the commodity (as measured by the sum of producer surplus and government tax revenues) is that the country's welfare remains little changed over a wide range of export tax rates around the optimal rate. An example of the change in welfare under different export tax rates is shown in Figure I1. This is the case of a country with a world market share of 12%. The optimal level of the export tax is 15%. Assumptions are that the world price elasticity of demand is -0.35 and the supply elasticity of all producers is 0.5 The total welfare hardly changes for tax rates of 0 to 40%. Simulations with different market shares produced similar results. However, the distribution of income between the producers and the government changes drastically with changes in the export tax. Figure 11 also shows, as theory predicts, that export revenue is at a maximm when the export tax is zero. 120 100 z 01> ~~~~~~~~~~~~~~~~~~~Producer Surplus 60 ~~~~60 - ~~~~~~~~~~~~~Govlt Revenue ma 40 - Total Welfare - -Export Revenue 20 it 0~~~~1 ELXPORT TAX RATE(1) Figure II: Changes in Welfare and Export Revenue with Export Tax 22 For perennial crops, because production is dependent on investments (new plantings), lower taxes result in higher long-term production potential. Hence, the level of the optimal tax is critically dependent on the viscount rate used. For example, if a zero export tax was implemented for five years in the above example of a country that has a 12% world market share, the country's welfare would be slightly less than the naximum in the short run but its welfare would be large in ten years. The discussion above suggests that the level of the export tax can be set within a fairly wide range without significantly affecting total welfare. This is an important point in practice, since high export taxes may not be practical. High export taxes encourage high rates of evasion either through smuggling or bribes. In addition, the tax may prove regressive if it places a high burden on low-income smallholders. If a country decides to impose an export tax, it is critical that the level be exanined frequently. The optimal tax level changes with changes in the market share and in price elasticities of demand and supply. Another consideration in examining export taxes is the degree to which the commodity is directly or indirectly subsidized or taxed along the production chain. Because of their traditional place in nany economies, policies regarding trade and production have frequently generated layers of institutions working at cross purposes. On the one hand, traditional export crops often receive preferential treatment in the allocation of extension services and transportation services which amounts to an indirect subsidy. More directly, producers are sometimes offered guaranteed prices above world market rates backed with public funds. At the same time, cesses are often levied directly or indirectly to finance over-staffed marketing boards. In the case of cocoa, Stryker et. al. (1990) found that the Ghanaian cocoa marketing board operations implicitly taxed cocoa at a rate of 20-50% from 1955 to 1985 - a rate much higher than the 9- 10% optimal tax calculated in Table 8. Additionally, over-valued exchange rates also serve as an indirect tax on exports and an indirect subsidy on input imports. Such an over-valuation can arise from direct exchange-rate controls, but can also arise indirectly - for example from import restrictions (See Krueger, Schiff and Valdez, 1991). Export taxes should not be placed as an additional layer on a complex structure of subsidization and taxation, but rather in place of often conflicting policy instruments. 23 Coordination of policies amnong SSA countries Because export revenues can be increased, at least in the short-rn, by reducing world exports of commodities that have price elasticities of less than unity, there have been a number of attempts to construct international commodity agreements to raise commodity prices. There are at present international agreemnents for natural rubber, coffee and cocoa but the economic provisions of the latter two are not operative. The economic provisions of the International Cocoa Agreement to stabilize world cocoa prices were based on buffer stock operations, but after a few years of operations in the early 1980s, the buffer stock fund was depleted due to rapidly increasing world cocoa production. The export quota system of The International Coffee Agreement stopped operating in July 1989 when members of the Agreement could not reach an agreement on the rules of operation for the quota system. The International Natural Rubber Agreement is based on an international buffer stock system, but international rubber prices have been hovering at the bottorn of the support range for the last several years. Recent experience with imremational commodity agreements supports the notion that, as a practical matter, it is impossible to support world prices above a market-clearing level for a sustained period of time. Williams and Wright (1992) and Larson and Colemen (1991) both discuss the predisposition of commodity management schemes to fail due to price movements. An additional problem is the asymmetric distribution of benefits arising from such schemes. The coordination of tax policies survey SSA countries would face this same obstacle. To illustrate the difficulty of operating a policy in which all SSA countries imposed the same export-tax rates, a simple model was built to evaluate the effects of export taxes imposed at the optimal rate by two countries, independently and jointly. World demand elasticity was assumed to be -0.35 and a!l supply elasticities were assumed to be 0.5. There are three producers - Conntry 1 with the market share of 10%, Country 2 with a market share of 25%, and the rest of world (ROW). All production is assumed to - -^rted. T-'le 9 shows changes in key %-.Ahec when export taxes are set at the optinml level for each country independently and when they are considering Country 1 and 2 as one unit. 24 Table 9: Changes in key variables when two countries move from taxing exports based on country sbauo to a uniform regional tax based on combined market share.a/ World market Der centsec ch&=g Supply .1.9 Price 5.7 Rest of the world Welfare 8.6 Export revenue 8.6 Market share 3.1 Country-level effects of moving to a urniform resional tax.rmt Country 1 (small) Producer surplus -48.0 C.Lvernment revenue 214.3 Total welfare .1.5 Export revenue *15.0 Market share .1. Country 2 (large) Producer surplus -19.5 Government revenue 31.8 Total welfare 3.3 Export revcnue .1.7 Market sharc 1.3 Reiional effects of niovint to a uniform regional tax-rate Country I & 2 combined: Producer surplus -29.5 Governnent revenue 54.9 Total welfare 2.0 Export revenue .5.5 Market share .3.1 a/ If imposed independently, the optinal tax rates are 12.6% and 34.7% for Countries I and 2, respectively. If impoaed jointly, the optimal regional tax rate is 46.5% because of the larger market share. See the text for assumptions made. Te simulation results show several interesting facts when the two countries impose the tax jointly, including: (i) The cornbined welfare of the two countries increases but by only small margin. In this example, the increase is only 2%. (ii) Because of the higher export tax, i.e., 46.5% compared with 12.6% and 34.7% when imposed independently, the producer surplus of both countries declines sharply; the produc r surplus of the smaller country declines considerably more than that of the larger one. The govenrment revenue of both countries increases sharply, especially that of the smaller one. 25 (iii) Total welfare of thi smaller country declines while that of the larger country increases. (iv) Market shares and export revenues of both countries decline. The reduction is considerably greater for the smaller country than for the larger country. (v) Welfare, export revenues, and market share of ROW increase substantially. The simulation results point to an obvious difficulty in coordination around the question of whether the large country will be willing to compensate for the loss incurred by the small country. Because the combined welfare is increased, the larger country would still gain after compensating the loss incurred by the smaller country. Possibly a more important problem is that the welfare, export revenue, and market share of the rest of the world increase significantly. In this example, the welfare gain by ROW is 8.6% while that by the two countries combined is only 2%. In the long-run, this would enable the rest of the world to increase productivity and its market share even further. D2iversification As mentioned above, some analysts argue that diversification should be a priority in the context of SSA's agricultural export strategies of SSA countri:s facing adding-up problems. However, given th in many SSA countries, a large number of people are engaged in production, processing, and marketing of the najor commodities and that these commodities are the only cash crops, it is difficult for any economic development strategy to be viable if these commodity subsectors are ignored or penalized. Diversification usually requires investment and often the only source of the capital is the traditional crop subsectors. As discussed below, it is possible to increase the producer surplus and government export tax revenue from the commodity facing an adding-up problem through productivity increases. Such a strategy may be a viable option for diversification in many SSA countries. Even though it puts additional government resources into the subsector, just as a profitable and dynamic agricultural sector often complements industrialization-a profitable and dynamic traditional commodity subsector can facilitate the development of a viable diversified agricultural sector. A forced diversification strategy that ignores the relative profitability of new commodities vis-a-vis traditional conunodities is likely to fail. There is no guarantee that diversification in and of itself will 26 increase the welfare of SSA countries. For example, some commodities for which SSA does not face an adding-up problem may also have very poor price prospects because of declining demand or sharply increasing supply of countries outside of the region. Additionally, Sub-Saharan Africa may lack a comparative advantage in producing those commodities. Diversifying into these commodities might make Sub-Saharan Africa worse off when compared to increasing productivity in traditional crops . Alternatively, where alternati es do exist, appropriate export taxes on commodities facing an adding-up problem will provide incentives for diversification because relative prices would give appropriate incentives to farmers as to what crop to grow, either for domestic consumption or export. Additionally, there has been a frequent bias in government spending in many SSA countries in favor of traditional export crops in terms of research, extension, marketing and distribution infrastructure, which has worked against the establishment and growth of other export activities. The reasons for this bias include government revenues from export taxes and the ease and speed with which production of traditional export crops can be increased compared with non-traditional ones. Removing biases in government services will also encourage the development of alternatives to traditional crops. Tlhe effects of extension services and technical change Some analysts discussing the adding-up problem for SSA countries appear to suggest that these countries and the international community should do nothing for these commodities and instead allocate resources to diversification. Such advice often stems from a confusion over price effects, profitability and welfare. Changes in applied technology that result in a fall in international prices can still lead to welfare increases. BL; careful analysis is required on how productivity or production is increased because the different way in which productivity or production is increased has different irnplications for the country's welfare. The relationship between productivity or production increase and welfare has been widely discussed in the economic literature.3 Any productivity and production increase can be classified into three 3 See for example, Lindner and Jarrett (1978) and Voon and Edwards (1992). 27 basic types depending on the way it shifts the supply curve in a price-quantity diagram-convergent, paallel, and divergent. (These three types are shown in Figure 12.) It is clear from Figure 12(a) that the convergent type of supply shift does not increase production but increases farmers' welfare given by the area abc. Because this does not increase production, it has no impact on the world price. Hence in this case the question of "adding-up" problem does not arise. It is a pure case where the impact is just on increasing producer surplus of existing producers. Such a shift can occur, for example, when research and extension services are concentrated on efficient farmers. Small share-holders are often assumed to be the least efficient producers and programs that target efficient producers are opposed on equity grounds. This is may be a mistaken assumption and careful consideration should be given to the impact of training and extension programs. In the case of a paral;el shift of the supply curve, the welfare gain is positive. The welfarc comparison is to be made between the areas of triangles aPof and bP,g in Figure 12(b). Because thw triangles are similar and Pg > Pof, area bPg > aPof. This type of shift increases supply and hence lowers world prices. This is the case when all farmers succeed in reducing production cost by the same amount. An example of such research is the development of yield-improving planting material. The effect on welfare is uncertain in the case of a divergent supply shift (Figure 12(c)). This type of shift could occur, for example, if effort is given to reducing the production costs of the less efficient farmers while leaving production cost of the more efficient farrners unchanged. In such a case, the price decline resulting from making the marginal farmer more productive can result in an overall decline in surplus. As a practical matter, the instances when adding-up effects are significant are exceedingly rare. Nonetheless, unless off-st by increased tax-rates (in which surplus gains go to the government instead of producers) programs targeting the least efficient producers can be counter-productive. In countries where an adding-up problem exists, extension and research programs which target inefficient farmers can generate a policy dilemma - especially if the least-efficient farmers are also the poorest. In terms of the optimal tax, recall that r = (p -C) Ip, so that for the most marginal farner, most, if not all, of the increased profits arising from cost-saving extension work must be taxed away by the 28 government. Otherwise, the country will produce in excess of the optimal level and total producar surplus will be reduced. Fe.-unately, at a practical level, there are few instances where countries face an adding-up problem. St:ll, in those few cases where the problem does exis., care should be taken to recognize that the price-effect of increased production reduces the value of the service to the marginal farmer when inefficient p P p POq qOc QQ PO a a~~~~~~~P ConvergentP gulu Dlvg1 a~~~~~~~~ b d b d d b 00 Qo001 00 GI ConvrgeM PuaaieI DIvetgud Figure 12: Three Types of Production Technical Change. caused by extension and research work which unduly emphasizes traditional crops at the expense of alternatives. Finally, when an adding-up problem does exist, programs devoted to area expansion, such as subsidized planting schemes may result not only in a misallocation of land resources, but may also result in welfare losses. Unlike the exarnple of cost-reductions for inefficient farmen which can be off-set through increases in the tax-rate, area expansion is likely to result in either constant or increasing narginal cosu. In the presence of an adding-up problem, the additional quantities reduce prices as well, generating a net loss in government and producer surplus. 29 Exchangates In examining appropriate exchange rate setting for countries whose major export itemns vre agricultural commnodities facing an adding-up problen, two critical facors need to be taken into account- exchange rates of competing countries and the marginal revenues of the incremental production caused by the exchange rate change. As discussed by Devarajan CLn1 (1993), the most common approach in practice to estimating the equilibrium exchange rate is to calculate the "purchasing power parity' (PPP) equilibrium exchange rate. According to this approach, the equilibrium nominal rate is calculated by equating the inflation adjusted value of the country's currency to that of trading partners. As Devarajan " point out, this approach has major flaws if there are major changes in relative world prices of commodities and in the equilibrium level of foreign capital inflows. For a country whose major export items are primary comnnodities, the relevant comrarison is between the country's real exchange rate and thoce of competing countries. An example could be an SSA countiy whose main export item is cocoa and its main destination is Western Europe. Assume that this country's imports consist mainly of capital goods from Western Europe. According to the PPP approach, this country's real exchange rate should follow the real exchange rate of Western Europe. However, if real exchange rates of other mnajor cocoa producing countries such as Malaysia and Indonesia depreciate significantly relative to Western European currencies, the SSA country will lose its competitiveness in exporting cocoa. The prime consideration in determining the real exchange rate level for such countries therefore should be movements in production costs of the mnajor export commodities as compared with other major producing countries expressed in a common currency. The ERV is a critical parameter in evaluating the exchange rate of a country that faces an adding- up problem. For such a country that depends heavily on a single export commodity and faces a balance-of- payment problem, a real devaluation would not help to alleviate the balance-of-payment problem unless the devaluation leads to the substantial expansion of exports of other commodities. This is because a devaluation would increase supply and hence exports of the traditional commodity but would not increase export revenues much due to the low ERV. In such countries, it becomes indispensable to impose a tax on 30 the traditional commodity to enhance the expansion of other exports. From experience, this is a common situation as the supply response of new exports is very slow-most likely because investors are unsure that the reform policies will be long-lasting. A devaluation cannot decicase profitability of producing export commodities. For a given output, proportional increase in revenues and costs will result in a proportional increase in profits. In practice, however, a chaz.ge in exchange rates will affect the relative profitability of alternative production methods. A devaluation increases the price for imported inputs such as pesticides, machinery, and some fertilizers while only indirectly affecting the price of "non-tradable" inputs. Since a variety of fanning methods is frequently used within a suigle country, the effect of devaluation on farm profitability will not be the same for all farmers. To this extent, changes in relative prices have an effect on supplies sinmilar to changes in the underlying technology. If inputs are generally imported, and low-cost producers are input-intensive, then an exchange rate devaluation tends to fltten the supply curve. This would be a divergent type of production increase in Figure 12. Low-cost producers will see an upward shift in costs and a decline in profits, while low-input high-cost producers see little change in their (already high) costs. The devs!uation in this circumstance will lead to increased production since revenues are increased while the effects on marginal costs are more limited. Howcver, a portion of the producer surplus previously enjoyed by the high-input users is lost to increases in input prices. Alternatively, if low-input producers are also low-cost producers, a devaluation has an effect similar to the introduction of a convergent technology of Figure 12 and low-cost producers will enjoy an increase in producer surplus. Generally, it is likely that relatively high-input technologies are also low-cost. This is because there are no constraints to not using inputs if it is cost-effective to do so while delivery systems, trade restrictions, or lack of credit may all hamper input use even when it is cost-effective. Care should be taken however in analyzing the specific technologies available in the country and to recognize the relationship between technologies, exchange rates, and prices. When low-cost production is also input-intensive, potentially large gains in producer surplus may be available when obstacles to input-use are removed for high-cost producers through credit or extension programs. At the same time, the potential gains to such programs may be reduced when the currency of the country is constantly devalued. 31 5. Concluding Remarks Tle paper examined agricultural commodity strategies for SSA countries with a focus on the adding-up problem. The adding-up problem has been raised frequently because of the poor performance of SSA's agricultural commodity exports and the increasing concentration of exported commodities in the last 15 years. However, the analysis shows that only a few countries in SSA individually face this problemn. The problem is a serious one for Cote d'lvoire in cocoa, and exists in a less serious form for Ghana in cocoa, Kenya in tea, and burley tobacco in Malawi. Some analysts discuss the adding-up problem in terms of SO ' as a whole and reasonably conclude there is a problem for cocoa, coffee, and tea. However, it does not appear feasible to design and implement agricultural commodity production and trade policies for the region as a whole because of the difficulty in coordinating policies to equitably distribute gains among SSA countries. In addition, the analysis suggests that if SSA countries agreed to impose the optimal export tax based on Sub-Saharan Africa as whole, the greatest benefit would go to producers in other regions such as Latin America and Asia. Recent failures of intemational commodity agreements and the disruption caused by their discontinuation highlight the difficulties of coordination of trade or production strategies among countries aimed at raising world prices. Some analysts hint that production of commodities facing an adding-up problem should be discouraged. Instead, these subsectors create a resource base that can be used by farmers and governments to create dynamic and diversified agricultural sectors. Given that these commodities are often the only cash crops in which the countries have a comparative advantage, it would be counter-productive to design an agricultural strategy based on discouraging production of these commodities. The few countries that do face a serious adding-up problem need to take specific consiierations in designing and implementing policies that affect production and exports of the commodity including: (i) Increasing production thru-ugh costly expansion of land area should be avoided. Such policies would likely reduce producer surplus of existing farners because of their negative impact on world prices. 32 (ii) Efforts should be made towards reducing production and nurketing costs. If accompanied where appropriate by an export tax, this would not lead to much increase in production but would increase farmers' profitability and government revenues. (iii) The analysis suggests that when an adding-up problem does not exist, a zero export tax would be the most appropriate policy for the long-term benefit of the subsector. Alternatively, when countries do face a serious adding-up problem, the imposition of an export tax near the optinml level would be the most efficient way to limit domestic production. Because the optirmal export tax level changes with world market conditions, it is imperative that the export tax level be reviewed frequently. The analysis in this paper shows that precise calculation of the optimal tax rate is frequently not necessary since the primary effect of choosing various tax rates in the neighborhood of the optimal level is to allocate revenue between producers and the government. Taxing exports at a less-than-optimal level often results in additional revenue for the agricultural stor without affecting total welfare. (iv) Imposition of an export tax could be desirable if a country facing a serious adding-up problen is to imnplement a real devaluation of its currency. One of the most important expected effect of a reed devaluation is to adjust the balance-of-payments toward equilibriun. However, a real devaluation would increase production and exports of the conmmodities facing a severe adding-up problem. Since increased export quantities do not increase export revenues when an adding-up problem exists, an export tax on the commodity could be required to enhance export revenues by diverting resources from traditional commnodities which faces adding-up problem to other commodities. (v) Biases which favor traditional crops should be elirinated as well as policies which penalize. Diversification can be encouraged by providing equal access to transportation and extension services which have historically favored traditional crops. 33 Annex Table 1: ERV, and Optimal Tax of SSA Coutries Producing Coffee Pzoduction Production Demand Elasticity ERV Optimal Avcrage Share in Shre in Facing Counuy Tax 1989 1990 1989 & 1990 SSA World (000 tons) (000 tons) (%) (shou) (long) (shoft) (long) (O) SSA 1235 1282 1258 100.0 20.7 -2.8 -5.01 0.64 0.80 20.0 Cote divoire 239 284 262 208 4.3 -14.8 -27.11 0.93 0.96 3.7 Ethiopia 200 204 202 16.1 3.3 -19.2 -35.36 0.95 0.97 2.8 Uganda 174 192 183 14.5 3.0 -21.3 -39.11 0.95 0.97 2.6 Zaire 107 98 102 3.1 1.7 -38.3 -70.49 0.97 0.99 1.4 Kenya 105 95 100 7.9 1.6 -39.3 -72.35 0.97 0.99 1.4 Cameroon 86 102 94 7.5 1.5 .41.6 -76.73 0.98 0.99 1.3 Madagascar 88 83 86 6.8 1.4 -45.9 -44.52 0.98 O.99 1.2 Tanzania 58 52 55 4.4 0.9 -71.9 -132.53 0.99 0.99 0.8 Rwanda 39 45 42 3.3 0.7 -93.8 -173.10 0.99 0.99 0.6 Burundi 32 35 33 2.6 0.5 -119.4 -220.19 0.99 1.00 0.5 Source: IECIT 34 Annex Table 2: ERV, and Optimal Tax of SSA Countries Producing Cocoa | Production Production Demand Elasticity ERV Optima Average Share in Sharc in Facing onutry Tax 1989 and 90 SSA World (000 tons) (%) (short) (long) (short) (long) (%) SSA 1322 100.0 54.5 -0.8 -1.49 40.19 0.33 67.3 Cote dlvoire 723 54.7 29.8 -1.8 -3.46 0.4S 0.71 28.9 Ghana 271 20.5 11.2 -5.5 -10.76 0.82 0.91 9.3 Nigeria 158 11.9 6.5 -9.7 -19.12 0.90 0.95 5.2 Cameroon 123 9.3 5.1 -12.5 -24.77 0.92 0.96 4.0 Togo 8 0.6 0.3 -196.1 -'92.05 0.99 1.00 0.3 Equatorial Guinea 8 0.6 0.3 -209.9 419.56 1.00 1.00 0.2 Sierra Leone 7 0.5 0.3 -226.5 -452.76 1.00 1.00 0.2 Zaire 6 0.5 0.2 -260.3 -520.33 1.00 1.00 0.2 Sao Tome A Principe S 0.3 0.2 -350.0 -699.86 1.00 1.00 0.1 35 Annex Table 3: ERY, and Optimal Tax of SSA Countries Producing Cotton Production Production Production Demand Elasticity ERV Opimal Average Shame in Share in Facing Country Tax 1989 and 90 SSA Wold (000 tons) (000 tons) (%) (short) (long) (shod) (long) (V.) SSA 957 100.0 5.4 4.0 -21.4 0.58 0.95 4.7 Sudan 121 12.6 0.7 -65.8 -175.2 O.9" 0.99 0.6 Cote d'ivoirm I1 12.3 0.7 -67.5 -179.8 0.99 0.9 0.6 Mali 98 10.2 0.6 41.4 -216.9 0.99 1.00 0.5 Zimbabwc 81 8.5 0.5 -98.2 -261.9 o.9 1.00 0.4 Tanzania 71 7.4 0.4 -113.1 -301.4 0.99 1.00 0.3 Burkina Faso 62 6.5 0.4 -128.1 -341.5 0.99 1.00 0.3 Chad 60 6.3 0.3 -133.0 -354.5 .99 1.00 0.3 Benin 47 4.9 0.3 -169.8 452.6 0.99 1.00 0.2 Cameroon 43 4.5 0.2 -183.7 -489.6 o." 1.00 0.2 Nigeria 35 4.0 0.2 -208.7 -556.3 1.00 1.00 0.2 TGO 34 3.6 0.2 -233.7 -623.2 1.00 1.00 0.2 36 Annes Table 4: ERV, and Optimal Tax of SSA Countries Producing Sugar Production Production Demand Elasticity ERV optimal Average Share in Share in Facing Countiry Tax 1989 and 90 SSA Wodd (000 tons) w/) (shoit) (long) (shod) (long) ) SSA 3913 I,0.O 3.7 -17.3 -29.21 0.94 0.97 3.4 Mfauritius 596 15.2 0.6 -116.1 -196.38 0." 0.99 0.5 Swaziland 502 12.3 0.5 -133.0 -233.45 o.9 1.00 0.4 ndbabwe 497 12.7 0.5 -139.2 -235.55 0.99 1.00 0.4 Kenya 474 12.1 0.4 -146.3 -247.51 0.99 1.00 0.4 Sudan 400 10.2 0.4 -173.4 -293.47 o.9 1.00 0.3 Ethiopia 190 4.8 0.2 -365.3 .618.93 1.00 1.00 0.2 Mbaawi 176 4.5 0.2 -394.0 .666.76 1.00 1.00 0.1 Cote d'Whire 141 3.8 0.1 -469.5 -794.43 1.00 1.00 0.1 Zambi 140 3.6 0.1 -497.6 -842.05 1.00 1.00 0.1 Madagascar 119 3.0 0.1 -582.1 -986.32 1.00 1.00 0.1 Tanzania 111 2.S 0.1 -625.5 -10S8.46 1.00 1.00 0.1 37 Annex Tabk 5: ERV, and Optdmal Tax of SSA Countries Producing Budley Tobacco Production Production Demand Elusticity ERV Optimal Average Share in Shae in Facing Country Tax 1990 1991 l990 and 1991 SSA World (000 tons) (000 tons) ((shor) (ong) (showt) (long) (*V) SSA 292.85 317.39 81.59 24.3 10.6 4.8 -7.9 0.79 0.87 12.6 Malawi 64.02 75.01 69.52 20.7 9.0 -6.2 -13.6 0.84 0.93 7.3 Zimbabwe 5.89 7.89 6.89 2.1 0.9 -66.8 -144.9 0.99 0.99 0.7 MAdagascar 1.55 1.55 1.55 0.5 0.2 -299.6 -649.4 1.00 1.00 0.2 Mozambique 1.15 1.15 1.15 0.3 0.1 -402.6 -872.7 1.00 1.00 0.1 Zambia 0.80 0.80 0.80 0.2 0.1 -579.0 -1,254.8 1.00 1.00 0.1 Zaire 0.66 0.66 0.66 0.2 0.1 -701.9 -1,521.2 1.00 1.00 0.1 Tanzania 0.55 0.55 0.55 0.2 0.1 -842.4 -I,B2S.5 1.00 1.00 0.1 Kenya 0.28 0.28 0.28 0.1 0.0 -1661.2 -3,612.5 1.00 1.00 0.0 Angola 0.20 0.20 0.20 0.1 0.0 -2317.6 -S.J21.6 1.00 1.00 0.0 SOURCE: IECIT 38 Annex Table 6: ERV, and Optimal Tax of SSA Countries Producing Tea Production Demand Elasticity ERV Optimal Average Sharc in Share in Facing Counly Tax 1989 and 90 SSA World (000 tons) (000 tons) () (short) (long) (short) (long) () SSA 299.4 100.0 16.3 -3.1 -6.04 0.6" 0.83 16.6 Kenya 188.8 63.1 10.3 -5.1 -9.99 0.S0 0.90 10.0 Malawi 39.2 13.1 2.1 -25.5 -50.73 0.96 O.9" 2.0 Tanzania 18.5 6.2 1.0 -54.3 -108.38 O.98 0.99 0.9 Zimbabwc 17.5 5.8 1.0 -57.5 -114.78 0.98 0.99 0.9 Rwanda 11.5 3.8 0.6 -87.9 -175.54 0.99 0.99 0.6 Mauritius 5.6 1.9 0.3 -179.1 -358.01 0.99 1.00 0.3 Uganda 5.6 1.9 0.3 -179.6 -359.01 0.99 1.00 0.3 Burundi 3.9 1.3 0.2 -259.3 -518.32 1.00 1.00 0.2 Zairc 3.1 1.0 0.2 -325.2 -650.25 1.00 1.00 0.2 Cameroon 2.6 0.9 0.1 -387.8 -775.43 1.00 1 00 0.1 39 References Akiyama, T. 'Is there a Case for an Optimal Export Tax on Perennial Crops?" World Bank Policy Research Working papers, WPS, 874, Feb. 1992. Aliyama, T., P. Varangis, M.E.Thigpen.. "Recent Developments in Marketing and Pricing Systems for Agricultural Export Commodities in Sub-Saharan Africa," World Bank Policy Research Working paper, WPS 431, May 1990. Akiyama, T., J. Coleman, P. Varangis. "Impacts of Policy Changes on Cocoa Sectors in Major Sub- Saharan Producing Countries," World Bank Policy Research Working Paper (forthcoming). Bhawti, J. "Imiserizing Growth: A Geometrical Note," Review of Economic Studies, 25 (June 1988) pp. 201-205. Brek, W.A., and A.G. Malliaris. Differential Equations, Stability and Chaos in Dynamic Economics. Amsterdam: North-Holland, 1989. Coleman, J. and M.E. Thigpen "Should Sub-Saharan Africa Expand Cotton Exports?", World Bank Policy Research Working Paper (forthcoming) Deaton, Angus, (1992), "Commnodity Prices, Stabilization, and Growth in Africa," mimeo, Princeton University. Devarajan S., D.L. Jeffrey, and S. Robinson, "External Shocks, Purchasing Power Parity, and the Equilibrium Real Exchange Rate," Department of Agricultural and Resource Economics, University of California at Berkeley Working Paper No. 611, May 1991. Godfrey M. "Trade and Exchange Rate Policy: A Further Contribution to the Debate," Crisis and Recovery in Sub-Saharan Africa, OECD, 1983. Krueger, Anne 0., Maurice Schiff, Alberto Valdez. Political Economy of Agricultural Pricing Policy, Volume 3: Africa and the Mediterranean. Baltimore: Johns Hopkins University Press, 1991. Johnson, H. "Equilibrium Growth in an Expanding Economy," The Canadian Journal of Economics and Political Scicnce, Vol. 19, no. 4 (November 1953) p. 495. Lindner, R.K. and F.G. Jarrett. "Supply Shifts and the Size of Research Benefits," American Journal of Agricultural Economics, Feb. 1978. Martin, W. "The Fallacy of Composition and Developing Country Exports of Manufactures." The World Economy. Vol. 16, No. 2, March 1993. Stewart, F. 'Are Adjustment Prlicies in Africa Consistent with Long-run Development Needs?", Development Policy Review. Vol. 9, No. 4, Dec. 1991. Stryker, J. Dirck, Emmanuel Dum=au, Jennifer Wohl, Peter Hammond, Andrew Cook, Katherine Coon. "Trade, Exchange Rate, and Agricultural Pricing Policies in Ghana" World Bank Comparative Study, Washington, D.C.: World Bank, 1990. 40 Trivedi, P.K. and T. Akiyazn. 'A Framework for Evaluating the Impact of Pricing Policies for Cocoa and Coffee in Cote d'Ivoire," The World Bank Economic Review. Vol. 6, no. 2, May 1992. Voon, T.J. and O.W. Edwards. "Research Payoff from Quality Improvement: ThI Case of Protein in Australian Wheat," American Journal of AgricultuMl Economics Aug. 1992. 41 Policy Research Working Paper Series Contact Title Author Date for paper WPS1221 Does Research and Development Nancy Birdsall November 1993 S. Raian Contribute to Economic Growth Changyong Rhee 33747 in Developing Countries? WPS1222 Trade Reform in Ten Sub-Saharan Faezeh Foroutan November 1993 S. Fallon Countries: Achievements and Failures 38009 WPS1223 How Robust Is a Poverty Profile? Martin Ravallion November 1993 P. Cook Benu Bidani 33902 WPS1224 Devaluation in Low-inflation Miguel A. Kiguel November 1993 R. Luz Economies Nita Ghei 39059 WPS1225 Intra-Sub-Saharan African Trade: Faezeh Foroutan November 1993 S. Fallon Is It Too Little? Lant Pritchett 38009 WPS1226 Forecasting Volatility in Commodity Kenneth F. Kroner November 1993 F. Hatab Markets Devin P. 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