Key Issues: Carbon Fertilization, Irrigation, and Trade

Transcription

1 3 Key Issues: Carbon Fertlzaton, Irrgaton, and Trade Before proceedng to the man estmates of ths study, t s mportant to hghlght three major ssues. The frst s carbon fertlzaton. The estmates developed n ths study depend crucally on the yeld enhancement assumed for ths effect. As set forth n ths chapter, recent scentfc studes usng open-feld rather than laboratory condtons fnd a consderably lower enhancement than often used n past studes. Accordngly, ths chapter consders these recent estmates to develop an ndependent central carbon fertlzaton effect for use n the estmates of ths study. Ths carbon fertlzaton effect s then mposed on the wthout carbon fertlzaton results from the agrcultural mpact models appled to obtan the estmates ncludng carbon fertlzaton. The second ssue s rrgaton. Ths chapter revews the controversy on whether model estmates have adequately taken rrgaton nto account. There s stll consderable room for doubt that they have done so. The estmates n ths study, however, do not attempt to quantfy any correspondng correcton. The thrd ssue s whether to ncorporate feedback from nternatonal trade when examnng the mpact of global warmng on agrculture. Ths chapter sets forth the reasons why such effects are not ncorporated n the country-specfc mpact estmates of ths study. Carbon Fertlzaton The extent to whch carbon fertlzaton could allevate any adverse effects of global warmng on agrculture has been a central ssue n analyss of 23

2 the severty of these effects. Carbon doxde s an nput n photosynthess, whch uses solar energy to combne water and carbon doxde to produce carbohydrates, wth oxygen as a waste product. 1 In addton, hgher atmospherc concentratons of carbon doxde reduce plants stomatal (pore) openngs and hence the loss of water to respraton. So-called C3 crops, whch nclude rce, wheat, soybeans, fne grans, legumes, and most trees, beneft substantally from addtonal atmospherc carbon doxde. Benefts for C4 crops, whch nclude maze, mllet, sorghum, and sugarcane, are much more lmted. 2 Recent research based on experments wth the free ar concentraton enrchment (FACE) method suggests that past estmates of the carbon fertlzaton effect have been substantally overstated as a consequence of relyng on studes made wthn chambers at small scales rather than feld crops under fully-open-ar condtons at an agronomc scale. Thus, Long et al. (2005, 1, 5) fnd that wth carbon doxde elevated to 550 to 575 parts per mllon (ppm), the FACE experments show the yeld ncrease s 11% for C3 crops and 7% for all fve major food crops, whch s onethrd to one-quarter of the drect effect of CO 2 modelled n the recent assessment for Europe and the USA by Darwn & Kennedy (2000). In a more recent study, Long et al. (2006) report that FACE studes ndcate that at 550 ppm carbon doxde concentraton, yeld ncreases amount to 13 percent for wheat n contrast to 31 percent n laboratory studes, 14 percent nstead of 32 percent for soybeans, and 0 percent nstead of 18 percent for C4 crops. Among the major crops, C3 speces account for roughly three-fourths and C4 for one-fourth of total value. 3 If the central C3 ncrement s set at 12 percent, consderng the two Long et al. studes, and a 1. Ths process occurs n two stages. In the frst, a lght-dependent reacton, the pgment chlorophyll absorbs lght and loses an electron, whch becomes stored n the hgh-energy molecules NADPH and ATP. In the second, a lght-ndependent reacton, these hgh-energy molecules are used along wth the enzyme RuBsCO to capture carbon doxde from the atmosphere n what s called the Calvn cycle. 2. In C3 crops RuBsCO s located n mesophyll cells, whch are n contact wth the atmosphere through stomatal pores n the epderms. In these cells, RuBsCO s not CO 2 saturated n today s atmosphere.... In contrast, n C4 crops... RuBsCO s localzed to bundle sheath cells n whch CO 2 s concentrated to three to sx tmes atmospherc [levels. Ths s] suffcent to saturate RuBsCO and n theory would prevent any ncrease n CO 2 uptake wth rsng [CO 2 ] (Long et al. 2006, 1918). However, these crops may also beneft ndrectly from ncreased effcency n water use as a consequence of reduced stomatal conductance wth rsng carbon doxde. 3. Global producton value crca 2004 stood at the followng estmated levels: wheat, $94 bllon; rce, $120 bllon; soybeans, $49 bllon; cotton, $23 bllon, or a total of $286 bllon for the four major C3 crops; and at $68 bllon for maze, $25 bllon for sugarcane, and $6 bllon for sorghum, or a total of $99 bllon for the three major C4 crops. These estmates are compled from USDA (2005, 2006), IMF (2006), UN FAOSTAT database, and Federal Regster (2006). It s assumed that the sugar output yeld of sugarcane s 0.063, the rato for Brazl, and the Phlppnes prce for sugar s appled. 24 GLOBAL WARMING AND AGRICULTURE

3 modest allowance of 3 percent yeld ncrease for C4 crops s made, then the weghted average ncrement n yeld from carbon fertlzaton would be 9 percent at 550 ppm. Ths study examnes the perod At the mdpont of 2085, the central scenaro used n ths study scenaro A2 of the Specal Report on Emssons Scenaros (SRES) from the Intergovernmental Panel on Clmate Change (IPCC) places atmospherc carbon doxde concentraton at 735 ppm (IPCC 2001a, 807). The carbon fertlzaton effect rses less than lnearly wth atmospherc carbon concentratons (Long et al. 2006, Mendelsohn and Schlesnger 1999). If Mendelsohn and Schlesnger (1999) s followed and the relatonshp s specfed as logarthmc, then at 735 ppm the effect should be about two-thrds larger than at 550 ppm. 4 On ths bass, the central estmate of the carbon fertlzaton effect by the 2080s s set n ths study at a 15 percent ncrease n yeld. Ths mpact s consderably smaller than that assumed n some past studes. 5 Two past studes n partcular are of relevance to ths study: Mendelsohn and Schlesnger (1999), or MS; and Mendelsohn, Morrson, Schlesnger, and Andronova (2000), or MMSA. Usng an atmospherc concentraton of 735 ppm of carbon doxde by the 2080s, and applyng the future world average temperature and precptaton for land weghted by farmland area 16.2 C and 2.44 mm per day (see table 4.3 n chapter 4) the MS reduced form equaton for output per hectare gves an estmate of $333.2 wthout carbon fertlzaton and $376.6 wth carbon fertlzaton, an ncrease of 13 percent. 6 Applyng the MS Rcardan functon gves correspondng estmates of land rental equvalent of $34 per hectare wthout carbon fertlzaton and $45.9 wth carbon fertlzaton, an ncrease of 32.1 percent. 7 As dscussed n chapter 5, for the Rcardan estmates t s necessary to translate the percent change n land rental equvalent nto corre- 4. Wth the present concentraton at 350 ppm, the typcal 550 ppm concentratons are a rato of 1.57 to today s concentraton, and a future concentraton of 735 ppm would be 2.1 tmes today s concentraton. The rato of the logarthm of the latter to that of the former s 1.64 to Note that Tubello et al. (2007) have argued that Long et al. (2006) overstate the dfference between FACE and non-face expermental results and contend that n any event the prncpal crop models have appled much more conservatve carbon fertlzaton than those cted by Long et al. For the purposes of the present study, the most mportant pont n ths debate s that the central estmate used here, 15 percent yeld enhancement at 735 ppm aganst a 350 ppm base, s fully consstent wth the preferred crop model cted n Tubello et al. (2007). Namely, the agroecologcal zone model cted n table 2 of Tubello et al. (2007) ndcates that a rse from 350 to 735 ppm would boost yelds by 16 percent for wheat and rce, 21 percent for soybeans, and 7 percent for maze. Applyng the correspondng world output value shares, the weghted ncrease would be 14.8 percent. 6. See equaton (5.1) n chapter See equaton (5.2) n chapter 5. CARBON FERTILIZATION, IRRIGATION, AND TRADE 25

4 spondng potental output changes, whch are about half as large. 8 When ths translaton s done, the 32 percent MS Rcardan carbon fertlzaton for land rental equvalent represents an output mpact on the order of 16 percent. For both the MS reduced form and Rcardan functons, then, the carbon fertlzaton effect s relatvely smlar to the 15 percent used n ths study (for 735 ppm). In contrast, n the subsequent MMSA study, the verson of the MS model used to arrve at global (rather than just US) estmates, the exercse just outlned generates a Rcardan model ncrease of land rental equvalent from $34 per hectare to $49.6 per hectare, an ncrease of 45.9 percent. Agan applyng a global rato of about half, carbon fertlzaton as estmated n MMSA would boost output potental by about 23 percent, whch s consderably larger than the 15 percent used n ths study. The MMSA functon explctly ncreased the carbon fertlzaton parameter used n the MS equaton, but t would appear that ths ncrease resulted n a sgnfcant overstatement of carbon fertlzaton. 9 The Irrgaton Queston A persstent queston about the Rcardan statstcal estmates of how agrculture responds to changng clmate has been whether they have adequately taken account of rrgaton. One ssue s whether benefts attrbuted to warmer clmates are overstated because n fact these benefts reflect hgh values of land and output per hectare attrbutable nstead to rrgaton combned wth the fact that there s a hgher ncdence of rrgaton n warmer regons. Another ssue s whether clmate mpact projectons usng these models address the avalablty of water for rrgaton. Evapotranspraton (the combned loss of mosture from sol through evaporaton and plants through stomatal transpraton) ncreases wth temperature. The need for rrgaton rses as condtons become drer. It rses as a functon of the dfference between evapotranspraton and precptaton. Because global warmng wll ncrease both temperature and precptaton, the mplcatons for sol mosture and the need for rrgaton depend on the outcome of the race between rsng temperature and rsng precptaton. An extremely smple test for the Unted States shows the ncdence of rrgaton s postvely related to temperature and negatvely related to 8. The ratos of net revenue per hectare to output per hectare used n chapter 5 range from a low of about 40 percent n the Unted States to a hgh of 78 percent n Afrca. Ths rato s appled to the percent change n land rental equvalent to obtan the correspondng percent change to be expected n output potental. 9. The MMSA Rcardan functon s smlar to equaton (5.2) n chapter 5 (the MS functon) but changes the coeffcent on the logarthm of the rato of carbon concentraton to today s 350 ppm from 480 to 687 (Mendelsohn et al. 2000, 559). 26 GLOBAL WARMING AND AGRICULTURE

5 precptaton. Usng state data for agrculture and state captal data for temperature and precptaton, fgure 3.1a shows the relatonshp across US states between the rato of rrgated crop area to harvested crop area (percent) and annual average daly temperature ( C). Fgure 3.1b shows the same ncdence of rrgaton as related to average annual precptaton (mm per year). 10 Broadly the scatter dagrams show hgher ncdence of rrgaton for hgher temperatures and lower ncdence of rrgaton wth hgher precptaton. There are three states that are outlers to the temperature trendlne: Nevada (rrgaton ncdence at 136 percent of harvested cropland), Utah (114 percent), and Wyomng (119 percent). 11 All three have extremely hgh rrgaton ncdence but relatvely low temperatures. The anomaly s explaned by the low precptaton n all three, as they become the upper-left observatons n fgure 3.1b. 12 Many of the states have low rrgaton ncdence, but some have extremely hgh ncdence, as ndcated by the dfference between medan (8.2 percent) and average rrgaton (29.5 percent). A smple statstcal regresson for these data shows the followng, wth t-statstcs n parentheses: Z = T P; adj. R 2 = 0.21 (1.57) (3.22) (3.29) Although the degree of explanaton s moderate at only about 20 percent, the coeffcents on temperature (T) and precptaton (P) are hghly sgnfcant. To antcpate the followng clmate analyss, for the Unted States the estmates n ths study ndcate that baselne global warmng by the 2080s would cause the farmland-weghted averages for annual temperatures to rse by 5.4 C and the correspondng averages for precptaton to fall by 4.3 mm per year. 13 If these changes are appled to the smple regresson equaton, the ncdence of rrgaton would need to rse by 20.3 percentage ponts as a consequence of clmate change. The ncrease would be almost entrely from hgher temperature; the slght declne n precptaton would have lttle effect, except n the sense that the falure of precptaton to rse would mean that the race between temperature and precptaton would be won hands down by temperature. 10. Temperature and precptaton are from NOAA (2007). Irrgated and harvested crop land are from USDA (2004). 11. Greater than 100 percent ncdence mples that some rrgated land s used for pasture rather than crops and/or that some rrgated land s left fallow. 12. Note also that Carson Cty at 4,687 feet elevaton and average annual temperature of 10.7 C may not be as representatve of statewde condtons as s the case for most captals. Thus, also n Nevada, Las Vegas at 2,028 feet has average annual temperature of 20.1 C. 13. Calculated from table 4.2 and appendx table E.1. CARBON FERTILIZATION, IRRIGATION, AND TRADE 27

6 Fgure 3.1a Irrgaton and temperature for US states rrgated crop area as percent of harvested crop area average annual daly temperature ( C) Fgure 3.1b Irrgaton and precptaton for US states rrgated crop area as percent of harvested crop area ,000 1,500 2,000 precptaton (mm per year) 28 GLOBAL WARMING AND AGRICULTURE

7 Vewed n ths way, the rrgaton ssue rases two questons for most model estmates. Frst, have they ncluded the costs of addtonal rrgaton, whch requres large captal outlays? Second, have they carefully consdered the avalablty of water for addtonal rrgaton? The broad answer to both questons would seem to be n the negatve, suggestng that the Rcardan models may well tend toward an optmstc bas regardng treatment of rrgaton. The semnal emprcal Rcardan functon for the Unted States s that estmated n Mendelsohn, Nordhaus, and Shaw (1994). In an early comment (Clne 1996), I argued that the applcaton of ther results to global warmng scenaros faced the problem that such an exercse mplctly assumed that water was nfntely avalable for rrgaton at the present prce, whereas there were strong grounds for concern about water scarcty and ncreased ncdence of droughts as a consequence of global warmng. In a subsequent comment, Darwn (1999) suggested that the Mendelsohn- Nordhaus-Shaw functon tself could contan a statstcal bas by falng to remove the nfluence of rrgaton on the measured relatonshp of productvty to temperature and precptaton (along the lnes just suggested). Quggn and Horowtz (1999) further crtczed the Mendelsohn- Nordhaus-Shaw functon by pontng out that ts quadratc term for October temperature had the wrong sgn (postve), ndcatng that there was no lmtng optmal temperature for that term. The two authors also usefully sharpened the argument on the Rcardan approach by pontng out that whereas some crop models lackng attenton to adaptaton mght be subject to the dumb farmer crtque, the Rcardan approach nstead mplctly assumes zero adjustment costs and therefore yelds a lowerbound estmate of the costs of clmate change (Quggn and Horowtz 1999, 1044). In response to the crtque of Darwn (1999) about possble rrgaton bas, Mendelsohn and Nordhaus (1999) reestmated ther model as follows. Frst they estmated an equaton for rrgaton as a functon of the clmate and control varables. Then they ncluded predcted rrgaton from ths equaton as an ndependent varable n an expanded clmate mpact Rcardan functon. They argued that t would be ncorrect to nclude rrgaton drectly (rather than predcted rrgaton) because of the endogenety of rrgaton to clmate. Then when they conducted ther clmate change mpact exercse usng the revsed Rcardan functon, they found that the effects were somewhat more rather than less favorable after removng the nfluence of rrgaton. 14 They concluded that concerns about rrgaton bas were not warranted. 14. The authors found that n the functon wthout rrgaton, a temperature ncrease of 2 C and precptaton ncrease of 8 percent would boost net revenue by 3.3 percent, whereas n ther revsed functon removng the nfluence of rrgaton, crop net revenue would rse by 10.4 percent. CARBON FERTILIZATION, IRRIGATION, AND TRADE 29

8 Ther equaton for ncdence of rrgaton has key nformaton n tself, however, that could nstead suggest concern about a possble substantal rse n the need for rrgaton n a hotter, drer clmate. If ther equaton s appled to ther suggested clmate scenaro ( 2 C temperature, 8 percent precptaton), the result s an estmated 19 percentage pont ncrease n the ncdence of rrgaton. 15 If the temperature ncrease were consderably larger and precptaton change neglgble or slghtly negatve, as suggested above for the 2080s baselne examned here, by mplcaton the expected ncrease n rrgaton would be much larger, usng the Mendelsohn- Nordhaus equaton. So once agan there are two key questons for ther analyss: Who would pay for the extra rrgaton, and would t be feasble gven possble water constrants? Moreover, ther concluson of bengn results turns crucally on the precptaton varable. Ther two-stage results boost the margnal effect of an extra 1 nch per month n precptaton from $123 per hectare to $218 per hectare. Ther nterpretaton s that once the nfluence of rrgaton s removed, precptaton s relatvely more mportant to agrcultural performance. But then ther large boost to precptaton n ther clmate change scenaro becomes the key to the favorable mpact, and as noted the set of clmate model estmates presented below shows a much less favorable precptaton change n the baselne by the 2080s. 16 More fundamentally, however, the Mendelsohn-Nordhaus reestmaton faled to escape the problem of the wrong sgn for a key quadratc term on temperature. Indeed, a closer nspecton of ther equaton shows that t has entrely mplausble estmates for hgh warmng as a result. In partcular, n ther formulaton the underlyng varables are temperature n degrees Fahrenhet mnus the average temperature, wth both lnear and quadratc terms on ths demeaned temperature varable. Ths yelds the followng structure: 15. Calculated from ther seasonal temperature and precptaton lnear and squared coeffcents appled to demeaned varables from the base US clmate from table 4.2, for the base, and ther specfed changes n temperature and precptaton. 16. Note further that the change n the temperature coeffcent n ther two-stage results s problematc. The margnal mpact of 1ºF swngs from $17 per hectare orgnally to $4 per hectare. If one accepts the noton that US agrculture on average s below optmal temperature, then ths margnal effect mght not be mplausble. But then the real queston becomes whether ther coeffcents on the squared terms for temperature are relable, because t s the nonlnear adverse effect of gong well beyond optmal temperature that s the concern. By the constructon of ther varables, whch are demeaned (subtract mean temperature from temperature and mean precptaton from precptaton), ther model unfortunately forces the nonlnear effects to be symmetrcal for both a declne and an ncrease n temperature. As noted above, recent studes suggest nstead an adverse asymmetry for temperature ncreases. Moreover, the mxture of postve and negatve coeffcents for the squared temperature terms across dfferent seasons means that ther functon s not strctly hll-shaped but questonably gves nonlnear postve gans to October temperatures, as noted by Darwn (1999). 30 GLOBAL WARMING AND AGRICULTURE

9 y= α+ β T + γ ( T) 2 where y s crop revenue per acre per year, s a constant term, s the seasonal month (January, Aprl, July, or October), and T s the ncrease n temperature (n degrees Fahrenhet) above the base perod averages. The level of base temperature tself does not appear because n the base perod the temperature term dsappears: Temperature s average temperature for the month, and the base demeaned varable s zero. For a clmate scenaro wth an ncrease n temperature specfed as T unformly across the four seasons, 17 the change n revenue per hectare s then smply: y= T β + ( T) 2 γ In the reestmated Rcardan functon n Mendelsohn and Nordhaus (1999), the sum of the lnear coeffcents on demeaned temperature s $4.10 per acre, and the sum of the quadratc coeffcents s $ So there s an unlmted rse n net revenue per hectare wth hgher temperatures. An extra 2 F boosts the net revenue output measure by about $14 per hectare. As the temperature ncrease doubles successvely to 4 F, 8 F, 16 F, and 32 F, the boost to output per hectare becomes respectvely $41, $130, $455, $1,688, and so forth. The clmate functon states lterally that f temperature rose to that on the sun (11,000 F), net revenue would rse by $121 mllon per hectare. In short, t volates both common sense and the underlyng hll-shaped Rcardan functon postulated by the authors. What one seems to be left wth n the reestmated Mendelsohn- Nordhaus analyss of rrgaton s one relable result and one faled result. The relable result s that rrgaton does ndeed rse for hotter and drer countes. The faled result s a Rcardan functon for the mpact of clmate on agrculture. The emprcal estmate should be rejected just as an emprcal estmate of an upward-slopng demand curve (hgher prce offered, larger volume purchased by consumers) should generally be rejected, regardless of the t-statstcs. On ths bass, the rrgaton ssue stands as follows: Frst, there should ndeed be concern that addtonal rrgaton wll be requred under global warmng. Second, there smply remans ambguty as to whether the Rcardan functons successfully elm- 17. As ndcated n appendx tables H.1 and H.2, the change n average temperature by for the US Lakes-Northeast regon, for example, s almost dentcal at 6.3 C for January, Aprl, and July and almost the same at 5.3 C for October. 18. The seasonal detal s as follows, for January, Aprl, July, and October, respectvely: lnear, 133, 91.1, 128, and 174; quadratc, 1.88, 4.66, 0.17, and 7.89 (Mendelsohn and Nordhaus 1999, 1054). CARBON FERTILIZATION, IRRIGATION, AND TRADE 31

10 nate any bas n estmate from rrgaton, because n the specfc test desgned for ths purpose Mendelsohn and Nordhaus nstead estmate a functon that must be rejected on frst prncples. 19 Trade as Moderator? Fnally, a crucal conceptual ssue s whether to examne the mpact of global warmng on agrculture wth or wthout ncorporatng nduced effects operatng through nternatonal trade. The estmates of ths study do not ncorporate trade feedbacks for the followng reasons. 20 Frst and foremost, there s a let them eat cake flavor to the noton that trade wll greatly reduce losses from global warmng. Poorer natons are most lkely to experence greater agrcultural losses. A focus on trade mplctly argues that these countres can lmt ther losses from global warmng by shftng to agrcultural mports rather than producng those products at home. The problem s that they may face dffcultes ncreasng export earnngs from other goods n order to pay for ther new food mport needs. Incorporaton of world trade moderaton of global warmng damage to agrculture should at the mnmum nclude correspondng estmates of the terms-of-trade losses of the poorer countres as they fnd t necessary to export addtonal volumes of (lkely) labor-ntensve manufactures n order to mport more food. Second, Clne (1992, appendx 3A) shows that n a closed system, whch s the case for the world as a whole, the welfare losses from a negatve shock to agrcultural yelds are at least as large n percentage terms as the percent declne n yelds. Bascally consumer surplus losses exceed pro- 19. Nor does the further work by Mendelsohn and Dnar (2003) appear to lay ths ssue to rest, because t asks a dfferent queston: whether farmers that have access to rrgaton water have hgher farm values (p. 331). Not surprsngly, t fnds that they do. But the study does not attempt to smulate the costs of addtonal rrgaton, or nvestgate the avalablty of water for the addtonal rrgaton, that could be necesstated by a hotter and drer (or hotter and only margnally wetter) clmate. 20. Note that although the regons for whch average yeld mpacts are reported n the crop model source used n ths study (Rosenzweg and Iglesas 2006) are defned for consstency wth one such trade model (the basc lnked system [BLS]), the yeld mpact estmates themselves are for the drect effect of clmate change wthout consderng such nduced effects (see table 5.7 n chapter 5). In general ncorporaton of nduced effects, whether domestc or from nternatonal trade, would be unlkely to change the drect yeld estmates by much. For example, an area experencng a negatve yeld shock from clmate change would be lkely to encounter a postve second-round yeld offset from the standpont of greater applcatons of fertlzer and other nonland nputs but a negatve second-round aggravaton from the ncorporaton of more margnal land. Trade would tend to moderate both effects, because less of the new shortfall of output would be resolved by hgher prces and nduced domestc output response; but ths trade moderaton would be of the second-round yeld effects, not of the frst-round drect clmate mpact. 32 GLOBAL WARMING AND AGRICULTURE

11 ducer surplus gans. 21 Reducton n global average yelds from clmate change cannot be offset by recourse to trade at the global level. Thrd, studes that focus on world agrcultural output change, rather than drect yeld mpact or ex ante mpact on agrcultural potental, tend to generate mpact estmates that are msleadngly small because they tend to report output change but not losses n net welfare after accountng for loss of consumer surplus. Demand for food s prce nelastc. As an llustraton, suppose demand were completely prce nelastc but yelds fell 50 percent. Output would have to rse back to the orgnal level at what could be enormous costs of addtonal nputs; yet a study reportng the output effect would fnd that there was no mpact whatsoever. Fourth, trade feedbacks are omtted n the present study n part because to nclude them would add an addtonal layer of hypothetcal and crcumstantal analyss to an already dffcult analyss focused on bophyscal effects. It s not even clear that there are partcularly meanngful medumterm agrcultural supply functons avalable on a multcountry bass n today s nternatonal economy, yet t would be necessary not only to dentfy them but also to project them for the dstant future. It s useful to recall that n 1973 the Unted States mposed an embargo on soybean exports n order to avod nflatonary effects of rsng prces; t s also the case that many natons are nclned to mpose agrcultural mport barrers n the name of food self-suffcency. Incorporatng probabltes of such dstortons would further complcate addng trade feedbacks to the analyss. In sum, for several reasons ncorporatng nduced effects based on a trade model could easly obscure rather than clarfy the central dagnoss of prospectve effects of unmtgated global warmng on world agrculture. 21. Consumer surplus s the amount of savng by consumers represented by the dfference between what they actually have to pay for the good and the amount they would be wllng to pay f necessary. Producer surplus s the correspondng dfference between what producers receve and what they would be wllng to accept f necessary. The sum of the two s the area between the downward-slopng demand curve and the upward-slopng supply curve. Because a reducton n agrcultural yeld shfts the supply curve upward wthout a correspondng upward shft n the demand curve, t unambguously reduces the sum of consumer and producer surplus. The percent reducton n the sum of producer and consumer surplus s lkely to be at least as large as the percent reducton n yeld. CARBON FERTILIZATION, IRRIGATION, AND TRADE 33