Malawi - Economic report on environmental policy (Vol. 2 of 2) : Technical annexes

Report No. 9888-MAI Malawi Economic Report on Environmental Policy (In Two Volumes) Volume Il: Technical Annexes March 20, 1992 Country Operations Division Southern Africa Department FOR OFFICIAL USE ONLY Document of the World Bank This document has a restricted distribution and may be used by recipients only In the performance of their oiticial duties. Its contents may not otherwise be diclosed without World Bank authorization.  CURRENCY EQUIVALENTS US$1 MK 2.79 MK I US$0.36 WEIGHTS AND MEASURES 1 Kilogram (kg) - 2.2 Poundr 1 Metric Ton (mt) = 2,204.6 Pounds 1 Liter (1) 2.116 US Pints 1 Hectare (ha) 2.471 Acres 1 Cubic Meter (cm3) = 35.3 Cubic Feet I Kilometer (km) = 0.621 Miles GLOSSARY OF ABBREVIATIONS ADD - Agricultura! Development Division ADMARC - Agricultural Development and Marketing Corporation AES - Agro-Economic Survey aic - average incremental costs ASA - Annual Survey of Agriculture ASAC - Agricultural Sector Adjustment Credit CEM - Country Economic Memorandum CITES - Convention on Intl. Trade in Endangered Species of Wild Fauna and Flora DEVPOL - Statement of Development Policies DLV - Department of Lands and Valuation DNPW - Department of National Parks and Wildlife DWSF - District Water Supply Fund EES - Estate Extension Service EPA - Environmental Planning Area ehu - erosion hazard unit EIA - Environmental Impact Assessment EP&D - Economic Planning and Development Department EU - Environment Unit, National Research Council FAO - Food and Agricultural Organization IITA - International Institute for Tropical Agriculture LHB - Land Husbandry Branch l/p/d - liters per day mai - main annual increment MBS - Malawi Bureau of Standards MOA - Ministry of Agriculture NCE - National Committee for the Environment PFP - Policy Framework Paper RDP - Rural Development Project SACA - Smallholder Agriculture Credit Administration San-Plat - sanitation platform latrine SLEMSA - Soil Loss Estimation Model for Southern Africa t/ha/yr - tons per hectare per year USAID - United States Agency for International Development USLE - Universal Soil Loss Estimation Model VIP - ventilated improved pit latrine GOVERNMENT OF MALAWI FISCAL YEAR Anril 1 tn " reh t1  FOR OFFICIAL USE ONLY Page No. VOLUME II:- TECHNICAL ANNEXES Annex 1: Methodological Note on Estimation of Soil Erosion Rate .... ......... I Annex 2: Autoregressive Trend Model of Relative Producer Price Stability .... .... 22 Annex 3: Methodological Note on Estima.ion of Deforestation Rate and Value ... ... 26 Annex 4: Methodological Note on Estimation of Water Extraction Rate .... ...... 62 Annex 5: Methodological Note on Estimation of Average Incremental Costs in Water . 70 Annex 6: Methodological Note on Estimation of Valuation of Protected Land ... ... 85 Annex 7: Inventory of Malawi Environmental Legislation ................... 95 Annex 8: Econometric Model of Private Sector Price Responsiveness in Afforestation 115 This report is based on the findings of a mission that visited Malawi in August 1990. Mission members were Richard Scobey (Mission Leader, AF6CO), Ben Kamugasha (AFTEN), Sven Jacobi (RWSGEA), Edward Barbier, Joshua Bishop, J1janne Burgess, Michael Colby, Moshe Finkel, William Hyde, Juan Seve, and Jane Walker (Consultants). Ben Kasomekera (Bunda College, Malawi) and Edward Laisi (Water Department, Malawi) also contributed background papers to the report. William Magrath (ASTEN) provided valuable comments as peer reviewer, Brigida Tuason (AF6CO) assisted in analytical work, and Georgette Johnson (AF6CO) provided secretarial support. This document has a restricted distribution and may be used by recipients only in the performance of their official duties. Its contents may not otherwise be disclosed without World Bank authorization.  Annex 1 Page 1 of 21 METHODOLOGICAL NOTE ON ESTIMATATION OF SOIL EROSION RATE I. Introduction 1. Soil fertility .ecline results from the leas of organic matter and chemical nutrients, through leaching and the removal of crops and residues, compaction and loss of soil structure, and physical erosion of top soil by rainfall. In this study we use the latter as a proxy for overall fertility decline. The justification for this simplification comes from studies showing that soil loss is a reliable predictor of changes in soil nutrient content, soil pH, and moisture retention (Lal 1981). In the following pages, we will use estimates of soil erosion to calculate expected annual crop yield losses, based on statistical relations experimentally derived in Nlgeria (Lal 1987). We further express yield losses in terms of foregone farm. income, to determine gross economic losses from land degradation, based on a simple model developed previously for Mali (Bishop, 1989). II. Rates of Land Degradation and Soil Erosion Existing Field Data 2. Data from field studies of fertility decline and soil loss in M4alawi are scanty. From the farmer's perspective, the most relevant measure of land degradation is yield decline. Results of continuous maize trials at Chitedze Research Station, from 1955 to 1963 and for six different treatments of crop residues, reveal a mean decline of 492 over eight years for unfertilized maize, or a 9.12 average annual decline during the period (Dept. of Agr. Annual Report for 1962/63, pub. 1965). A more recent depiction of yield decline for unfertilized local maize compares average yields for four ADDIs in 1957-62 versus 1985-87, revealing a mean total decline of 41? over the period, or an average annual decline of about 2? (Twyford, 1988). 3. Another measure of fertility decline is a decrease in organic matter and-plat nutrients under cultivation. Analysis of soil sample data from fertilizer trials carried out at Bvumbwe Agricultural Research Station, on land continuously cropped with tea over 25 years and with minimal application of fertilizer (45 kg N ha-' yr-1), revealed a 412 total decline in organic matter, a 38Z decline in total Nitrogen, and a 5? decline in total Phosphorus, relative to virgin land (Maida & t ~~~Chll$ma, 1981). 4. The meisure of land degradation employed in this analysis is physical soil loss, in tons per hectare. Se located five studies that reported soil erosion under various crop cover and land husbandry regimes in Malawi. The reported soil losses are not strictly  -2- Annex 1 Paae 2 of 2. comparable, due to widely varying plot sizes (from 1 - 170,000 mi). On tha average, however, annual soil loss under traditional cultivation (i.e. maize, weeded and ridged) is about 19 t/ha. Average annual rainfall recorded at the five stations was 950 mm, and the mean slope was 142. Predictive Models 5. The leading predictive model for soil erosion research is the Universal Sol.l Loss Estimation (USLE) model, developed in the U.S.A. (Wischmeier and Smith, 1978). Although widely tested and corroborated, some authors dispute the validity of the USLE model under tropical conditions (Stocking 1987). 6. Among many proposed alternative models is the Soil Loss Estimation Model for Southern Africa (SLEMSA), developed in Zimbabwe (Elwell, 1978; Elwell and Stocking 1982). SLEMSA was designed for use in countries with limited capacity to generate the physical data required by the USLE and other models. A preliminary evaluation of SLEMSA under Halawian conditions compared the predictions of the model to actual soil loss measured on experimental catchments near the Bvumbwe Agricultural Research Station (Mwendera 1988). The results were inconclusive from a statistical standpoint, due to insufficient data. 7. Recently a modified version of ax MSA was developed, again in Zimbabwe, for reconnaissance level evaP'- ,ion of erosion hazard (Stocking et al., 1988), The methodology is designed to make relative assessments of the risk of erosion over large areas, expressed in Erosion Hazard Units (EHU). The model uses precipitation data to estimate rainfall energy (E), which is combined with an index of soil erodibility to calculate an erosion hazard index (lb). The protection provided by vegetal cover is also incorporated, along with average slope (X). The authors stress that the model is not designed to predict soil losses in tons per hectare, since it fails to account for the depoaltion of eroded sediments within catchments. The technique was first applied in an Erosion Hazard Happing of Zimbabwe (Madhiri and Manyanza, 1989). Erosion Hazard MagRina of Malawi S. An evalu' of erosion hazard in Malawi was carried out by two members of tl Husbandry Branch of the Department of Agriculture (Khon. Ad Machira, 1987), using the methodology developed in Zimbabwe. The authors prepared a 10xlO km grid map of Malawi at 11,000,000 scale, which displays the mean erosion hazard (EHU) for 1,044 grid squares. The results are also presented in tabular form in an appendix to their draft report, with rainfall energy (E), erosion hazard index (ld)' vegetal cover ratio (C), mean slope (X) and ENU  -3- Annex 1 Page 3 of 21 listed for 1,048 grid squares. 1/ EHU values range from 0 to a maximum of 7,195, with a mean value of 328 (weighted by the estimated proportion of each grid square falling inside the boundaries of Malawi). Mean slope on all areas is 6.32. In their report the authors-present a simplified EHU map (scale 1:3,000,000), for which EHU scores have been converted into eight categories. For each category they further estimate expected annual soil loss in tons per hectare. 9. While recognizing the danger of exaggeration inherent in converting EHU into soil loss, we adopt the estimates of annual erosion made by Khonje and Machira in the analysis that follows. The reader is asked to consider the argument presented below as an illustration of the possible extent, distribution, and costs of land degradation, rather than as an exact representation. 10. The conversion rule used by Khonje and Machira is a step function, and ignores intermediate values within categories. We transform their rule into a general equation for converting EHU into expected soil loss, by simple regression analysis. The best fit was established with a set of three equations. A maximum soil loss rate of 50 t/ha/yr was assumed for all grid squares with EHU > 1000. For: 0 < EHU < 500 . . . . . . E - 1.968(EHU)04 (1) Adj. Rs = 0.976 T-statistic - 15.7 500 c EhU < 1000 . . . . . E - 30 + 0.02(EHU) (2) 1000 < MM . . . . . . . . . E - 50 (3) Land Use Data Base 11. General information on land use was derived from 1:1,000,000 maps provided by the Land Husbandry Branch, showing the limits of Districts, Rural Development Projects (RDP), Special ^rop Authorities (SCA), National Parks, Forest and Game Reserves. By tracing and overlaying all of these maps with the erosion hazard map of Khonje and Machira, and estimating the proportion of each EHU grid square lying within a particular administrative unit, we compiled a data base of 1,855 land use units. The mean surface area of the map units is about I/ Our copy of ft report was noomplete and lacked pans of the appendbL Moreover, 127 gd squares shown on the map and listed In the report do not share the sarne values. For this analysis we genwally use the values roported In the appendix, In preference to those on the map, except where the former are msng in our copy. We were able to reornstu mean slope values for rd squares missing In the report appendix, by exapoat from EHU values shown on the map.  -4- Annex 1 PaRe 4 of 21 51 kM2. For each unit we recorded six attributes, of which the first three are taken directly from Khonje and Machira: (i) grid coordinates, (ii) EHU score, (iii) mean slope (0.82, 2.62, 5.22, 9.02, or 13.52), (iv) estimated proportion of the grid square falling within the boundaries of Malawi, (v) estimated proportion of the grid square falling within a specific administrative area, (vi) the name of the specific administrative area. 12. The last of these attributes assigns each map unit one of 155 labels, corresponding to the RDP, district, special crop authority, game or forest reserve in which it lies. The data base thus generated should not be considered a definitive analysis of land use in Malawi. It is --ough that our estimates of the surface area of major land use categories correspond more or less to previously published figures. Excluded Areas 13. The land use data base permits the distlnction of reserved areas, which are excluded from our analysis of the costs of soil erosion, on the assumption that most if not all of this land is uncultivated. We also assume that some unreserved swampy land is either not cultivated or receives significant deposits of eroded sediment (i.e. no net soil loss). Finally, the very steepest slopes are assumed uncultivated. 14. We consulted three sources which give estimatee of the total area of 3uncultivable* swamps and steep slopes in Malawi: The National Physical Development Plan (1986), Brunt, Mitchell and Zimmerman (FAO 1984), and Stobbs and Jeffers (1985). Their figures were used to guide the selection of rules for excluding certain grid squares from our analysis. In the end we define and exclude as uncultivated swampy land all those grid squares with mean slope equal to 0.81 and EHU scores below 8. Uncultivated steep slopes were defined as all squares with mean slope equal to 13.5Z. The latter rule results in an excluded area somewhat smaller than other estimates of land with slopes over 121, which are considered unarable by the Land Husbandry Branch, but are in fact often cultivated. 15. With these rules of exclusion and the data base described above, we calculate the total surface of each administrative area, distinguishing uncultivated reserves, swampy land and steep slopes. Gross arable land is what remains and is the area assumed subject to crop losses arising from erosion. A full tabulation of our results versus other estimates is given in Appendix 1.  -5- Annex 1 Paae S o_' 2. Estimated Soil Loss 16. For each mar unit not excluded, we estimate the mean annual rate of soil erosion (t/ha) based on the equations derived from Khonje and Machira. Summing across map units, we can calculate the mean rate of soil loss by RDP and by District on gross arable land (weightsd by the surface area o_ each affected map unit). Detailed results are presented in Appendix 2. For Malawi as a whole, we estimate a mean current rate of soil erosion of 20 t/ha/yr on gross arable land. Recalling that we assume a maximum rate of 50 t/ha/yr on any map unit, the highest estimates of erosion or. arable land occur in Nkhata Bay District (43 t/ha), Chirauzulu District (39 t/ha), and Dowa Hills RDP (36 tlha). The minimum estimate (10 t/ha) occurs in Balaka and Kawinga RDP's. II. Costs of Soil Erosion Off-Site and On-Site Costs 17. Soil erosion can impose economic costs in two fundamental ways: through on-site reductions in crop productivity and farm income, and through off-site effects resulting from increased runoff, siltation, and water flow irregularities. The latter may affect the quality and reliability of urban water supply, the life span of hydro-electric power facilities, dredging costs for irrigation schemes, and fisheries productivity, 18. Data to estimate the off-site costs of erosion in Malawi are unavailable, but a number of factors suggest that these costs may be low. Ground water is plentiful in most areas, while filtering costs are a very small fraction of water supply costs. Malawi also has little hydro-electric and irrigation infrastructure. Fisheries may be more seriously affected, but the data needed to determine costs imposed by eroded sediments are not available. On the other hand, the size of the agricultural sector, combined with apparent market failures which can lead farmers to deplete top soil at an inefficient rate, suggest that on-site costs may be quite high. 19. The on-site costs of soil erosion may be captured and evaluated in a number of ways: in terms of reduced crop yields, the replacement cost of eroded plant nutrients, or r-ost directly in terms of the reduced resale or rental values of agricultural land. The latter would be the most direct reflection of a reduction in the discounted present value of the income generating potential of a particular plot of land, relative to alternative investments. Agricultural land markets in Malawi hardly exist, however, and there is no data. 20. Evaluation of the replacement cost of eroded nutrients is an approach that has been applied in Zimbabwe (Stocking, 1986). The method is based on a set of statistical relations linking soil loss to nutrient  -6- Annex 1 Page 6 of 21 losses, derived from multi-year data from across Zimbabwe. Financial analysis estimated annual losses of Nitrogen and Phosphorus worth US$150 million on arable land alone (30,000 km2). As pointed out in the report, these losses understate the true cost of erosion, sa they do not account for losses of soil organic matter, which can affect soil structure, water-holding capacity and nutrient availability. 2/ 21. Evaluation of yield losses has the benefit of capturing all of the on-site effects of soil erosion on soil fertility and thus on farm productivity. Yields reflect not only the presence of major nutrients, but many other attributes of soil fertility. The problem is to find a link between soil loss and crop yields. Existing Data on the Erosion-Yield Relation 22. There are few data linking crop yields to soil erosion in Malawi. Experiments at Nkhande Research Station on a 442 slope show yields under traditional cultivation falling 622 between 1985/86 and 1986/87, from 815 to 308 kg/ha, where annual soil loss was 76 t/ha. On an adjoining alley-cropped plot, soil loss averaged only 3.7 t/ha/yr, and yields rose over the same period from 2,050 to 2,700 kg/ha (Chome, 1989). While tho example is illustrative of the effects of soil loss, it cannot provide a general rule for estimating yield losses arising from erosion. Predictive Models 23. For this analysis we use a simple model to predict crop yield losses from estimated rates of erosion. The model is a generalized version of statistizal relations between crop yields and soil loss, which were estimated using data from side-by-side, multi-year trials carried out in Nigeria at the International Institute for Tropical Agriculture (Lal, 1987). The IITA equations predict the effects of cumulative natural soil loss, in tons per hectare, on yields of maize and cowpea, relative to yields on newly cleared (uneroded plots). They are of the form: Y Q C-O (4) wheres Y = ;ield in tons per hectare C - yield on uneroded (newly cleared) land p - coefficient varying by crop and slope x - cumulative soil loss (t/ha) gy We do not use this approach for the present analysis, alhough data from the Soi Erosion Research Project at Bvumbwe would permit an estimation of the relation between soil loss and nutini loss under Malawi condons (Amphlett, 1988).  -7- Annex 1 Page 7 of 21 24. Lal estimated eight equations, one for each crop and four slopes (1, 5, 10, and 15Z). The estimated coefficients (p) varied between 0.002 and 0.036 for cowpea, and between 0.003 and 0.017 for maize, with the greatest losses recorded on gentle slopes. All but one of the Beta coefficients are significant to 5Z.. Correlation coefficients (r) were between 0.66 and 0.99. 25. Agricultural conditions in Malawi and southwestern Nigeria are of course not comparable, but we can assume that the general form of the crop response to soil erosion will be similar. Note that the specification of the equation implies a constant elasticity of yield with respect to cumulative erosion. In other words, the percentage yield loss in the first year is exactly the same as the percentage loss in the tenth year, assuming a constant rate of erosion. It is enough to know the annual rate of soil loss and mean current yields to estimate current crop losses. We thus drop the constant (C) and calculate a percentage yield decline for every level of soil erosion. To account for the uncertain sensitivity of crop yields to soil loss under Malawi conditions, we use a range of coefficients (p) and estimate a wide range of yield losses. The coefficients tested here are p 0.002, 0.004, 0.006, 0.010, and 0.015. 26. We apply the equation described above to every map unit in the data base, excluding reserved and unarable land. Results by RDP and by District are presented in Annex 2. For Malawi as a whole, estimated mean annual yield losses lie between 42 and 252, for p equals 0.002 and 0.015 respectively. Maximum yield loss lies between 102 and 53X, for noil loss of 50 t/ha/yr. Crop Budgets 27. To value yield losses arising from soil erosion, we use crop budgets provided by the PI:nning Division of the Ministry of Agriculture (MOA). We assume that farmers will reduce the use of variable inputs in the same proportion as gross revenues decline. Applying the estimated percentage yield loss directly to gross crop margins, we obtain an estimate of economic losses arising from erosion. Gross muArgins are defined as gross revenue per hectare (mean yield multililied by official ADMARC prices), less the total cost per hectare of using all recommended inputs (seed, fertilizer, and pesticides), but not including labour inputs. In other words, intermediate inputs are excluded, leaving value added. Labour is assumed here to be a fixed cost of production. An 41ternative financial analysis from the farmer's point of view applies estimated percentage yield losses to net farm income, on the assumption that labour is not fixed. 28. Gross margins for twelve crops or crop mixtures are taken from current MOA data tables, using values for 1989/90. Where values are not available for specific crops, we use figures taken from the Agro- economic Survey (AES) Report No. 55 (1987). AES gross margins are  Annex 1 Pame 8 of 21 inflated from 1984/85 to 1989/90, using the growth rate of gross margins for the same or similar crops, as reported in the MOA data tables. AES data also includes net farm income, which re simLlarly inflate to 1989/90. Both gross margins and net income as used here are reported in Appendix 3. Cropping Pattern 29. Estimates of the total surface area cultivated each year vary widely among different sources. The baseline figures used &re from the 1987/88 3rd Crop Estimate, prepared by the Pl_nning Division (MOA). These give the total cultivated surface area, by crop and by Agricultural Development Division (ADD). According to this source, the total cultivated area of Malawi in the 1987/88 crop year was 18,218 km2. 30. Our calculations also account for the relative importance of different crops in each ADD. Data on cropping patterns are taken from the Annual Survey of Agriculture (ASA) for 1980/81 to 1985/86, as reported by the World Bank (NRDP, 1989), combined with data from the 1987/88 ASA and the AES Report No. 55. Note that unfertilized 'local' (indigenous) maize accounts for about 37? of the total cultivated surface area of Malawi, while all maize varieties taken together account for 69Z of the cultivated surface. Major cash crops, including cotton, tobacco, coffee and tea only account for about 5 of total cultivated area. Detail for each of sixteen crops, by ADD, is presented in Appendix 3. 31. By combining information on gross margins and cropping patterns we estimate the mean contribution of each crop to average gross margins per hectare on cultivated land. Rice is excluded from the analysis, on the assumption that it is grown on relatively flat lowland soils, which are not subject to serious soil erosion. We also exclude root crops, despite their importance in cropping systems, for lack of budgetary data. 32. Summing the contributions of each crop in each ADD, we calculate composite gross margins fer all crops taken together, in Kwacha per hectare. For Malawi as a whole, composite gross margins are estimated at 249 K/ha in 1989/90 (weighted by the baseline estimate of cultivated surface in each ADD). 3/ Again maize accounts for about 702 of this figure. The highest value is in Lilongwe ADD (302 K/ha), while the lowest is in Karonga ADD (161 K/ha). Detailed results by crop and by ADD are presented in Appendix 4. yI Multiplying composite gss margins by the baseline cultiaed sufac aea, we obtain a value of 453 million Kwacha, whih may be considered a rough estimate of dt contuton of dth crops to total 1988 agrkultural GDP (1.224 bilion IQ.  Annex 1 Page 9 of 21 Economic Losses: Baseline Results 33. Finally we apply estimated percentage yield losses, for various values of p, to composite gross margins. The resul_ is an estimate of average annual losses due to erosion, in Kwacha per hectare. For Malawi as a whole, estimated annual losses are in the range of 10 - 64 K/ha (for P - 0.002 and 0.015, respectively), or between 4? and 262 of composite gross margins, excluding rice and root crops. The greatest economic losses occur in Lilongwe ADD (13 - 81 K/ha, for p - 0.0C2 and 0.015), due to the relatively high gross margins obtained there. 34. Multiplving mean annual losses per hectare by baseline estimates of cultivated area, we calculate total losses by ADD, for various values of p. Summing across ADD's, we arrive at rough estimate of the annual loss of agricu..tural income arising from soil erosion. For 0 - 0.002 and p - 0.015, we obtain roughly 18 and 116 million Kwacha, respectively. To put these numbers in perspective, they correspond to 0.52 and 3.12 of Malawi's gross domestic product (GDP) in 1988. This is the range within which we would expect the true value of current foregone agricultural income to fall. Results by ADD are presented in Appendix 4. Further ManiDulations .1- Hiaher Estimates of-Cropped Area. Some assessments of total cultivated area by ADD are considerably higher than the baseline 3rd crop estimates obtained from the Ministry of Agriculture. Land use data from Mzuzu, Kasungu, Lilongwe, Blantyre and Ngabu ADD's suggest cultivated surface areas up to twice those reported in baseline estimates. Using these higher values where available, we obtain a total cultivated surface area of at least 25,556 km'. Aggregate income losses are correspondingly higher, ranging between 0.7Z and 4.52 of 1988 GDP. Detailed results by ADD and for different values of p are contained in Appendix 5. 36. Financial Anal2sis. Farmers will tend to define erosion losses more narrowly, in terms of reduced net revenues (i.e. farm income net of all inputs including labour). Data on net revenues for various crops is provided by AES Report No. 55 (1987). We assume that farmers will adjust labour and other inputs in the same degree as yields decline, and thus apply percentage yield losses directly to composite nst revenues, which are calculated in the same manner as composite gross margins. The resulting estimates of annual financial losses range from 5 to 33 K/ha, for Malawi as a whole, or between 42 and 262 of composite net farm income. Detailed results are presented in Appendix 5. 37. Recurrent losses. Soil eroston in one year has an effect on yields in future years as well, as soil fertility declines absolutely. For simplification we may assume that the nominal loss in the baseline year is repeated in subsequent years. The present value of current and  - 10 - Annex I Pate 10 of 21 discounted future losses arising from one year of average soil loss is thus calculated as the sum of a geometric series, which simplifies as: n+l -a 1 a ) (5) where: L- =NPV current and future losses L,= current one-year loss a l/l+r n time horizon (years) r D discount rate 38. The choice of a rate of time preference for discounting future income losses is not obvious. From a public policy perspective, a low rate seems appropriate, since society can spread risk more effectively than private individuals. To suggest the social rate of time preference, we adopt a low discount rate of 52 per year. We assume a ten year planning horizon, although the scarcity of arable land in Malawi and the increasing rarity of fallowing could easily justify a longer period. 39. When we add the impact of current erosion on future yields, the range of estimated field level and aggregate losses for Malawi as a whole rise dramatically. With a 52 discount rate and a ten year planning horizon, estimated losses increase more than eight-foldl Using composite gross margins, we thus obtain field level losses between 88 and 556 KRha for every year of soil loss, or between 352 and 2242 of composite (annual) gross margins (p - 0.002 to 0.015). Estimated aggregate losses based on these figures are equivalent to 42 to 272 of 1988 GDP. Detailed results of capitalizing estimated gross margin and net revenue losses are presented in Appendix 4. 40. Private rates of time preference will generally be somewhat higher than our estimate for society as a whole. Evidence from studies of the informal credit sector in Malawi suggest private rates of interest as high as 50 to 1002 per year. While interest rates are not necessarily an accurate reflection of time preference, we can see from equation (5) that as the discount rate (r) becomes large, L, will tend to approach L,. In other words, smallholder farmers will tend to ignore all but current yield losses arising from soil erosion.  - 12. - Annex I Paas 11 of 21 APEDZ I LAND tt DATA Table 1.1 KAROOA ND tUS AA CANED TOTAL NAT PARtB COMBINE LWREBER TOTAL TOTAL SETTLE DASOS STEEP SaA,S A RDp/OI87RICT & SOWEESURFAACE & G,R. a.R. /F.R. "LPACE ARA8LE CUL-T: A INK1RS L SWAM4PS SPEB SLOPES KARU9 ROP/DISTRICT: OUR ESTIMATE 8.870 880 1,119 2.20 960 0 1,800 1,30a MOA/BA3.INE 1.168 184 N.P.D.P. 8.868 880 409 2,680 1,070 208 28 2,0O1 CI4MTPA RDP/OIMIICTz MA ESTIMATE 4,219 621 760 8.460 921 68 2.484 2,809 MCA/BASNELt .,88o 124 N.P.D.P. 4,290 760 1,005 8.268 1,124 16o 27 2,841 . ~~~TOTAL KADD-A 8 OUR ESTIMDTE 7.898 1,171 1,8679 8720 1,881 6 8,788 8,88 MGA/SA8*NIE 2,2 an 0a N.P.D.P. 7,e4J 1,1210 1,494 B,lISl 2,197 88 48 7STos a JgFER 7,681 .8578 478 84 1o0 491 6s MOA Srd Crep 87/88 668 Table 1.2 MDWJ LAD use DATA TOTAL NAT PARKS C01NED Lt9UV6 TOTAL TOTAL SErTLE DAos STEP SWAMPS A RDP/DSTRIC A SWES SURPACE A O.R. O.R./P.R. S04PAC* ARASLE CULT. A IN14AS L 8SWA8 SLOPES SLOW STH MZIMBA 00P: OM ESTMTE 8,4185 0 64 2,861 1 ,41 130 490 620 MtA/BASELSNE 8.811 848 2,968 2,092 8sa 106 775 8e8 N.P.D.P. IMZIIA 8 a60 2,144 7s6 HAOO/CATCHENT 3,811 0 811 2,970 190 2284 1i 497 80 CENITRAL MZIA FOP: tR ESrMATE 8,92 0 11a 8,612 ,162 180 800 480 MCA/BASELNE 8 926 118 s8eos 8,298 842 282 288 808 N.P.D.P./MZIMBA S 846 2 907 1 994 "DOO/cATHMENT 8,926 0 118 8,606 8,198 8,488 16 28 278 810 MM ESTDIATE 8.479 486 804 2,48 2,848 0 640 640 M.P.D.P.flqZIPe 8,2241,7 e4fl10 DISTRlcrT 0* ESTIMATE 10, F0 484 1,888 9069 7,449 g0o 1,80 1,610 N.P.0.P. 10,480 404 642 988 6 724 1,078 102 4,111 sT O 0A J 10e,029 9.6e8 1,688 9S4 871 RJ884I DISTICr: OUR ESTIMATE 4,498 2,:28 2,928 2,.128 86 1O0 1.7U5 1,68 N.P.D.P. 4.787 2,a8 1a,s 1 .210 760 471 28 1,480 sT708s A JE 4,47' 4,249 107 28 1 'a 218 o0* EsTAE 7 978 2.70a 2 8a" 8, 11 2.718 100 2.SO 2,408 MOA/ELINE 7,81 82024 4.268 649 211 170 a 8,989 KZAW/CATQENT 7,812 2,812 21891 4.901 2,218 8.281 1N 469 1,878 A,844 NMATA SVY P/DIST.: wa ESTIMATE 4,18 0 1,188 8, a060 1.080 0 912 0 2 081 M" 8L11 4,427 1.064 5,848 1.224 118 129 1,991 2,120 $m/C"TCHmmof #442 0 1,198 8.301 8 41 1.689 44 18 .8 I,ms N.P.O.P. 4,088 0 1,804 2,784 480 S88 27 1.698 STOOlS A J 4.879 4,27 180 as 64 68 147 TOTAL MZW Z80: an EfTMTE 19 418 21709 5.061 14 .81 86 no0 8,2 8, 16,976 4,574 14,402 7,485 1,10 68 0789 7,444 MUDD/2C^MT-ENT e19.478 2 ,12 4,888 14,941 6',S0 10.660 220 988 4,a11 8,08' N.P.D.P. 10,185 21,49 4.807 14,888 7 2,t 182 7,448 STOS a JEFS 1868s 16,187 1,98 o 1 806 9a8 MCA 8sd Cee 87/68 1,417  - 12 - Anmex 1 Page 12 of 21 Table 1.9 KASNOU WLAN USE DATA TOTAL MAT PARKS COWItNED UWESS TOTAL TOTAL SErTLE DAM46O STEEP SWAMPS A ROP/DISTRICT A SOUKES SURFACE A O.R. C.R./P.R. URFACE ARA" CULT. A INiR>A A SWAMPS SLOPES SLOPES 44CH114.1 6DP/0ISTRIC'T: MA* ESTIMATE 3.161 0 230 2,928 2,064 627 32 889 MOA/BAU LINE 3.34B 0 214 3,132 2.225 1.187 388 166 740 N.P.D.P. 3.388 0 192 3,164 2.066 1.361 42 956 KALOOAND USE 82 3 ,03 2.007 130 Sf 312 STOOS A JEFFERS 3.217 8,090 790 63 363 25 368 OUR ESTIMATE 1 696 0 80 1.663 168 10 0 10 MOA/6ASELINE 1,747 0 23 1.724 1.341 699 130 ISO 239 KADo/LAW USE 82 1,490 1.014 67 200 IiOA EAST 80DP: OkR ESTIMTE 1,240 0 58 1163 470 0 713 715 : DMA/BASELI4N 1.366 0 46 1.31 M20 498 302 128 480 KADD/LAND USE 62 1,428 990 8 37 DOWA DISTRICT: 0M ESTDUATE 2 720 0 s 2.65 1,910 10 71 723 M.P.D.P. 2.a9 0 4S 2,948 2,226 1.217 64 e31 ;~~~~~ -- --- - ----------- ----- ----- - --------- - - -- -- -- -- -- -- -- -- -- -- -- -- -- - - - NTCHSSS DISTRICT: OUR ESTIMATE 1.965 a 210 1,783 1,240 0 51S 615 N.P.D.P. 1.656 0 97 1,U06 n2S 478 1 767 STO8 A JEF