

Line 143: 
Line 143: 
 === <span style="fontsize:large;">Overview</span> ===   === <span style="fontsize:large;">Overview</span> === 
   
−  Briefly, each year the agriculture model begins by estimating the production of crops, meat, and fish. It then turns to the demand for these commodities, followed by trade. The model then looks at changes in stocks and potential shortages related to calorie availability. These influence prices for the coming year, as well as desired investment, which are passed to the economic model, which determines the actual amount of investment that will be available. With this knowledge, the model can then estimate values for changes in land development, agricultural capital, and livestock for the coming year.  +  Briefly, each year the agriculture model begins by estimating the production (pre and postproduction loss) of crops, meat, and fish. It then turns to the demand for these commodities. This begins with a computation of caloric demand from crops, meat, and fish, which is translated into demand for food going directly to consumers. Other demands for crops, meat, and fish are for feed, industrial uses (e.g. biofuels), and food manufacturing. Losses in the production, distribution and consumption of agricultural commodities are also accounted for. This is followed by computations for trade. The model then considers the balance between the demands and the available supply based on production, imports, and exports. Any excess supply increases stocks. In the case of excess demand, stocks are drawn down; this can result in shortages if there are not enough stocks, which leads to an inability to meet all of the demands. Levels of, and changes in, stocks influence prices for the coming year, as well as desired investment, which are passed to the economic model, which determines the actual amount of investment that will be available. With this knowledge, the model can then estimate values for changes in land development, agricultural capital, and livestock for the coming year. 
   
−  This help section presents and discusses the equations that are central to each of these steps in the agricultural model. Along the way, it also presents information related to the actions in the preprocessor and first year of the agriculture model, which are important in setting the stage for the forecasts.
 +  <span style="fontsize:xlarge;">Agricultural Supply</span> 
   
−  == <span style="fontsize:xlarge;">Agricultural Supply</span> ==
 +  Crop, meat, and fish supply have very different bases and IFs determines them in separate procedures. 
   
−  <span>Crop, meat, and fish supply have very different bases and IFs determines them in separate procedures.</span>  +  <span style="fontsize:large;">Crop Production</span> 
   
−  ==== <span style="fontsize:large;">Crop Production</span> ====  +  Crop production, preloss, (AGPppl<sub>f=1</sub>) i is the product of total yield and land devoted to crops (LD<sub>l=1</sub>). 
   
−  Crop production (AGP<sub>f=1</sub>) i is the product of yield and land devoted to crops (LD<sub>l=1</sub>).
 +  <![if gte msEquation 12]><m:oMathPara><m:oMath><m:sSub><m:sSubPr><span 
−   +  style='fontfamily:"Cambria Math",serif;msoasciifontfamily:"Cambria Math"; 
−  <math>AGP_{r,f=1} = YL_{r} * LD_{r,l=1} </math>
 +  msohansifontfamily:"Cambria Math";color:#252525;fontstyle:italic; 
−   +  msobidifontstyle:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i 
−  We focus here on the determination of yield; the amount of land devoted to crops is addressed in the [[Agriculture#Land_DynamicsLand Dynamics]] section.
 +  style='msobidifontstyle:normal'><span style='fontfamily:"Cambria Math",serif; 
−   +  color:#252525'><m:r>AGPppl</m:r></span></i></m:e><m:sub><i 
−  Yield functions are almost invariably some kind of saturating exponential that represents decreasing marginal returns on inputs such as fertilizer or farm machinery. Such functions have been used, for instance in World 3 (Meadows, 1974), SARUM, (SARU, 1977), the Bariloche Model (Herrera, et al., 1976), and AGRIMOD (Levis, et al., 1977). IFs also uses a saturating exponential, but relies on a CobbDouglas form. The CobbDouglas function is used in part to maintain symmetry with the economic model but more fundamentally to introduce labor as a factor of production. Especially in less developed countries (LDCs) where a rural labor surplus exists, there is little question that labor, and especially labor efficiency improvement, can be an important production factor.
 +  style='msobidifontstyle:normal'><span style='fontfamily:"Cambria Math",serif; 
−   +  color:#252525'><m:r>r</m:r><m:r>,</m:r><m:r>f</m:r><m:r>=1</m:r></span></i></m:sub></m:sSub><i 
−  In the first year of the model, yield (YL) is computed simply as the ratio of crop production (AGP<sub>f=1</sub>) to cropland (LD<sub>l=1</sub>). The determinations of the initial values of these variables are described elsewhere in this document. It is bound, however, to be no greater than 20 tons per hectare in any country.
 +  style='msobidifontstyle:normal'><span style='fontfamily:"Cambria Math",serif; 
−   +  color:#252525'><m:r>=</m:r></span></i><m:sSub><m:sSubPr><span 
−  In forecast years, IFs computes yield in stages. The first provides a basic yield (BYL) representing change in longterm factors such as capital, labor and technology. The second stage uses this basic yield as an input and modifies it based on prices, so as to represent changes in shorterterm factors (e.g. amounts of fertilizer used, even the percentage of land actually under cultivation). Finally, in a third stage, yields are adjusted in response to changing climate conditions.
 +  style='fontfamily:"Cambria Math",serif;msoasciifontfamily:"Cambria Math"; 
−   +  msohansifontfamily:"Cambria Math";color:#252525;fontstyle:italic; 
−  The basic yield (byl) relates yield to agriculture capital (KAG), agricultural labor (LABS), technological advance (AGTEC), a scaling parameter (CD), an exponent (CDALF), and a saturation coefficient (SATK).
 +  msobidifontstyle:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i 
−   +  style='msobidifontstyle:normal'><span style='fontfamily:"Cambria Math",serif; 
−  :<math>byl_{r}=cD_{r}*{(1+AGTEC_{r})}_{t1}*KAG_{r}^{CDALF_{r,s=1}}*LABS_{r,s=1}^{{(1CDALF}_{r,s=1)}}*SATK_{r}</math>  +  color:#252525'><m:r>YL</m:r></span></i></m:e><m:sub><i style='msobidifontstyle: 
−   +  normal'><span style='fontfamily:"Cambria Math",serif;color:#252525'><m:r>r</m:r></span></i></m:sub></m:sSub><i 
−  The equations for KAG and LABS are described elsewhere (see the [[Agriculture#Capital_DynamicsCapital Dynamics]] and the economic model, respectively).
 +  style='msobidifontstyle:normal'><span style='fontfamily:"Cambria Math",serif; 
−   +  color:#252525'><m:r>*</m:r></span></i><m:sSub><m:sSubPr><span 
−  cD is a scaling factor calculated in the first year of the model based upon the base year yield (YL), capital (KAG), and labor supply (LABS). It is similar to the shift factors elsewhere in the model, which are used to match predicted values in the base year to actual values. It does not change over time.
 +  style='fontfamily:"Cambria Math",serif;msoasciifontfamily:"Cambria Math"; 
−   +  msohansifontfamily:"Cambria Math";color:#252525;fontstyle:italic; 
−  :<math>CD_{r}=\frac{YL_{r,t=1}}{{KAG_{r,t=1}^{CDALF_{r,s=1}}}*{LABS_{r,S=1,t=1}^{(1CDALF_{r,s=1})}}}</math>  +  msobidifontstyle:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i 
−   +  style='msobidifontstyle:normal'><span style='fontfamily:"Cambria Math",serif; 
−  CDALF is the standard CobbDouglas alpha reflecting the relative elasticities of yield to capital and labor. It is computed each year in a function, rooted in data on factor shares from the Global Trade and Analysis Project, driven by GDP per capita at PPP.
 +  color:#252525'><m:r>LD</m:r></span></i></m:e><m:sub><i style='msobidifontstyle: 
−   +  normal'><span style='fontfamily:"Cambria Math",serif;color:#252525'><m:r>r</m:r><m:r>,</m:r><m:r>l</m:r><m:r>=1</m:r></span></i></m:sub></m:sSub></m:oMath></m:oMathPara><![endif]><![if gte vml 1]><v:shapetype id="_x0000_t75" 
−  AGTEC is a factorneutral technological progress coefficient similar to a multifactor productivity coefficient. It is initially set to 1 and changes each year based upon a technological growth rate (TECHGROAG).
 +  coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" 
−   +  filled="f" stroked="f"> 
−  :<math>AGTECH_{r}=AGTECH_{r,t1}*(1+TECHGROAG_{r})</math>
 +  <v:stroke joinstyle="miter"/> 
−   +  <v:formulas> 
−  The algorithmic structure for computing the annual values of TECHGRO involves four elements:
 +  <v:f eqn="if lineDrawn pixelLineWidth 0"/> 
−   +  <v:f eqn="sum @0 1 0"/> 
−  The difference between a targeted yield growth calculated the first year and the portion of that growth not initially related to growth of capital and labor (hence the underlying initial technology element of agricultural production growth); call it AGTECHINIT. This element is assumed to decrease by half over 100 years.
 +  <v:f eqn="sum 0 0 @1"/> 
−   +  <v:f eqn="prod @2 1 2"/> 
−  The gap between desired global crop stock levels and actual stocks (hence the global pressure for technological advance in agriculture); call it AGTECHPRESS. This contribution is introduced by way of the ADJUSTR function of IFs.<ref> The ADJSTR function, used throughout the model, is a PID controller that builds in some anticipatory and smoothing behavior to equilibrium processes by calculating an adjustment factor. It considers both the gap between the current value of the specific variable of interest, here crop stocks, and a target value, as well as change in the gap since the last time step. Two parameters control the degree to which these two "differences" affect the calculation of the adjustment factor. In this case, these are the global, usercontrollable parameters '''''elfdpr1'' ''' and '''''elfdpr2'' '''.</ref>
 +  <v:f eqn="prod @3 21600 pixelWidth"/> 
−   +  <v:f eqn="prod @3 21600 pixelHeight"/> 
−  The difference between the productivity of the agricultural sector calculated in the economic model and the initial year's value of that (hence reflecting changes in the contributions of human, social, physical, and knowledge capital to technological advance of the society generally); call if AGMFPLT.
 +  <v:f eqn="sum @0 0 1"/> 
−   +  <v:f eqn="prod @6 1 2"/> 
−  The degree to which crop production is approaching upper limits of potential; this again involves the saturation coefficient (SATK).
 +  <v:f eqn="prod @7 21600 pixelWidth"/> 
−   +  <v:f eqn="sum @8 21600 0"/> 
−  The algorithmic structure this is:
 +  <v:f eqn="prod @7 21600 pixelHeight"/> 
−   +  <v:f eqn="sum @10 21600 0"/> 
−  :<math>TECHGROAG_{r}=F(AGTECHINIT_{r},AGTECHPRESS_r,AGMFPLT_{r}, SATK_{r})</math>
 +  </v:formulas> 
−   +  <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> 
−  The saturation coefficient is a multiplier of the CobbDouglas function and of the technological change element. It is the ratio of the gap between a maximum possible yield (YLLim) and a moving average of yields to the gap between a maximum possible yield and the initial yield, raised to an exogenous yield exponent ('''''ylexp'' '''). With positive parameters the form produces decreasing marginal returns.
 +  <o:lock v:ext="edit" aspectratio="t"/> 
−   +  </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:2in; 
−  :<math>SATK_{r+1}=(\frac{YLLim_{r}syl_{r}}{YLLim_{r}YL_{r,t=1}})^{ylexp}</math>
 +  height:29.25pt'> 
−   +  <v:imagedata src="file:///C:\Users\Kanishka\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png" 
−  ''where''
 +  o:title="" chromakey="white"/> 
−   +  </v:shape><![endif]> 
−  syl<sub>r</sub> is a moving average of byl, the historical component of which is weighted by 1 minus the usercontrolled global parameter '''''ylhw'' '''.
 +  
−   +  
−  '''''ylexp'' ''' global parameter
 +  
−   +  
−  The maximum possible yield (YLLim) is estimated for each country and can change over time. It is calculated as the maximum of 1.5 times the initial yield (YL<sub>r,t=1</sub>) and the multiple of an external usercontrolled parameter ('''''ylmax'' ''') and an adjustment factor (YLMaxM).
 +  
−   +  
−  :<math>YLLim_{r}=max (\mathbf{ylmax}_{r}*YLMaxM_{r},1.5*YL_{r,t=1})</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  '''''ylmax'' ''' is a countryspecific parameter
 +  
−   +  
−  The adjustment factor YLMaxM allows for some additional growth in the yields for poorer countries
 +  
−   +  
−  :<math>YLMaxM_{r}=1*(1DevWeight_{r})+((\frac{YL_{r}}{YlMaxFound})^{0.35}*DevWeight_{r})</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  DevWeight<sub>r</sub> is the GDPPCP<sub>r</sub>/30, with a maximum value of 1
 +  
−   +  
−  YlMaxFound is the maximum value of YL found in the first year
 +  
−   +  
−  Before moving to the next stage, a check is made to see if the growth in byl is within reason. Specifically, byl is not allowed to exceed the moving average of byl (syl) times a given growth rate (ylgrbound). This bound is the maximum of a usercontrolled global parameter  '''''ylmaxgr'' ''' and an initial country specific target growth rate (tgryli<sub>r</sub>).<ref>There is also an adjustment whereby '''''ylmaxgr'' ''' is reduced for countries with syl>5, falling to a value of 0.01 when syl>=8.</ref> This latter target growth rate in yield is set in the first year and is a function of current crop demand (AGDEM), expected crop demand (etdem), and a target growth rate in cropland.
 +  
−   +  
−  :<math>tgryli_{r}=\frac{etdem}{AGDEM_{r,s=1}}1\mathbf{tgrld}_{r}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  '''''<span>tgrld</span> '' ''' <span>is a countryspecific parameter indicating target growth in crop land</span>
 +  
−   +  
−  <span>etdem is an initial year estimate of the sum of industrial, feed and food demand for crops in the following year</span>
 +  
−   +  
−  <span>At this point, the basic yield (BYL) is adjusted by a number of factors. The first of these is a simple countryspecific usercontrolled multiplier – '''''ylm'' '''. '''''ylm'' ''' can be used to represent the effects of any number of exogenous factors, such as political/social management (e.g., collectivization of agriculture).</span>
 +  
−   +  
−  <span>The basic yield represents the longterm tendency in yield but agricultural production levels are quite responsive to shortterm factors such as fertilizer use levels and intensity of cultivation. Those shortterm factors under farmer control (therefore excluding weather) depend in turn on prices, or more specifically on the profit (FPROFITR) that the farmer expects. Because of computational sequence, we use domestic food stocks as a proxy for profit level.</span>
 +  
−   +  
−  <span>In this second stage, the recomputed yield (YL) is multiplied by a stock adjustment factor.</span>
 +  
−   +  
−  :<math>YL_{r}=BYL_{r}*stockadjustmentfactor_{r,f=2}(\mathbf{elfdpr1,elfdpr2})</math>  +  
−   +  
−  <span>The stock adjustment factor uses the ADJSTR function to calculate an adjustment factor related to the current stocks, the recent change in stocks, and a desired stock level. The desired stock level is given as a fraction (agdstl) of the sum of crop demand (AGDEM<sub>f=1</sub>) and crop production (AGP<sub>f=1</sub>). agdstl is set to be 1.5 times '''''dstl'' ''', which is a global parameter that can be adjusted by the user.</span>
 +  
−   +  
−  <span>The focus in IFs on yield response to prices differs somewhat from the normal use of price elasticities of supply. For reference, Rosegrant, AgcaoiliSombila, and Perez (1995: 5) report that price elasticities for crops are quite small, in the range of .05 to .4.</span>  +  
−   +  
−  <span>In the third stage. IFs considers the potential effects of a changing climate on crop yields. This is separated into two parts: the direct effect of atmospheric carbon dioxide concentrations and the effects of changes in temperature and precipitation.</span>
 +  
−   +  
−  <span>The direct effect of atmospheric carbon dioxide assumes a linear relationship between changes in the atmospheric concentration from a base year of 1990 and the percentage change in crop yields.</span>
 +  
−   +  
−  :<math>CO2Fert_{t+1}=\mathbf{envco2fert}*\frac{CO2PPMCO2PPM_{t=1990}}{CO2PPM_{t=1990}}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  '''''<span>envco2fert</span> '' ''' <span>is a global, usercontrollable parameter</span>
 +  
−   +  
−  <span>CO2PPM<sub>t=1990</sub> is hard coded as 354.19 parts per million</span>
 +  
−   +  
−  <span>The effect of changes in annual average temperature and precipitation are based upon two assumptions: 1) there is an optimal temperature (Topt) for crop growth, with yields falling both below and above this temperature and 2) there is a logarithmic relationship between precipitation and crop yields. The choice of this functional form was informed by work reviewed in Cline (2007). Together, these result in the following equation: </span>
 +  
−   +  
−  :<math>ClimateEffect_{t+1}=100*(\frac{e^{0.5*\frac{(TO_{r}+DeltaT_{r}Topt)^{2}}{SigmaTsqd}}*ln(P0_{r}*(\frac{DeltaP_{r}}{100}+1))}{e^{0.5*\frac{(T0_{r}Topt)^{2}}{SigmaTsqd}}*ln(P0_{r})}1)</math>
 +  
−   +  
−  ''where''  +  
−   +  
−  <span>T0 and P0 are countryspecific annual average temperature (degrees C) and precipitation (mm/year) for the period 198099.</span>
 +  
−   +  
−  <span>DeltaT and DeltaP are country specific changes in annual average temperature (degrees C) and precipitation (percent) compared to the period 198099. These are tied to global average temperature changes and described in the documentation of the IFs environment model.</span>
 +  
−   +  
−  <span>Topt is the average annual temperature at which yield is maximized. It is hard coded with a value of 0.602 degrees C.</span>
 +  
−   +  
−  <span>SigmaTsqd is a shape parameter determining how quickly yields decline when the temperature moves away from the optimum. It is hard coded with a value of 309.809.</span>
 +  
−   +  
−  <span>CO2Fert and ClimateEffect are multiplied by each other to determine the effect on crop yields.</span>
 +  
−   +  
−  <span>There are two final checks on crop yields. They are not allowed to be less than onefifth of the estimate of basic yield (BYL) and they cannot exceed the countryspecific maximum ('''''ylmax'' ''') or 50 tons per hectare.</span>
 +  
−  <div>
 +  
−  
 +  
−  <div><references /></div></div>
 +  
−  ==== <span style="fontsize:large;">Meat Production</span> ====
 +  
−   +  
−  <span datamcemark="1">Meat production, in metric tons, is given as the multiple of the herd size (LVHERD) and the slaughter rate ('''''slr'' '''). The latter is a global parameter.</span>
 +  
−   +  
−  :<math>AGP_{r,f=2}=LVHERD_{r}*\mathbf{slr}</math>  +  
−   +  
−  <span datamcemark="1">The dynamics of the livestock herd are described in the [[Agriculture#Livestock_DynamicsLivestock Dynamics]] section.</span>
 +  
−   +  
−  ==== <span style="fontsize:large;">Fish Production</span> ====
 +  
−   +  
−  The production of fish has two components, wild catch and aquaculture. Total global wild fish catch ('''''ofscth'' '''), and each region's share in it ('''''rfssh<sub>r</sub> '' ''') are exogenous parameters that can be set by the user.
 +  
−   +  
−  The amount of aquaculture (AQUACUL) in the first year is provided by historical data; these values can be modified by the user. Production is assumed to grow over time. The default growth rate in the first year for all countries is 3.5 percent, but this value can be modified by the user, by country, with the parameter '''''aquaculgr'' '''. This growth rate declines to 0 over a number of years given by the global parameter '''''aquaculconv'' '''. Finally, users can change the amount of aquaculture production, by country, with the multiplier '''''aquaculm'' '''.
 +  
−   +  
−  :<math>AQUACUL_{r}=AQUACUL_{r,t1}*(1+aquaculgr_{r,t})+aquaculm_{r}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  ''<span>aquaculgr<sub>r,t</sub> declines from aquaculgr<sub>r,t=1</sub> </span> '' <span>to 0 over '''''aquaculconv'' ''' years</span>
 +  
−   +  
−  <span>Total fish production (FISH) is given as:</span>  +  
−   +  
−  :<math>FISH_{r,t}=\mathbf{ofscth}_{r}*\mathbf{rfssh}_{r}+AQUACUL_{r,t}</math>
 +  
−   +  
−  ==== <span style="fontsize:large;">Production Losses</span> ====
 +  
−   +  
−  <span>Some food production will never make it to markets, but will be lost in the field or in distribution systems to pests, spoilage, etc. For crops, an initial estimate of the loss in the first year, LOSSI, is given as a function of GDP per capita using a table function t</span><span>hat captures the tendency of loss to decrease with higher income levels (see figure below). </span>This is reset to 0 in the preprocessor if the estimate of cereal production in the first year is zero. If the loss seems too high, specifically if it is greater than or equal to 0.9  cereal exports/cereal production, then the loss for crops is recomputed as the maximum of 0.05 and 0.9 – cereal exports/cereal production. The estimate of loss in the first year for meat<span>is assumed to be onehalf of the initial estimate for crops; no losses are assumed for fish.</span> <span>In future years, for crops and meat, the loss is calculated as the loss in the first year multiplied by the ratio of the loss estimated from the table function above using current GDP per capita to GDP per capita in the first year; therefore, as GDP per capita increases relative to the first year, loss decreases. A common loss multiplier ('''''lossm'' ''') is also available, allowing users to adjust crop and meat losses. Finally, losses are bound between 0 and 0.8. At present, fish loss remains constant at 0 for all years.</span>
 +  
−   +  
−  :<span><math>Loss_{r,f=1,2}=\frac{TF(GDPPC_{r})}{TF(GDPPC_{r,t=1})}*Loss_{r,f=1,2,t=1}*\mathbf{lossm_{r}}</math></span>
 +  
−   +  
−  [[File:Production losses.pngbordercenterProduction losses.png]]
 +  
−   +  
−  == <span style="fontsize:xlarge;">Agricultural Demand</span> ==
 +  
−   +  
−  IFs computes demand for three agricultural categories—crops, meat, and fish. Total human food demand (for both crops and meat) is responsive to calorie demand, which in turn responds to GDP per capita (as a proxy for income). The division of calorie demand between demand for calories from crops and from meat changes in response also to GDP per capita (increasing in income). The calculation sequence of human food demand in IFs thus begins with determination of calorie demand, determines how much of that is satisfied by the typically increasing share from meat (bounding that share with reasonable upper limits), and how much remains to be satisfied from crops. At this point IFs does not track calories from fish. Once the remaining needed calories from crops are determined, the physical demand for crops in million metric tons can also be determined.
 +  
−   +  
−  Crop demand also involves demand for industrial use and animal feed. Total crop demand is the sum of those two demands and that for food crops.
 +  
−   +  
−  ==== <span style="fontsize:large;">Initial Agricultural Demands</span> ====
 +  
−   +  
−  A common process across categories is used to estimate initial values for the first years. It relies upon the first year values of production, imports, exports, and losses, all of which are generated in the preprocessor and discussed elsewhere in this document, to compute an apparent level of demand or consumption. The reason for this is that demand data are much less available for food and agriculture than are production and trade data. An initial estimate of demand in each category is given as the sum of postloss production and imports minus exports:
 +  
−   +  
−  :<math>AGDEM_{r,f=13,t=1}=AGP_{r,f=13,t=1}*LOSS_{r,f=13,t=1}+AGM_{r,f=13,t=1}AGX_{r,f=13,t=1}</math>
 +  
−   +  
−  An initial portion of this first estimate of demand is set aside for the purposes of satisfying the need for growth in food stocks as underlying total food demand and supply change (using initial economic growth as a proxy for that annual stock growth). See also the section on stocks. That adjusted demand then becomes the basis, along with production, for an estimate of food stocks.
 +  
−   +  
−  :<math>AGDEM_{r,f=13,t=1}=AGDEM_{r,f=13,t=1}(AGDEM_{r,f=13,t=1}+AGP_{r,f=13,t=1})*agdstl*igdpr_{r,t=1}</math>  +  
−   +  
−  :<math>FSTOCK_{r,f=13}=(AGP_{r,f=13}+AGDEM_{r,f=13})*agdstl</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  agdstl is a parameter used to set desired stock levels for agricultural commodities. It is set to be 1.5 times '''''dstl'' ''', which is a global parameter that can be adjusted by the user
 +  
−   +  
−  igdpr is the initial growth rate in GDP
 +  
−   +  
−  Given the resulting initial model year value for food stocks, it is then possible to calculate a more precise increment of stock change needed and add that back into the demand.
 +  
−   +  
−  :<math>AGDEM_{r,f=13,t=1}=AGDEM_{r,f=13,t=1}+FSTOCK_{r,f=13,t=1}*igdpr_{r,t=1}</math>  +  
−   +  
−  ==== <span style="fontsize:large;">Total Calorie Demand (and the Share from Meat)</span> ====
 +  
−   +  
−  In the first year of the model, a predicted level of calories per capita (CalPerCap) is estimated as an increasing function of average income.<ref>Equation is CalPerCap = 2180.6+368.87*ln(GDPPCP).</ref> This is bound from above by an assumed maximum value, given by the global parameter '''''calmax'' '''.[[File:Total calorie dd and share from meat.pngbordercenterTotal calorie dd and share from meat.png]]
 +  
−   +  
−  The predicted per capita value is converted to total calorie demand (caldem) by multiplying by the population (POP). A multiplicative shift factor (calactpredrat), used in the forecast years, is then calculated by dividing by the value of calories available (CLAVAL) by this demand.
 +  
−   +  
−  :<math>calactpredrat_{r}=\frac{CLAVAL_{r,t=1}}{caldem_{r,t=1}}</math>
 +  
−   +  
−  ''where''
 +  
−   +  
−  CLAVAL is calorie availability; its calculation is described below in the section on calorie availability
 +  
−   +  
−  This value of calactpredrat gradually converges to 1 over a period given by the global parameter '''''agconv'' ''' and appears in future equations with the name adjustforinitialdevc.
 +  
−   +  
−  In the forecast years, a predicted value of per capita calorie demand (CalPerCap) is once again calculated as a function of average income using the equation above, with a maximum value given by '''''calmax'' '''. A base level of calories per capita (calbase) is also calculated, which is given as the minimum of 3000 or '''''calmax'' ''' minus 300. Because comparative cross sections show a growth of around 4 calories per capita per year independent of average income, a factor representing this increase (caldgr) is calculated as:
 +  
−   +  
−  :<math>caldgr_{r,t}=caldgr_{r,t1}+4*(\frac{\mathbf{calmax}MAX(calbase,MIN(\mathbf{calmax},CalPerCap_{r}))}{\mathbf{calmax}calbase})</math>
 +  
−   +  
−  Thus, depending on the exact values of '''''calmax'' ''', calbase, and CalPerCap, caldgr grows each year by a value that centers around 4 calories. This value is then added to the predicted value in calculating the total demand for calories. The equation also takes into account '''''calmax'' ''' and the multiplicative shift factor on calories per capita noted above.
 +  
−   +  
−  :<math>caldem_{r}=MIN(\mathbf{calmax},CalPerCap_{r}+caldgr_{r})*POP_{r}*adjustforinitialdevc_{r}</math>  +  
−   +  
−  This total calorie demand is divided into demand from meat and demand from crops. Meat demand in tons (AGDEM, category 2) is discussed in the following section. Here we focus on how this is converted to calories. Two countryspecific parameters, lvcfr and sclavf, calculated in the first year of the model are key to this conversion.
 +  
−   +  
−  lvcfr is a countryspecific factor converting livestock in tons to calories. This is initially set equal to the global parameter '''''lvcf'' ''', but may be adjusted downward. This is done in cases where the initial estimate of the share of calories from meat exceeds a maximum value: given by t, i.e., if
 +  
−   +  
−  :<math>\frac{AGDEM_{r,f=2,t=1}*lvcfr_{r}}{FDEM_{r,t=1}+AGDEM_{r,f=2,t=1}*lvcfr_{r}}>\mathbf{calmeatm}</math>
 +  
−   +  
−  ''where''  +  
−   +  
−  '''''calmeatm'' ''' is a global parameter indicating the maximum share of calories to come from meat
 +  
−   +  
−  In this case, lvcfr is repeated reduced by 10 percent until the share of total calories coming from meat falls below '''''calmeatm'' '''.
 +  
−   +  
−  sclavf is a countryspecific multiplicative shift factor that converts the total annual demand for food crops and crop equivalents from meat to daily calorie availability
 +  
−   +  
−  :<math>sclavf_{r}=\frac{CLAVAL_{r,t=1}}{FDEM_{r,t=1}+AGDEM_{r,f=2,t=1}*lvcfr_{r}}</math>
 +  
−   +  
−  Note that sclavf can take on a value greater that or less than 1.
 +  
−   +  
−  lvcfr and sclavf maintain the same value in all the forecast years.
 +  
−   +  
−    +  
−   +  
−  <references />
 +  
−   +  
−  ==== <span style="fontsize:large;">Meat Demand and Its Calorie Contribution</span> ====
 +  
−   +  
−  In the first model year apparent meat demand is used to compute the calories that its consumption contributes to the need of the population. In subsequent years the calculations begin with meat demand again, and conclude with calculation of the calories provided by it. This is needed subsequently to determine the calories required from crops.
 +  
−   +  
−  In the first year of the model's forecasts an apparent consumption of meat is calculated as for other agricultural demand components (in terms of production plus imports and subtracting exports). In the first year, two other countryspecific values are calculated that are used to estimate this value in the forecast years—meatmaxr and meatactpredrat.
 +  
−   +  
−  meatmaxr is a countryspecific maximum for per capita meat demand in tons. It is calculated as the maximum of a global parameter ('''''meatmax'' ''') and per capita total meat demand (AGDEM, category 2 divided by POP).
 +  
−   +  
−  meatactpredrat, which acts as a shift factor, is the ratio of actual total meat demand (in tons) to a predicted value (MeatDem). First, a predicted per capita value is estimated as an increasing function of GDP per capita.<ref>Equation is Meat Demand per Capita = .0109999999403954GDPPCP0.684800028800964</ref>
 +  
−   +  
−  This is not allowed to exceed meatmaxr and is then multiplied by the population to yield the predicted value of total MeatDem. meatactpredrat is then calculated as
 +  
−   +  
−  :<math>meatactpredrat_{r}=\frac{AGDEM_{r,f=2,t=1}}{MeatDem_{r}}</math>  +  
−   +  
−  meatmaxr is held constant in all forecast years. For most countries, the value of meatactpredrat gradually converges to 1 over a period given by the global parameter '''''agconv'' '''. The exception is for certain countries in South Asia, specifically India, Nepal, and Mauritius, for which it does not converge. In either case, it is represented in equations in future year as adjustforinitialdevm.
 +  
−   +  
−  In the forecast years, IFs then computes the demand for meat in tons as a function of population, average income, world food prices, the shift factor, and a multiplier that allows users to directly increase or decrease demand. As in the first year, per capita demand (tonspercap) is initially estimated as a function of average income, using the same function presented above. This is then converted to total demand in the following equation.
 +  
−   +  
−  :<math>AGDEM_{r,f=2}=tonspercap_{r}*POP_{r}*adjustforinitialdevm*(\frac{WAP_{f=2}}{WAP_{f=2,t=1}})^{\mathbf{elasmd}}</math>
 +  
−   +  
−  ''where''
 +  
−   +  
−  '''''elasmd'' ''' is a global parameter representing the elasticity of meat demand to changes in the world price relative the first year
 +  
−   +  
−  A number of further adjustments are made to the meat demand, in the following order:
 +  
−   +  
−  #The estimated value is restricted to be no greater than that given by multiplying the size of the population (POP) by the maximum for per capita meat demand in tons (meatmaxr)
 +  
−  #This adjusted value is multiplied by a demand multiplier ('''''agdemm<sub>r,f=2</sub> '' '''), which can raise or lower demand.
 +  
−  #If the initial estimate of calories from meat (calfrommeat) exceeds the maximum amount of calories allowed to come from meat, given by '''''calmeatm'' ''' * caldem, then the demand for meat in tons is recalculated as:
 +  
−   +  
−  :<math>AGDEM_{r,f=2}=(\frac{\mathbf{calmeatm}*caldem_{r}}{lvcfr_{r}*sclavf_{r}})</math>
 +  
−   +  
−  Note that this implies a reduction in the total demand for meat in tons.
 +  
−   +  
−  In order to undertake the third adjustment, and to prepare for the calculation of calories needed from crops, the meat demand needs to be converted from tons to calories. An initial estimate of calories from meat (calfrommeat) is calculated from the total demand for meat in tons, adjusted by lvcfr and sclavf:
 +  
−   +  
−  :<math>calfrommeat_{r}=AGDEM_{r,f=2}*lvcfr_{r}*sclavf_{r}</math>
 +  
−   +  
−  Should this exceed the maximum amount of calories allowed to come from meat, given by '''''calmeatm'' ''' * caldem, then two adjustments are made. First, calfrommeat is set equal to this maximum amount
 +  
−   +  
−  :<math>calfrommeat_{r}=\mathbf{calmeatm}*caldem_{r}</math>
 +  
−   +  
−  and the total demand for meat in tons is recalculated
 +  
−   +  
−  :<math>AGDEM_{r,f=2}=\frac{\mathbf{calmeatm}*caldem_{r}}{lvcfr_{r}*sclavf_{r}}</math>  +  
−   +  
−  Note that this implies a reduction in the total demand for meat in tons.
 +  
−   +  
−  Now that the demands for total calories and calories from meat are known, calories to be demanded from crops (mostly grain) can be calculated simply as
 +  
−   +  
−  :<math>calfromgrain_{r}=caldem_{r}calfrommeat_{r}</math>  +  
−  <div><br/>
 +  
−  
 +  
−  <references /></div>
 +  
−  ==== <span style="fontsize:large;">Fish Demand</span> ====
 +  
−   +  
−  Currently IFs does not calculate calories from fish and determine that contribution to total calorie demand. We anticipate that model extension in the future.
 +  
−   +  
−  The calculation of fish demand (AGDEM, category 3) in the first year was described at the start of the Demand section as having the same apparent consumption approach as used for other agricultural demands (production plus imports minus exports and adjustment stocks). In the first year, a calculation is also made of fish demand per capita (fishdemipc), which is simply the ratio of AGDEM, category 3 to population (POP).
 +  
−   +  
−  In the forecast year, fish demand per capita is assumed to grow with growth in average income, with some adjustments. First, predicted values for fish demand per capita are calculated as a function of income in the first and current year using the function depicted in the diagram below<ref>Equation is Fish Demand per Capita = 0.0121 + 0.00102*GDPPCP</ref>.[[File:Fish demand.pngcenterFish demand.png]]
 +  
−   +  
−  The initial estimate of fish demand per capita is the value for the initial year (fishdemipc) multiplied by the ratio of the predicted value in the current year (tonspercap) to the predicted value in the first year (tonspercapi)
 +  
−   +  
−  :<math>fishdempc_{r}=fishdemipc_{r}*\frac{tonspercap_{r}}{tonspercapi_{r}}</math>
 +  
−   +  
−  Once the per capita demand exceeds 50 percent of the initial value, a new logic kicks in.
 +  
−   +  
−  fishdempc is also not allowed to exceed the value in the first year or 0.1, whichever is larger.
 +  
−   +  
−  Finally, total demand for fish is determined by multiplying the per capita value by the population (POP), with a price adjustment.
 +  
−   +  
−  :<math>AGDEM_{r,f=3}=fishdemp_{r}*POP_{r}*(\frac{WAP_{f=3}}{WAP_{f=3,t=1}})^{\mathbf{0.6}}</math>
 +  
−  <div><div><br/>
 +  
−    +  
−   +  
−  <references />
 +  
−   +  
−  ==== <span style="fontsize:large;">Crop Demand for Food (FDEM) and Its Calorie Contribution</span> ====
 +  
−   +  
−  Total crop demand (AGDEM, category 1) has three components: feed (FEDDEM), industrial (INDEM) and food (FDEM). Here we describe the basic calculations for food use of crops. Note that in forecast years additional adjustments are made to a number of the demand variables, so the discussion here will not fully complete the determination of FDEM.
 +  
−   +  
−  The demand for crops for food in the base year is not computed in the preprocessor. Rather, in the first year of the model, the demand for crops for food (FDEM) is calculated as the residual of total agricultural demand for crops minus the demand for crops for feed and for industry.<ref>It is bound to be between 0.1 and 1000.</ref>
 +  
−   +  
−  :<math>FDEM_{r,t=1}=AGDEM_{r,f=1,t=1}FEDDEM_{r,t=1}INDEM_{r,t=1}</math>
 +  
−   +  
−  Given earlier calculations of the total demand for calories and of the share of that demand to be met by meat, it was possible to calculate the calories needed from crops, mostly grain around the world (calfromgrain). From this it is possible to calculate food demand using the factor relating the conversion from crops to calories (sclavf), an adjustment based on world crop prices, and a multiplier that can be used to increase or decrease demand.
 +  
−   +  
−  :<math>FDEM_{r}=(\frac{calfromgrain_{r}}{sclavf_{r}})*(\frac{WAP_{t,f=1}}{WAPf_{t=1,f=1}})^\mathbf{elascd}*\mathbf{agdemm}_{r,f=1}</math>
 +  
−   +  
−  FDEM is bound from above based on the assumed maximum calories per capita ('''''calmax'' '''), and the multiplicative shift factor on calories per capita (adjustforinitialdevc).
 +  
−   +  
−  :<math>maximum FDEM_{r}=\mathbf{calmax}*POP_{r}*adjustforinitialdevc_r</math>
 +  
−  <div><br/>
 +  
−  
 +  
−   +  
−  <references />
 +  
−   +  
−  ==== <span style="fontsize:large;">Feed Demand for Crops</span> ====
 +  
−   +  
−  Feed demand represents the amount of crops that need to be produced to complement what livestock receive from grazing.
 +  
−   +  
−  In the preprocessor, feed demand (FeedDem) is initially estimated as a percentage of the apparent consumption of cereals, which grows with average income, implying that as countries develop, more of their grain production is used to feed livestock. The function is depicted on the right<ref>The specific equation is 13.427 +14.421*ln(GDPPCP), up to GDPPCP=35. The code sets minimum and maximum values of 1 and 80 percent, respectively.</ref>:[[File:Feed demand for crops.pngcenterFeed demand for crops.png]]
 +  
−   +  
−  If the model estimates that the productivity of grazing land in terms of feed equivalent produced per unit area is below a minimum level, however, then FeedDem is adjusted downward. It determines this by first estimating the feed requirements per unit livestock (fedreq). This is estimated as an increasing function of average income as shown in the figure below.[[File:Feed demand for crops 2.pngcenterFeed demand for crops 2.png]]
 +  
−   +  
−  This function takes into account the fact that at low levels of income most meat consumption is typically poultry (with a conversion ratio of grain to meat of about 2to1), while at higher levels of income, pork (4to1) and then beef (7to1) become increasing portions of meat demand (Brown, 1995: 4547).
 +  
−   +  
−  With the value of fedreq, the productivity of grazing land can be estimated as the difference between the total feed requirement for the number of livestock minus the feed demand divided by the amount of grazing land.
 +  
−   +  
−  :<math>GLandCAP_{r}=\frac{LiveHerd_{r}*fedreq_{r}FeedDem_{r}}{LDGraz_{r}}</math>
 +  
−   +  
−  ''where''  +  
−   +  
−  LiveHerd is the size of the livestock herd
 +  
−   +  
−  LDGraz is the amount of grazing land
 +  
−   +  
−  If the value of GLandCAP is less than a minimum (MinLDProd—currently hard coded as 0.01 tons of meat per hectare, based on values for the Saudi desert), then FeedDem is recalculated as the difference between the total feed requirement for the number of livestock minus the amount of feed equivalent produced by grazing using the minimum productivity.
 +  
−   +  
−  :<math>FeedDem_{r}=LiveHerd_{r}*fedreq_{r}MinLDProd*LDGraz_{r}</math>
 +  
−   +  
−  Note that this occurs when the feed from crops meets most, if not all, of the total feed requirements, implying little or no need for feed equivalents from grazing land.
 +  
−   +  
−  In the first year of the model, grazing land productivity (now called GLDCAP) and an adjustment to feed requirements per unit livestock (fedreqm) are calculated for each country. GLDCAP is initially backcalculated based on the known values of the size of the livestock herd (now called LVHERD), the feed requirement per unit livestock (fedreq —calculated as a function of GDPPC as shown above), the feed demand (now called FEDDEM), and the amount of grazing land (now called LD<sub>l=2</sub>):
 +  
−   +  
−  :<math>GLDCAP_{r}=\frac{LVHERD_{r,t=1}*fedreq_{r,t=1}FEDDEM_{r,t=1}}{LD_{r,l=2,t=1}}</math>
 +  
−   +  
−  This yields a productivity of grazing land that perfectly meets the difference between the total feed requirement and that provided by crops.
 +  
−   +  
−  Again, if the calculated value of GLDCAP is less than the assumed minimum level (MinLDProd), however, then adjustments are made. First, an adjustment factor (fedreqm) is calculated by assuming that a minimum amount of feed equivalents from grazing land are produced even if this results in a total amount of feed that is larger than necessary to meet the total feed requirement:
 +  
−   +  
−  :<math>fedreqm_{r}=\frac{LD_{r,l=2,t=1}*MinLDProd+FEDDEM_{r,t=1}}{LVHERD_{r,t=1}*fedreq_{r,t=1}}</math>
 +  
−   +  
−  Note that this value is always greater than or equal to 1 given the condition for making the adjustment. When no adjustment is made, fedreqm is set to 1.
 +  
−   +  
−  After the calculation of this adjustment factor, GLDCAP is recalculated as
 +  
−   +  
−  :<math>GLDCAP_{r}=\frac{LVHERD_{r,t=1}*fedreq_{r,t=1}*fedreqm_{r}FEDDEM_{r,t=1}}{LD_{r,l=2,t=1}}</math>
 +  
−   +  
−  which basically implies that GLDCAP will always at least as large as MinLDProd after the adjustment.
 +  
−   +  
−  The values of GLDCAP and fedreqm calculated in the first year are held constant for all forecast years
 +  
−   +  
−  In the forecast years, FEDDEM is calculated as a function of the size of the livestock herd (LVHERD), the feed requirements per unit livestock (fedreq), the amount of grazing land (LD<sub>l=2</sub>), and the productivity of grazing land (GLDCAP), but adjustments are also made reflecting the effect of global crop prices on grazing intensity (WAP<sub>f=1</sub>), changes in the efficiency with which feed is converted into. meat, and the adjustment factor fedreqm calculated in the first year. There is also a parameter with which the user can cause a brute force increase or decrease in FEDDEM ('''''agdemm<sub>f=1</sub> '' ''').
 +  
−   +  
−  <span>The model first calculates the amount of crop equivalent produced from grazing land using the following equation:</span>
 +  
−   +  
−  :<math>GLFeedEq_{r}=(LD_{r,l=2}*GLDCAP_{r})*(\frac{WAP_{f=1}}{WAP_{f=1,t1}})^{\mathbf{elglinpr}}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  '''''elglinpr'' ''' is a global parameter for the elasticity of livestock grazing intensity to annual changes in world crop prices; the basic assumption is that increasing prices should lead to increased grazing intensity and therefore greater productivity of grazing land<ref>The code, as written, ignores price effects that would reduce GLFeedEq. Since '''''elglinpr'' ''' is generally positive, this implies that decreases in world crop prices are ignored.</ref>.
 +  
−  <div>
 +  
−  This production of crop equivalents from grazing land is then subtracted from total feed requirement in the following equation:
 +  
−   +  
−  :<math>FEDDEM_{r}=(LVHERD_{r}*fedreq_{r}*fedreqm_{r}*max(0.5,(1\frac{\mathbf{livhdpro}}{100})^{t1})GLFeedEq_{r})*\mathbf{agdemm}_{r,f=1})</math>
 +  
−   +  
−  ''where''  +  
−   +  
−  '''''livhdpro'' ''' is a global parameter related to the rate at which the productivity of crops in producing meat improves over time. This part of the equation implies that the amount of feed needed to produce a unit of meat declines over time to a minimum of half the original amount required
 +  
−   +  
−  '''''agdemm'' '''(category 1) is a countryspecific multiplier that can be used to increase or decrease crop demand
 +  
−  </div><div><br/>
 +  
−  
 +  
−  <div>
 +  
−  <references />
 +  
−   +  
−  ==== <span style="fontsize:large;">Industrial Demand for Crops</span> ====
 +  
−   +  
−  Industrial demand for crops (IndDem) is initially estimated for the first year in the preprocessor. It is determined, arbitrarily, as one tenth of crop supply, which equals post loss crop production plus imports minus exports.
 +  
−   +  
−  :<math>IndDem_{r}=0.1*(AGPTot_{r}*(1LossCrop_{r})AGXCrop_{r}+AGMCrop_{r})</math>  +  
−   +  
−  It can then be decreased (increased) if the initial estimates of crop demand for food are considered too low (high).
 +  
−   +  
−  In the first year, two values related to industrial demand for crops (now called INDEM) are calculated. The first of these is a multiplicative shift factor (INDEMK), which is calculated as the ratio of relates actual to predicted industrial demand for crops. The predicted value is given by a function that relates per capita industrial demand to GDP per capita, which is shown below. <ref> Equation is INDEM = 0.0376 + 0.000704 * GDPPCP</ref> This multiplicative shift factor remains constant over time.[[File:Industrial demand for crops.pngcenterIndustrial demand for crops.png]]
 +  
−   +  
−  The same function is used to calculate an expected demand for the next year (eindem). The predicted value from the function is computed using the expected level of GDP per capita (egdppcp); this value is multiplied by the expected population (epop) and the multiplicative shift factor (INDEMK) to calculate the expected demand. This expected demand is used in conjunction with the expected demands for crops for feed and crops for food to determine the initial target growth rate in yield (tgryli) discussed in the section on crop production above.
 +  
−   +  
−  In the forecast years, the initial value of industrial demand for crops is also estimated using the table function above to get a predicted value for industrial demand per capita, which is then multiplied by population (POP) and the multiplicative shift factor (INDEMK). At this point, a regionspecific multiplier ('''''agdemm<sub>f=1</sub> '' ''') can either increase or decrease the initial estimate of INDEM.
 +  
−   +  
−  The first adjustment to INDEM is related to the world energy price (WEP) and reflects the use of crops for fuel production. Specifically, as the world energy price increases relative to the price in the first year, the industrial demand for crops increases.
 +  
−   +  
−  :<math>INDEM_{r}=INDEM_{r}*(1+\frac{WEP_{t}}{WEP_{t=1}}*FoodforFuel)</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  WEP is world energy price
 +  
−   +  
−  FoodforFuel is the elasticity of industrial use of crops to world energy prices. It starts at a value given by the global parameter '''''elagind'' ''', and declines to a value of 0 over 50 years.
 +  
−   +  
−  The second adjustment relates to the world crop price (WAP<sub>f=1</sub>); as this increases relative to the price in the first year, industrial demand for crops declines.
 +  
−   +  
−  :<math>INDEM_{r}=INDEM_{r}*(\frac{WAP_{f=1,t}}{WAP_{f=1,t}})^\mathbf{elascd}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  WAP is world crop price
 +  
−   +  
−  '''''elascd'' ''' is a global parameter specifying the elasticity of crop demand to global food prices
 +  
−   +  
−  A third adjustment is based on an assumed cap on per capita industrial demand for crops (IndemCapperPop —hard coded, declines from 0.17 to 0.12 over 50 years). Specifically, INDEM is not allowed to exceed IndemCapperPop * POP.
 +  
−   +  
−  Finally, INDEM can be reduced if the sum of expenditures on food crops at world prices (FDEM*WAP<sub>f=1</sub>) and meat (AGDEM<sub>f=2</sub>*WAP<sub>f=2</sub>) exceeds 85 percent of household consumption expenditures as calculated in the economic model.
 +  
−   +  
−   +  
−  <div>
 +  
−  
 +  
−   +  
−  <references />
 +  
−   +  
−  ==== <span style="fontsize:large;">Final Agricultural Demand Adjustments in Forecast Years</span> ====
 +  
−   +  
−  Two final adjustments are made to a number of the agricultural demand variables in the forecast years. First, if the total per capita calories from meat and crops exceed the maximum calories, i.e.
 +  
−   +  
−  :<math>sclavf_{r}*\frac{FDEM_{r}+AGDEM_{r,f=2}*lvcfr_{r}}{POP_{r}}>\mathbf{calmax}</math>
 +  
−   +  
−  then the demand for crops for food and the demand for meat in tons are scaled by the ratio of the maximum to the estimated calories
 +  
−   +  
−  :<math>FDEM_{r}=FDEM_{r}*\frac{\mathbf{calmax}}{sclavf_{r}*\frac{FDEM_{r}+AGDEM_{r,f=2}*lvcfr_{r}}{POP_{r}}}</math>  +  
−   +  
−  :<math>AGDEM_{r,f=2}=AGDEM_{r,f=2}*\frac{\mathbf{calmax}}{sclavf_{r}*\frac{FDEM_{r}+AGDEM_{r,f=2}*lvcfr_{r}}{POP_{r}}}</math>  +  
−   +  
−  Second, if the preliminary estimate of total food demand in monetary terms (csprelim), is too large of a share of consumption, i.e., if
 +  
−   +  
−  :<math>csprelim_{r}=CSF_{r}*(FDEM_{r}*WAP_{f=1,t=1}+AGDEM_{r,f=2}*WAP_{f=2,t=1})>0.85*C_{r,t=1}</math>
 +  
−   +  
−  ''where''  +  
−   +  
−  CSF is the ratio of consumer spending in the agricultural sector in the first year (CS<sub>r,s=1,t=1</sub>) to DemVal<sub>r</sub>, a weighted sum of demands for agricultural products for food in the first year
 +  
−   +  
−  :<math>DemVal_{r}=FDEM_{r,t=1}*WAP_{f=1,t=1}+AGDEM_{r,f=2,t=1}*WAP_{f=2,t=1}+AGDEM_{r,f=3,t=1}*WAP_{f=3,t=1}</math>
 +  
−   +  
−  C is total household consumption in the first year
 +  
−   +  
−  When this is the case, a series of steps are taken to bring these values back in line.
 +  
−   +  
−  1. The necessary reduction (necreduc<sub>r</sub>), which is in monetary terms, is calculated as csprelim<sub>r</sub> – 0.85*C<sub>r</sub>
 +  
−   +  
−  2. A reduction factor (reducfact) is calculated as
 +  
−   +  
−  :<math>reducfact_{r}=\frac{necreduc_{r}}{csprelim}*2</math>
 +  
−   +  
−  with a maximum value of 1
 +  
−   +  
−  3. The physical demands for crops for feed (FEDDEM), crops for industry (INDEM), and meat in tons (AGP, category 2) are all reduced by reducfact, and the value of the meat reduction is saved for the next step
 +  
−   +  
−  :<math>FEDDEM_{r}=FEDDEM_{r}*(1reducfact_{r})</math> <math>INDEM_{r}=INDEM_{r}*(1reducfact_{r})</math>
 +  
−  :<math>meatreduc_{r}=AGDEM_{r,f2}*reducfact_{r}</math> <math>AGDEM_{r,f=2}=AGDEM_{r,f2}*(1reducfact_{r})</math>
 +  
−   +  
−  4. An estimate of the necessary reductions in crops for food, in monetary terms is estimated by subtracting the savings obtained through the reduction in meat demand
 +  
−   +  
−  :<math>foodreduc_{r}=recreduc_{r}meatreduc_{r}*CSF_{r}*WAP_{f=2,t=1}</math>  +  
−   +  
−  5. The physical demand for crops for food (FDEM) is then reduced as follows
 +  
−   +  
−  :<math>FDEM_{r}=Max(0.1*FDEM_{r},FDEM_{r}\frac{foodreduc_{r}}{CSF_{r}*WAP_{f=1,t=1}})</math>
 +  
−   +  
−  Note that this ensures that FDEM is not reduced by more than ninety percent.
 +  
−   +  
−  Finally, given the changes above, the total demand for crops is recalculated as the sum of the final values of feed, industry, and food demand.
 +  
−   +  
−  :<math>AGDEM_{r,f=1}=FEDDEM_{r}+INDEM_{r}+FDEM_{r}</math>
 +  
−  </div></div></div></div></div></div>
 +  
−  == <span style="fontsize:xlarge;">Trade</span> ==
 +  
−   +  
−  Consistent with the approaches within both the economic model and the energy model, trade of agricultural products in IFs uses a pooled approach rather than a bilateral one. That is, we can see the total exports and imports of each country/region, but not the specific volume of trade between any two. Offered exports and demanded imports from each country/region are responsive to the past shares of export and import bases and are summed globally. The average of the totals is taken as the actual level of global trade and the country exports and imports are normalized to that level.
 +  
−   +  
−  Price differentials across countries do not influence agricultural trade. Although the IFs project has experimented over time with making such trade responsive to prices, there is an increasing tendency globally for food prices to be more closely aligned across countries than was true historically. Moreover, the use within IFs of local relative food surpluses or deficits (as indicated by stock levels) to adjust trade patterns is an effective proxy for the use of prices.
 +  
−   +  
−  The initial year values of the imports (AGM) and exports (AGX) of the three agricultural commodities in physical quantities are determined in the preprocessor. Since we only have historical data on the imports and exports of fish in monetary terms, these need to be converted to physical terms. This is done by multiplying the monetary values, which are in $billion, by 1000*/2200 to get physical values in million tons. In addition, exports of fish are limited to be less than 70 percent of total fish available and imports less than 1 percent of total fish available. For each of the three agricultural commodity groupings, if there is an imbalance between global imports and global exports in the preprocessor, the latter takes precedence and national imports are adjusted to bring global imports into line with global exports.
 +  
−   +  
−  In the first year, seven variables are set related to trade for each commodity: XKAVE, MKAVE, XKAVMAX, MKAVMAX at the country level and wxc<sub>t=1</sub>, wmd<sub>t=1</sub>, and WAP<sub>t=1</sub> at the global level.
 +  
−   +  
−  XKAVE and MKAVE are moving average values of export and import propensity, respectively. They are specified as the ratio of agricultural exports and imports to a base value (xbase) for each commodity. For exports, this is basically the sum of production and demand for that commodity; for imports, it is just demand.
 +  
−   +  
−  :<math>XKAVE_{r,f=13,t=1}=\frac{AGX_{r,f=13,t=1}}{AGP_{r,f=13,t=1}+AGDEM_{r,f=13,t=1}}</math> <math>MKAVE_{r,f=13,t=1}=\frac{AGM_{r,f=13,t=1}}{AGDEM_{r,f=13,t=1}}</math>  +  
−   +  
−  XKAVMAX and MKAVMAX are maximum values of XKAVE and MKAVE. For crops and meat, XKAVMAX is set to 1.1 times XKAVE, but is not allowed to exceed a value of 0.7; MKAVMAX is set to 1.5 times XKAVE, but also is not allowed to exceed a value of 0.7. For fish, XKAVMAX is set to 1.1 times XKAVE, with a bound of 0.95; MKAVE is set to 1.5 times MKAVE, with a bound of 2. These values are held constant for all future years.
 +  
−   +  
−  XPriceTermLag, and MPriceTermLag are set to 0 for all commodities. wxc and wmd are the total world agricultural exports and imports; these are set to a value of 1 in the first year. WAP is the initial world price index for each commodity, which is set to 100.
 +  
−   +  
−  In the forecast years, the process for determining agricultural imports and exports involves the following steps:
 +  
−   +  
−  #Estimating the agricultural export capacity and agricultural import demand for each country.
 +  
−  #Reconciling the differences between global agricultural export capacity and global agricultural import demand.
 +  
−  #Computing the actual levels of agricultural exports and agricultural imports for each country
 +  
−   +  
−  The agricultural export capacity is estimated by multiplying the export propensity (XKAVE) by the current year’s production and demand. It is also limited by XKAVMAX:
 +  
−   +  
−  :<math>AGX_{r,f=13}=MIN(XKAVE_{r,f=13},XKAVMAX_{r,f=13})*(AGP_{r,f=13}+AGDEM_{r,f=13})</math>
 +  
−   +  
−  Similarly, the agricultural import demand is estimated by multiplying the import propensity (MKAVE) by the current year’s demand, with a limit set by MKAVMAX
 +  
−   +  
−  :<math>AGM_{r,f=13}=MIN(MKAVE_{r,f=13},MKAVMAX_{r,f=13})*AGDEM_{r,f=13}</math>
 +  
−   +  
−  For each country, values are also estimated for its net surplus or deficit (surpdef) for each commodity. This is based on the following factors: 1) postloss production, 2) domestic demand, 3) the difference between current and desired stocks, and 4) a trade term
 +  
−   +  
−  :<math>surpdef_{r,f=13}=AGP_{r,f=13}*(1LOSS_{r,f=13})AGDEM_{r,f=13}+cumstk_{r,f=13}agdstl*(AGP_{r,f=13}+AGDEM_{r,f=13})+TradeTerm_{r,f=13}</math>
 +  
−   +  
−  The first three factors are straightforward. Production minus demand reflects a basic net surplus, which is then adjusted by any net surplus in stocks. The TradeTerm is related the relative role a country plays in global imports and exports and is given as:
 +  
−   +  
−  :<math>TradeTerm_{r,f=13}=(\frac{AGM_{r,f=13}}{wmd_{f=13,t1}}\frac{AGX_{r,f=13}}{wxc_{f=13,t1}})*\frac{wmd_{f=13,t1}+wxc_{f=13,t1}}{2}</math>
 +  
−   +  
−  The TradeTerm is positive (negative) when a country has a larger (smaller) share of the global imports than it does of the global exports of a particular commodity and vice versa. Since the TradeTerm is is added to surpdef, it acts as a balancing mechanism; countries that appear as relatively larger (smaller) importers get a positive (negative) boost to their estimated net surplus, which tends to reduce (increase) imports as shown below.
 +  
−   +  
−  At this point, the global sum of exports and imports across countries will likely differ. Therefore, a procedure is required to balance these. In preparation for this one more global variable and several countrylevel variables are calculated. The global variable is globalsurdefrate, which is the ratio of the sum across countries of net surplus divided by the sum across countries of demand and production, which is the stock base.
 +  
−   +  
−  :<math>globalsurdefrate_{f=13}=\frac{\Sigma_{r}surpdef_{r,f=13}}{\Sigma_{r}(AGDEM_{r,f=13}+AGP_{r,f=13})}</math>  +  
−   +  
−  The countrylevel variables are as follows:
 +  
−   +  
−  The first term modifies the country’s net surplus, increasing (decreasing) it when the global net surplus is negative (positive).
 +  
−   +  
−  :<math>countryextrasurdef_{r,f=13}=surpdef_{r,f=13}globalsurdefrate_{f=13}*(AGDEM_{r,f=13}+AGP_{r,f=13})</math>
 +  
−   +  
−  The second term modifies how rapidly the net surplus is closed.
 +  
−   +  
−  :<math>countryextrasurdefadj_{r,f=13}=\frac{countryextrasurdef_{r,f=13}}{5}</math>
 +  
−   +  
−  The third term is simply the ratio of exports to the sum of imports and exports.
 +  
−   +  
−  :<math>exportshare_{r,f=13}=\frac{AGX_{r,f=13}}{AGX_{r,f=13}+AGM_{r,f=13}}</math>
 +  
−   +  
−  The next step is to calculate whether it is necessary to increase (decrease) imports and decrease (increase) exports for each country, and by how much. Whether a country needs to increase its initial estimates of imports and decrease its initial estimates of exports, or vice versa, is determined by the sign of countryextrasurdef. If this value is negative, i.e., the country has a net deficit, it will need to reduce exports and increase imports. The opposite holds for when countryextrasurdef is positive.
 +  
−   +  
−  As for the amount by which imports and exports need to be increased or decreased, this is a function, in general, of the size of the necessary adjustment and the export share:
 +  
−   +  
−  :<math>AGX_{r,f=13}=AGX_{r,f=13}+countryextrasurfdefadj_{f=13}*exportshare_{r,f=13}</math> <math>AGM_{r,f=13}=AGM_{r,f=13}countryextrasurfdefadj_{f=13}*(1exportshare_{r,f=13})</math>
 +  
−   +  
−  Note that the sign of countryextrasurdef and the fact that exportshare is a value between 0 and 1 ensure that when exports increases, imports fall, and vice versa.<ref>Two other variables, defadjmul and ImportBoost, are included in the calculations to make some finer adjustments to the changes in exports and imports; these relate to the observed behavior for specific countries and are not discussed in detail here.</ref> Finally, in this adjustment process, exports and imports are not allowed to fall by more than half or more than double.
 +  
−   +  
−  This process may not fully reconcile global trade, so a final adjustment is made by setting world trade (WT) as the average of global exports and imports and then adjusting the country values accordingly:
 +  
−   +  
−  :<math>WT_{f=13}=\frac{\Sigma_{r}AGX_{r,f=13}+\Sigma_{r}AGM_{r,f=13}}{2}</math> <math>AGX_{r,f=13}=AGX_{r,f=13}*\frac{WT_{f=13}}{\Sigma_{r}AGX_{r,f=13}}</math> <math>AGM_{r,f=13}=AGM_{r,f=13}*\frac{WT_{f=13}}{\Sigma_{r}AGM_{r,f=13}}</math>
 +  
−   +  
−  IFs can now update the moving average export (XKAVE) and import (MKAVE) propensities for the next time step. The weights given to history are set by the global parameters '''''xhw'' ''' and '''''mhw'' '''. For small exporters, i.e., where exports are less than one tenth of the sum of production and demand, '''''xhw'' ''' is reduced by 40 percent, allowing for faster adjustment. XKAVE and MKAVE are updated as
 +  
−   +  
−  :<math>XKAVE_{r,f=13,t+1}=XKAVE_{r,f=13}+(1\mathbf{xhw})*\frac{AGX_{r,f=13}}{AGP_{r,f=13}+AGDEM_{r,f=13}}</math>
 +  
−  :<math>MKAVE_{r,f=13,t+1}=XMAVE_{r,f=13}+(1\mathbf{mhw})*\frac{AGM_{r,f=13}}{AGDEM_{r,f=13}}</math>
 +  
−   +  
−  For crops, the import propensity is bound from below by a factor given by potential GDP (GDPPOT), demand (AGDEM), the conversion factor between agricultural imports in physical terms and dollar values (msf, see section on links to the economic model), and the initial world price for agriculture (WAP).
 +  
−   +  
−  :<math>XKAVE_{r,f=13,t+1}\ge\frac{0.6*GDPPOT_{r}}{AGDEM_{r,f=13}*msf_{r}*WAP_{f,t=1}}</math>
 +  
−   +  
−  Finally, XKAVE and MKAVE are bound from above by XKAVMAX and MKAVMAX, respectively.
 +  
−  <div>
 +  
−  
 +  
−  <references /></div>
 +  
−  == <span style="fontsize:xlarge;">Stocks</span> ==
 +  
−   +  
−  Due to a lack of good historical data, in the first year, stocks for all three agricultural commodities are assumed to equal desired stocks. These are set to a fraction (''agdstl) ''of total production (AGP) and demand (AGDEM) for each commodity.
 +  
−   +  
−  :<math>FSTOCK_{r,f=13}=(AGP_{r,f=13}+AGDEM_{r,f=13})*agdstl</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  agdstl is a parameter used to set desired stock levels for agricultural commodities. It is set to be 1.5 times '''''dstl'' ''', which is a global parameter that can be adjusted by the user
 +  
−   +  
−  In future years, basic stock levels (cumstk) increase with production (AGP) as adjusted for loss before reaching market (LOSS), decrease with demand or consumption (AGDEM), and adjust for net imports (AGMAGX).
 +  
−   +  
−  :<math>cumstk_{r=13}=FSTOCK_{r,f=13,t1}+StkAdj_{r,f=13}</math> <math>StkAdj_{r,f=13}=AGP_{r,f=13}*(1LOSS_{r,f=13})AGDEM_{r,f=13}+(AGM_{r,f}AGX_{r,f=13})</math>  +  
−   +  
−  Of course, the actual stock values (FSTOCK) are not allowed to go negative. If the basic stock level is negative, stocks are set at zero and a shortage (SHO) exists, which affects calorie availability. If the basic stock level is positive there is no shortage and stocks equal the basic level.
 +  
−   +  
−  :if <math>cumstk_{r,f=13}<0</math> then <math>SHO_{r,f=13}=StkAdj_{r,f=13}</math> and <math>FSTOCK_{r,f=13}=0</math>  +  
−   +  
−  :if <math>cumstk_{r,f=13}>0</math> then <math>SHO_{r,f=13}=0</math> and <math>FSTOCK_{r,f=13}=cumstk_{r,f}</math>  +  
−   +  
−  == <span style="fontsize:xlarge;">Calorie Availability</span> ==
 +  
−   +  
−  Daily per capita calorie availability (CLPC) is initialized in the preprocessor. Where available, data is taken from the FAO<ref>Note this occurs in DATAPOP, not DATAAGRI. The historic data series is SERIESCalPCap. Missing data are estimated based on access to water and sanitation or average income.</ref>. It is multiplied by population (POP) to yield total daily calorie availability and brought into the model with the name CLAVAL. We already saw that this first year value is used in the calculation of two countryspecific factors: 1) calactpredrat, which is a shift factor determined as the ratio of calorie availability to predicted calorie demand in the first year, and 2) sclavf, which is a conversion factor relating the total annual demand for food crops and crop equivalents from meat to daily calorie availability.
 +  
−   +  
−  In the forecast years, CLAVAL depends upon the demand for food crops and meat, but also any shortages in crops or meat. The specific shortage is calculated as
 +  
−   +  
−  :<math>{claval_1}_{r}=SHO_{r,f=1}*\frac{FDEM_{r}}{AGDEM_{r,f=1}}+SHO_{r,f=2}*lvcfr_{r}</math>
 +  
−   +  
−  CLAVAL is then calculated as
 +  
−   +  
−  :<math>CLAVAL_{r}=sclavf_{r}*(FDEM_{r}+AGDEM_{r,f=2}*lvcfr_{r}{claval_1}_{r}</math>
 +  
−   +  
−  Calorie availability combines with regional calorie need in the population model for the calculation of possible starvation deaths (a seldom used variable because in official death statistics people do not die of starvation but rather of diseases associated with undernutrition); the population and health models therefore look instead to the impact of calorie availability on undernutrition and health. <references />
 +  
−   +  
−  == <span style="fontsize:xlarge;">Prices</span> ==
 +  
−   +  
−  IFs keeps track of both national (FPRI) and world (WAP) price indices for each of the three agricultural commodities. All of these are set to an index value of 100 in the building of the base.
 +  
−   +  
−  The national crop price indices (FPRI, category (1) respond to: 1) changes in global costs of crop production, the latter being expressed as the ratio of global accumulated capital investment in crops to global production and 2) changes in the level of domestic crop stocks. The first factor should provide a longterm basis for rising or falling prices tied to changing technology and other factors of production; the second factor generally should represent shorterterm market variations from that longterm level.
 +  
−   +  
−  The impact of global costs is given by dividing the ratio of global investment in crops to global production (wkagagpr) in the current year to that same ratio in the first year. The effect of stocks on crop prices (Mul) is calculated using the same ADJSTR function introduced in the description of crop supply, which considers the difference between both the current crop stocks and a desired vale and between current crop stocks and those in the previous year. Two parameters control the degree to which these two ‘differences’ affect the calculation of the adjustment factor. In this case, these are the global, usercontrollable parameters '''''fpricr1'' ''' and '''''fpricr2'' '''. All together the equation for domestic crop price indices in the coming year is given as
 +  
−   +  
−  :<math>FPRI_{r,f=1,t+1}=WAP_{f=1,t=1}*\frac{wkagagpr_{r,t}}{wkagagpr_{r,t=1}}*Mul_{r}</math>  +  
−   +  
−  The domestic crop price indices are also bound between 0.01 and 1000.
 +  
−   +  
−  The national meat price indices are linked the global crop price. Specifically, they are given as a moving average of the global crop price index.
 +  
−   +  
−  :<math>FPRI_{r,f=2,t+1}=\mathbf{fprihw}*FPRI_{r,f=2,t}+(1\mathbf{fprihw})*WAP_{f=1,t}</math>
 +  
−   +  
−  ''where''
 +  
−   +  
−  '''''fprihw'' ''' is a global parameter used to control the speed at which the domestic meat price changes.
 +  
−   +  
−  The national fish price indices are all set equal to the global fish price index. The determination of the global fish price is similar to that for the national crop price, but here the stock of interest is the global stock and there is no effect related to costs. The ADJSTR function is used once again to calculate the adjustment factor (MUL), this time focusing on the desired global fish stock, the difference between this and the current global fish stock, and the change in the global fish stock in the past year. Again, two parameters control the degree to which these two "differences" affect the calculation of the adjustment factor. In this case, these are the global, usercontrollable parameters '''''fprim1'' ''' and '''''fprim2'' ''' [file:///C:/Users/Ara/Desktop/Agricultural%20Documentation%20v19_AG.docx#_msocom_1 [U1]] . The global and national fish prices are thus calculated as
 +  
−   +  
−  :<math>FPRI_{r,f=3,t+1}=WAP_{f=3,t+1}=WAP_{f=3,t}*Mul</math>  +  
−   +  
−  The world price indices for crops and meat are computed, in the following year, as a weighted average of the domestic prices, with the weights given by crop and meat production:
 +  
−   +  
−  :<math>WAP_{r,f=12,t+1}=\frac{\Sigma_{r}(FPRI_{r,f=12,t+1}*AGP_{r,f=12,t+1})}{\Sigma_{r}AGP_{r,f=12,t+1}}</math>
 +  
−   +  
−  == <span style="fontsize:xlarge;">Returns and Profits</span> ==
 +  
−   +  
−  IFs estimates the net returns in agriculture (AGReturn) for each commodity, based upon production costs and net revenues. Agricultural profits (FPROFIT) depend on the gross returns to production (GReturn) relative to the costs of production. At some points in the evolution of IFs we have used these profits as a guide to rates of investment; the current formulation for investment does not use them.
 +  
−   +  
−  The production costs for crops are estimated as the cost of cropland, priced at the cost of new land development (CLD), plus the investment in agricultural capital (KAG). The net revenues are given as total yield times the domestic crop price index. This results in
 +  
−   +  
−  :<math>ProdCost_{r,f=1,t}=LD_{r,l=1,t}*CLD_{r,t}+KAG_{r,t}</math> <math>GReturn_{r,f=1,t}=(LD_{r,l=1,t}*byl_{r,t})*FPRI_{r,f=1,t+1}</math>  +  
−   +  
−  For meat, production costs are estimated by the value of the crop equivalents produced by grazing and the cost of feed, where the value is given by the domestic meat price index. The net revenues are based on the size of the herd and the domestic meat price index. This results in
 +  
−   +  
−  :<math>ProdCost_{r,f=2,t}=(LD_{r,l=2,t}*GLDCAP_{r,t}+FEDDEM_{r,t})*FPRI_{r,f=2,t+1}</math>  +  
−  :<math>GReturn_{r,f=2,t}=LVHERD_{r,t}*FPRI_{r,f=2,t+1}</math>
 +  
−   +  
−  For fish, the production costs are simply estimated by the total production of fish times the domestic meat price index. The net revenues are given as the total production of fish times the domestic fish price index. This implies
 +  
−   +  
−  :<math>ProdCost_{r,f=3,t}=FISH_{r,t}*FPRI_{r,f=2,t+1}</math>  +  
−   +  
−  :<math>GReturn_{r,f=3,t}=FISH_{r,t}*FPRI_{r,f=3,t+1}</math>  +  
−   +  
−  The net returns for each commodity can then be calculated as
 +  
−   +  
−  :<math>AGReturn_{r,f=13,t}=\frac{GReturn_{r,f=13,t}}{ProdCost_{r,f=13,t}}</math>
 +  
−   +  
−  These net returns are used to account for changes in profits over time, using the variable FPROFITR, which influences investment in agriculture. This variable is calculated for each commodity as
 +  
−   +  
−  :<math>FPROFIT_{r,f=13,t}=\frac{AGReturn_{r,f=13,t}}{AGReturn_{r,f=13,t=1}}</math>  +  
−   +  
−  A similar variable (wfprofitr) is calculated at the global level as a production weighted average of country/region values, but only for crops.
 +  
−   +  
−  == <span style="fontsize:xlarge;">Investment</span> ==
 +  
−   +  
−  Investment in agriculture is relatively complex in IFs, because changes in investment are the key factor that allows us to clear the agricultural market in the long term. It is very similar to investment in energy, except that we do not need to compute typespecific investments—capital in agriculture is only used for the production function of crops.
 +  
−   +  
−  We calculate a total agricultural investment need (INAG) to take to the economic model and place into the computation for investment among sectors. This investment involves multiple factors. These begin with the rate of investment within GDP of the previous year applied to the GDP of the current year, adjustment factors related to domestic and global crop stocks, and changes in the ratio of global crop demand to global GDP. This is expressed as
 +  
−   +  
−  :<math>INAG_{r,t}=INAG_{r,t1}*\frac{GDP_{r,t}}{GDP_{r,t1}}*mulwst_{t}*mulst_{r,t}*\frac{(\frac{WAGDEM_{r,t}}{WGDP_{r,t}})}{(\frac{WAGDEM_{r,t1}}{WGDP_{r,t1}})}</math>
 +  
−   +  
−  ''where''  +  
−   +  
−  mulwst and mulst are adjustment factors related to global and domestic crop stocks, respectively. Both use the ADJSTR function described earlier. For mulwst, the values for the effects of the gaps between existing and desired stocks, and for the change in stocks, are hard coded with values of 0.3 and 0.9, respectively. For mulst, these parameters are hard coded with values of 0.2 and 0.4, respectively.
 +  
−   +  
−  WAGDEM is the total global demand for crops
 +  
−   +  
−  As an initial check against too rapid of a shift in demand for agricultural investment, INAG is not allowed to increase by more than 30 percent or decrease by more than 25 percent from the actual investment in the current year. A second check ensures that the demand is no less than 0.5 percent and no greater than 40 percent of current agricultural capital (KAG).
 +  
−   +  
−  At this point the countryspecific multiplier '''''aginvm'' ''' can boost or reduce INAG. One final check ensures that as long as GDP in the country is larger than it was in the first year, the demand for agricultural investment is not allowed to decline at an annual rate of more than 1 percent per year from the first year.
 +  
−   +  
−  Investment need (INAG) then enters the economic model, which returns an adjusted value that feeds into further calculations in the agriculture model.
 +  
−   +  
−  == <span style="fontsize:xlarge;">Economic Linkages</span> ==
 +  
−   +  
−  Several variables, such as gross production, stocks, consumer spending, trade, prices and investment, are common to both the economic model and the two physical models. But hardly ever will the economic and physical models produce identical values, even during the first time step when both utilize "data." Thus, although we want the physical model value to override that of the economic model, it cannot simply replace it. Instead IFs extensively uses a procedure of computing an adjustment coefficient during the first time step. That coefficient is the ratio of the value in the economic model to the value in the physical model. In subsequent years IFs uses that coefficient to adjust the value from the physical model before its introduction into the economic model.
 +  
−   +  
−  Gross production (ZS) in the agricultural sector illustrates this procedure. The value of gross production in the agricultural model is the sum of the products of agricultural production (AGP) and prices (WAP) in each agricultural category. Multiplying that times an adjustment factor (ZSF) computed in the first time stop to assure intermodel consistency produces gross production for the economic (ZS). World average prices (WAP) are used in all the economic/physical model conversions because they assure that global sums (e.g. of exports and imports) will balance.<ref>s in the subscript represents economic sector. s = 1 is defined as the agriculture sector.</ref>
 +  
−   +  
−  :<math>ZS_{r,s=1}=ZSF_{r}*\Sigma_{f}(WAP_{f,t=1}*AGP_{r,f,t})</math>  +  
−   +  
−  ''where''  +  
−   +  
−  :<math>ZSF_{r}=\frac{\mathbf{ZS}_{r,s=1}}{\Sigma_{f}(WAP_{f,t=1}*AGP_{r,f,t=1}}</math>
 +  
−   +  
−  Similarly, food stocks in each category (FSTOCK) and an adjustment factor (FSF) produce stocks (ST) for the economic model.
 +  
−   +  
−  :<math>ST_{r,s=1}=FSF_{r}*\Sigma_{f}(FSTOCK_{r,f,t}*WAP_{f,t=1})</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  :<math>FSF_{r}=\frac{\mathbf{ST}_{r,s=1}}{\Sigma_{f}(FSTOCK_{r,f,t=1}*WAP_{f,t=1})}</math>
 +  
−   +  
−  A similar translation is made for consumer spending on agricultural commodities, recognizing that not all crop demand is directly by consumers. <math>CS_{r,s=1}=CSF_{r}*(FDEM_{r,t}*WAP_{f=1,t=1}+\Sigma_{f=2,3}(AGDEM_{r,f,t}*WAP_{f,t=1}))</math>
 +  
−   +  
−  ''where''
 +  
−   +  
−  :<math>CSF_{r}=\frac{\mathbf{CS}_{r,s=1}}{FDEM_{r,t=1}*WAP_{f=1,t=1}+\Sigma_{f=2,3}(AGDEM_{r,f,t}*WAP_{f,t=1})}</math>  +  
−   +  
−  In the same fashion exports (AGX) and imports (AGM) from the agricultural model allow calculation of exports (XS) and imports (MS) for the economic model.
 +  
−   +  
−  :<math>XS_{r,s=1}=xsf_{r}*\Sigma_{f}(AGX_{r,f,t}*WAP_{f,t=1})</math>
 +  
−   +  
−  ''where''
 +  
−   +  
−  :<math>xsf_{r}=\frac{\mathbf{XS}_{r,s=1}}{\Sigma_{f}(AGX_{r,f,t=1}*WAP_{f,t=1})}</math>
 +  
−   +  
−  and
 +  
−   +  
−  :<math>MS_{r,s=1}=msf_{r}*\Sigma_{f}(AGX_{r,f,t}*WAP_{f,t=1})</math>
 +  
−   +  
−  ''where''
 +  
−   +  
−  :<math>msf_{r}=\frac{\mathbf{MS}_{r,s=1}}{\Sigma_{f}(AGN_{r,f,t}*WAP_{f,t=1})}</math>  +  
−   +  
−  A check and, if necessary, adjustment is made ensure that the monetary values of imports and exports match up at the global level.
 +  
−   +  
−  :<math>XS_{r,s=1}=XS_{r,s=1}*\frac{\frac{\Sigma_{r}(XS_{r,s=1})+\Sigma_{r}(MS_{r,s=1})}{2}}{\Sigma_{r}(XS_{r,s=1})}</math>  +  
−   +  
−  and
 +  
−   +  
−  :<math>MS_{r,s=1}=MS_{r,s=1}*\frac{\frac{\Sigma_{r}(XS_{r,s=1})+\Sigma_{r}(MS_{r,s=1})}{2}}{\Sigma_{r}(MS_{r,s=1})}</math>
 +  
−   +  
−  With respect to prices, the agriculture model passes to the economic model a value (PRI), which reflects the ratio of the current domestic crop price index to the initial world crop price index.
 +  
−   +  
−  :<math>PRI_{r,s=1}=\frac{FPRI_{r,f=1}}{WAP_{r,f=1,t=1}}</math>
 +  
−   +  
−  Finally, investment need (INAG) is passed to the economic model under the variable name IDS, category 1 (agriculture).
 +  
−  <div><br/>
 +  
−  
 +  
−  <references /></div>
 +  
−  == <span style="fontsize:xlarge;">Capital Dynamics</span> ==
 +  
−   +  
−  The economic model of IFs returns a (potentially) modified value of IDS, category 1, reflecting the total amount of capital available for agriculture. This value is assigned to the variable iaval, which overrides the value of INAG calculated earlier (earlier it was basically investment demand; after return from the economic model it becomes investment supply).<ref>IFs does have a global parameter '''''agon'' ''' that can be used to break the link between the agriculture and economic model, in which case INAG is not overwritten. This is done by setting '''''agon'' ''' to a value less than 0.5. Doing so treats the agriculture model as a partial equilibrium model rather than a general equilibrium model.</ref> The agriculture model divides the investment available for agriculture (iaval) into investment for cropland development and investment for other agriculture capital. The coefficient IALK indicates the portion going to cropland development.
 +  
−   +  
−  IALK is set to a default value of 0.25 for all countries in the preprocessor. In forecast years, IALK changes from this initial value depending on change in the ratio of return on land (RETR) to return on capital (RETK).
 +  
−   +  
−  IFs calculates the return rate on land as the crop yield (YL) in the first year divided by the current cost of developing a unit of cropland (CLD).
 +  
−   +  
−  :<math>RETLD_{r}=\frac{YL_{r,t=1}}{CLD_{r,t}}</math>  +  
−   +  
−  The return on capital depends on the difference between the hypothetical level of crop yield (HYL) that could be obtained from an additional unit investment in agricultural capital and the current crop yield. Recalling how crop yield is estimated, the hypothetical crop yield is given as
 +  
−   +  
−  :<math>HypothYL_{r}=cD_{r}*agtec_{r}*(KAG_{r}+1)^{ALPHA_{r}}*(labagi_{r})^{(1ALPHA_{r})}*satk_{r}</math>  +  
−   +  
−  and the return on capital is given as
 +  
−   +  
−  :<math>RETCap_{r}=LD_{r,l=1}*(HypothYL_{r}byl_{r})</math>  +  
−   +  
−  The ratio of the return to land to the return to capital (RETRAT) is given as
 +  
−   +  
−  :<math>RETRAT_{r}=\frac{RETLD_{r}}{RTCap_{r}}</math>  +  
−   +  
−  The adjustment of IALK uses the same first and second order adjustment mechanism that we have seen before with the ADJSTR function. Here the ‘target’ level is the ratio of the return to land to the return to capital in the first year.
 +  
−   +  
−  :<math>IALK_{r,t+1}=IALK_{r,t=1}*(1+\frac{RETRAT_{r}RETRAT_{r,t=1}}{1})^{\mathbf{eliasp1}}*(1+\frac{RETRAT_{r}RETRAT_{r,t1}}{1})^{\mathbf{eliasp2}}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  '''''eliasp1'' ''' and '''''eliasp2'' ''' are global parameters
 +  
−   +  
−  Two final checks are made on the value of IALK. First, it is not allowed to exceed a value related to the cost of replacing depreciated investment in land
 +  
−   +  
−  :<math>IALK_{r,t+1}\le\frac{(0.05*LD_{r,l=3}+\mathbf{dkl}*LD_{r,l=1})*CLD_{r}}{iaval_{r}}</math>
 +  
−   +  
−  Second, IALK is bound between 0.1 and 0.8.
 +  
−   +  
−  Finally the model updates agricultural capital (KAG) for the next year by subtracting depreciation as represented by agricultural capital lifetime ('''''lks'' '''), adding the residual (nonland) investment, and adjusting for any civilian damage from warfare (CIVDM – see international politics model documentation).
 +  
−   +  
−  :<math>KAG_{r,t+1}=KAG_{r,t}\frac{KAG_{r,t}}{\mathbf{lks}_{s=1}}+iaval_{r}*(1IALK_{r,t+1})*(1CIVDM_{r})</math>  +  
−   +  
−  <references />  +  
−   +  
−  == <span style="fontsize:xlarge;">Land Dynamics</span> ==
 +  
−   +  
−  Land in IFs is divided into five categories—crop, grazing, forest, urban, and other land. Historical data on total land area (LDTot), crop land (LD<sub>l=1</sub>), grazing land (LD<sub>l=2</sub>), forest land (LD<sub>l=3</sub>), and other land (LD<sub>l=4</sub>) are taken from FAO data. Historical data on urban land (LD<sub>l=5</sub>) is taken from WRI. A few adjustments to the historical data are made in the preprocessor.
 +  
−   +  
−  *Cropland is not allowed to exceed total crop production divided by 14, which places an effective limit on yield of 14 tons per hectare.
 +  
−  *Grazing land, forest land, and other land are bound from below to be at least 1000 hectares.
 +  
−  *If urban land is more than three quarters the area of other land, land is shifted from urban to other land
 +  
−   +  
−  After these changes, total land area is recomputed as the sum of the area of the individual land categories.
 +  
−   +  
−  The preprocessor also reads in a value for potentially arable land (landarablepot), which affects the amount of potential cropland in the model.
 +  
−   +  
−  One final variable is estimated related to land in the preprocessor. This is the target rate of growth of cropland (tgrld). When data is available, this is currently estimated as the growth rate of cropland between the years 1992 and 2001.
 +  
−   +  
−  :<math>tgrld_{r}=(\frac{LD_{r,l=1,yr=2001}}{LD_{r,l=1,yr=1992}})^{1/9}1</math>  +  
−   +  
−  <span>When no data are available for cropland in either 1992 or 2001, the target rate of growth of cropland is estimated as a function of average income</span>
 +  
−   +  
−  :<math>tgrld_{r}=0.0090.011*MIN(1,\frac{GDPPCP_{r}}{30})</math>
 +  
−   +  
−  <span>with a maximum growth rate given as a function of cropland as a share of total land</span>
 +  
−   +  
−  :<math>tgrld_{r}\le tmaxgrow_{r}=0.0150.01*MIN(1,0.5*\frac{LD_{r,l=1}}{LDTot_{r}})</math>  +  
−   +  
−  Finally, this target growth rate is restricted to fall between 0.003 and +0.01.
 +  
−   +  
−  In the first year, IFs estimates an initial unit cost of cropland development (CLD) as
 +  
−   +  
−  :<math>CLD_{r,t=1}=\frac{IDS_{r,s=1,t=1}*IALK_{r,t=1}}{LD_{r,l=1,t=1}*(\mathbf{dkl}+tgrld_{r})}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  IDS is the total investment in agriculture
 +  
−   +  
−  IALK is the share of agricultural investment going to cropland development
 +  
−   +  
−  '''dkl''' is a global parameter indicating the depreciation rate of investment in cropland, essentially a maintenance cost for existing cropland
 +  
−   +  
−  ''tgrld is the target growth rate for cropland''
 +  
−   +  
−  A related factor (SCLDF), to be used in determining the cost of land development in future years, is also calculated in the first year
 +  
−   +  
−  :<math>SCLDF_{r}=\frac{CLD_{r,t=1}}{LD_{r,l=1,t=1}}</math>  +  
−   +  
−  <span>IFs calculates changes in land use for the coming year as a result of four key dynamic processes. First, changes in urban land may result from income and population changes. Second, economic shifts related to investment, particularly in the agricultural sector, can affect the amount of cropland. Third, IFs there can be expansion or retirement of grazing land for undefined reasons. Finally, in certain scenarios, specific changes in forest land can result from policies related to issues such as conservation and environmental protection</span>
 +  
−   +  
−  ==== <span style="fontsize:large;">Changes in Urban Land from Income and Population Changes</span> ====
 +  
−   +  
−  Changes in urban land result from changes in population and income. IFs first estimates a predicted level of urban land (LandUrbanPred), which is then compared to current urban land. Any changes are assumed to affect all other land types proportionately, unless this leads to not enough land in a particular category. The assumptions about the drivers of the predicted level of urban land differ somewhat between countries depending upon their state of development, as measured by average income, in the base year.
 +  
−   +  
−  For initially not as well off countries, GDPPCP in the base year < 5, the predicted level of urban land (LandUrbanPred) is estimated as a function of population and income growth. The growth with income is based on an estimated relationship between income and urban land per capita (landurbanr) summarized in the figure on the right<ref>Equation is Urban land per Capita = 0.021 + 0.0039*GDPPCP when GDPPCP < 1.92 in the base year and Urban land per Capita = 0.01 + 0.0283*ln(GDPPCP) when GDPPCP >= 1.92 in the base year.</ref>.[[File:Changes in Urban land from Y and population changes.pngcenterChanges in Urban land from Y and population changes.png]]
 +  
−   +  
−  The predicted level of urban land (LandUrbanPred) is then given as
 +  
−   +  
−  :<math>LandUrbanPred_{r}=LD_{r,l=4,t=1}*(\frac{POP_{r,t}}{POP_{r,t=1}})*(\frac{landurbanr_{r,t}}{landurbanr_{r,t=1}})</math>
 +  
−   +  
−  For initially well off countries, GDPPCP in the base year > 5, the predicted level of urban land is estimated as a function of population change. If population increases from the base year, is assumed to be same as urban land in the base year. If population declines from the base year, the predicted urban land area is estimated to decline, but only half as much as the population decline
 +  
−   +  
−  :<math>LandUrbanPred_{r}=LD_{r,l=4,t=1}*(1(10.5*\frac{POP_{r,t}}{POP_{r,t=1}}))</math>
 +  
−   +  
−  The change in urban land (NUrbLD) is then calculated as
 +  
−   +  
−  :<math>NUrbLD_{r}=LandUrbanPred_{r}LD_{r,l=4}</math>
 +  
−   +  
−  Limits are placed on the change in urban land area. First, if urban land is growing, the amount of increase in a single year cannot exceed 1/100<sup>th</sup> of a variable that is related to the change in the nonurban share of all other land from the base year (NonUrbanShrR)
 +  
−   +  
−  :<math>NonUrbanShrR_{r}=(\frac{NonUrbanShr_{r,t}}{NonUrbanShr_{r,t=1}})^2</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  :<math>NonUrbanShr_{r,t=1,t}=\frac{\Sigma_{l}LD_{r,l=14,t}}{\Sigma_{l}LD_{r,l=15,t}}</math>
 +  
−   +  
−  Second, if urban land is declining, it is not permitted to fall below 10,000 hectares. Third, the changes are assumed to affect all other land categories proportionately.
 +  
−   +  
−  :<math>Reduc_{r,l=14}=NUrbLD_{r}*\frac{LD_{r,l=14}}{\Sigma_{l}LD_{r,l=14}}</math>
 +  
−   +  
−  However, this is not allowed to result in the area for a given land category falling below 1,000 hectares. Thus, there may be a slight reduction in the amount of new urban land in certain cases.
 +  
−   +  
−  
 +  
−   +  
−  <references />
 +  
−   +  
−  ==== <span style="fontsize:large;">Changes in Cropland Due to Investment and/or Depreciation</span> ====  +  
−   +  
−  The changes in cropland are driven by the economics of land. Specifically, they are a function of the profitability of cropland. Also, they are assumed to affect, at least directly, only the forest and the other land categories.
 +  
−   +  
−  A maximum amount of cropland expansion each year (MaxLandExpansion) is fixed by the amount of forest land, the amount of other lands, the amount of potential arable land, and the existing amount of cropland. The maximum amount of expansion must be at least 2/100<sup>th</sup> of the existing cropland, but beyond that it cannot exceed either the total amount of forest and other land or the difference between 110% of the potential arable land (landarablepot) and current cropland.
 +  
−   +  
−  The change in the amount of cropland and the initially estimated share of agricultural investment going to cropland in the following year are computed differently depending upon the maximum amount of cropland expansion relative to the amount of existing cropland and the current level of average income in a country. Specifically, if the maximum amount of cropland expansion is less than 10 percent of existing cropland or if the average income in the country is greater than $10,000 (GDPPCP > 10), then it is assumed that there is no change in cropland (lddev = 0) and that no agricultural investment is targeted for cropland development (IALK = 0).<ref>Given that IALK represents a share value, it is also bound to be <= 1.</ref>
 +  
−   +  
−  If neither of the conditions mentioned in the previous paragraph is met, i.e., if the country is not too wealthy and there is an ‘adequate’ amount of land for expanding cropland, the amount of change in cropland (lddev) is initially calculated as
 +  
−   +  
−  :<math>lddev_{r}=(\frac{iaval_{r}*IALK_{r}}{CLD_{r}}LD_{r,l=1}*\mathbf{dkl})*\mathbf{ldcropm}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  iaval is the total amount of funds available for investment in agriculture
 +  
−   +  
−  IALK is the share of agricultural investment going to cropland development
 +  
−   +  
−  CLD is the unit cost of cropland development
 +  
−   +  
−  '''''dkl'' ''' is the depreciation rate of investment in cropland (essential a maintenance cost for existing cropland)
 +  
−   +  
−  '''''ldcropm'' ''' is a countryspecific multiplier that can be used to increase or decrease changes in cropland
 +  
−   +  
−  Note that this equation takes into account the need to maintain existing cropland. Also, at this point, the value of lddev is bound from below to ensure that it does not imply a greater than 10 percent decrease in existing cropland. For relatively poor countries (GDPPCP < 10), the constraint is even stricter. Specifically, IFs calls for a shift in funds to ensure that no cropland is lost. The desired shift in funds is given as
 +  
−   +  
−  :<math>DesShift_{r}=CLD_{r}*lddev_{r}</math>  +  
−   +  
−  The actual shift in funds is limited to 90 percent of the available funds, however, where the available funds are the investment in agriculture not initially designated for cropland development
 +  
−   +  
−  :<math>Shift_{r}=MIN(0.9*iaval_{r}*(1IALK_{r}),DesShift_{r})</math>  +  
−   +  
−  The value of lddev given the actual shift in funds is given as
 +  
−   +  
−  :<math>lddev_{r}=lddev_{r}+\frac{Shift_{r}}{CLD_{r}}</math>
 +  
−   +  
−  In addition, the share of investment in agriculture designated for cropland development is updated to be
 +  
−   +  
−  :<math>IALK_{r}=IALK_{r}+\frac{Shift_{r}}{iaval_{r}}</math>  +  
−   +  
−  The changes in cropland are linked to changes in land in the forest and ‘other’ categories. The amount coming from/going to forests reflects the share of forest land relative to ‘other’ land, as well as the current level of development
 +  
−   +  
−  :<math>LDDEVFor_{r}=lddev_{r}*\frac{LD_{r,l=3}}{LD_{r,l=3}+LD_{r,l=4}}*ForShrPar_{r}</math>
 +  
−   +  
−  ''where''
 +  
−   +  
−  ForShrPar is given by the function depicted below that
 +  
−   +  
−  [[File:Changes in cropland due to Investment and or Depreciation.pngcenterChanges in cropland due to Investment and or Depreciation.png]]
 +  
−  <div>
 +  
−  The solid line holds when land is being converted from forests to cropland (lddev > 0) and the dotted line holds when land is being converted from cropland to forests (lddev < 0). In either case, this implies that the less of the change is related to forest land than would be expected by its share. Two other qualifiers are that the changes in forest land (LDDEVFor) and the changes in ‘other’ land cannot exceed 90 percent of existing land in these categories and the shifts cannot result in either land category falling below 1,000 hectares. These limits feedback to the change in cropland, finally resulting in the following
 +  
−   +  
−  :<math>lddev_{r}=LDDEVFor_{r}+LDDEVOth_{r}</math>
 +  
−   +  
−  :<math>LD_{r,l=1}=LD_{r,l=1}+lddev_{r}</math>  +  
−  :<math>LD_{r,l=3}=LD_{r,l=3}LDDEVFor_{r}</math>  +  
−   +  
−  :<math>CLD_{r,t+1}=CLD_{r,t=1}*\frac{LD_{r,l=1,t}}{LD_{r,l=1,t=1}}*RemRat_{r}^{1.5}</math>
 +  
−   +  
−  Turning back to the future cost of cropland development, this is estimated differently based only on whether there is ‘adequate’ room for cropland land expansion, defined as when the maximum amount of cropland expansion is greater than 10 percent of existing cropland. If this is the case, the future price of cropland is estimated as
 +  
−   +  
−  :<math>RemRat_{r}=\frac{MaxLandExpansion_{r,t=1}}{MAX(0.1*MaxLandExpansion_{r,t=1},MaxLandExpansion_{r,t})}</math>  +  
−   +  
−  ''where''
 +  
−   +  
−  RemRat is the ratio of the maximum land for expansion in the first year to the maximum land for expansion in the current year, with a maximum value of 10
 +  
−   +  
−  :<math>CLD_{r,t+1}=MAX(CLD_{r,t},CLD_{r,t=1},\frac{LD_{r,l=1,t}}{LD_{r,l=1,t=1}},CLD_{r,t=1}*(1+2*(\frac{t2009}{100}))</math>
 +  
−   +  
−  This basically states that the price of cropland development grows linearly with growth in cropland and exponentially with declines in available land for cropland expansion.
 +  
−   +  
−  Alternatively, if the maximum amount of cropland expansion in a given year is less than or equal to10 percent of existing cropland, the cost of bringing new land under cultivation is assumed to grow at the maximum of either 2 percent per year from the cost in the first year or the growth of cropland from the first year. Furthermore, it is not allowed to decline. Thus,
 +  
−   +  
−  :<math>ForestShr_{r}=\frac{LD_{r,l=3}}{LD_{r,l=3}+LD_{r,l=4}}</math>  +  
−  </div>
 +  
−  
 +  
−   +  
−  <references />
 +  
−   +  
−  ==== <span style="fontsize:large;">Changes in Grazing Land</span> ====
 +  
−   +  
−  IFs assumes that relatively poor countries (GDPPCP < 10) will continue to develop additional grazing land, whereas relatively rich countries (GDPPCP > 15) will retire grazing land. No change is expected in countries with average income between $10,000 and $15,000. The annual expansion of grazing land in poor countries is initially estimated as 0.5 percent of the amount of grazing land in the first year. The retirement of grazing land in richer countries is initially estimated as 0.2 percent of current grazing land.
 +  
−   +  
−  As with cropland, any changes in grazing land will be compensated by changes in forest and ‘other’ land. Each category is initially assumed to be affected proportionately, e.g.,
 +  
−   +  
−  :<math>ForestShr_{r}=\frac{LD_{r,l=3}}{LD_{r,l=3}+LD_{r,l=4}}</math>
 +  
−   +  
−  Unlike the case for changes in cropland, there is no adjustment to the forest share as a function of income or the direction of change in grazing land. As with the changes in cropland, however, the changes in forest and ‘other’ land cannot exceed 90 percent of existing land in these categories and the shifts cannot result in either land category falling below 1,000 hectares. Again, these limits feed back to the change in grazing land.
 +  
−   +  
−  ==== <span style="fontsize:large;">Change in Forest Land due to a Policy Choice</span> ====
 +  
−   +  
−  The model user can also force the land in forest area to increase or decrease at the expense of crop and grazing land via a forest multiplier '''''forestm'' '''. The change in forestland, LDSHIFT, is bound. In the case of an increase, i.e., '''''forestm'' ''' > 1, the amount of added land is limited to 20 percent of crop and grazing land; in the case of a decrease, i.e., '''''forestm'' ''' < 1, the amount of forest land removed is limited to 20 percent of existing forest land.
 +  
−   +  
−  :<math>\frac{LD_{r,l=3}}{5}<LANDSHIFT_{r}<\frac{LD_{r,l=1}+LD_{r,l=2}}{5}</math>  +  
−   +  
−  :<math>LD_{r,l=3}=LD_{r,l=3}+LANDSHIFT_{r}</math>  +  
−   +  
−  The amount of land taken from cropland and grazing land is proportional to the amount of each.
 +  
−   +  
−  :<math>CropShare_{r}=\frac{LD_{r,l=1}}{LD_{r,l=1}+LD_{r,l=2}}</math>  +  
−   +  
−  :<math>LD_{r,l=1}=LD_{r,l=1}+LANDSHIFT_{r}*CROPSHARE_{r}</math>
 +  
−   +  
−  :<math>LD_{r,l=2}=LD_{r,l=2}+LANDSHIFT_r*(1CROPSHARE_{r})</math>  +  
−   +  
−  ==== <span style="fontsize:large;">Final Checks and Renormalization of Land Use</span> ====
 +  
−   +  
−  Two final adjustments are made to the land area values to clean up any quirks that might have be introduced in the previous processes. First, the values for each category are bound between one thousand and ten billion hectares. Second, the values are normalized so that the sum of the categories equals the total amount of land.
 +  
−   +  
−  :<math>LD_{r,l=15,t+1}=LD_{r,l=15}*\frac{LD_{r,l=15}}{\Sigma_{l}LD_{r,l=15}}</math>
 +  
−   +  
−  Finally, a value for world forest area (WFORST) is calculated at the end of this process by summing forestland area across all countries.
 +  
−   +  
−  :<math>WFORST_{t+1}=\Sigma_{l}LD_{r,l=3}</math>  +  
−   +  
−  == <span style="fontsize:xlarge;">Livestock Dynamics</span> ==
 +  
−   +  
−  In addition to capital and land, the other "stock" or "level" variable with important temporal dynamics is the livestock herd (LVHERD). The size of the herd size (LVHERD) in the first year is calculated simply as the base year value of meat production divided by the slaughter rate, '''''slr'' '''.[http://www.du.edu/ifs/help/understand/agriculture/equations/livestock.html#footnote [1]]
 +  
−   +  
−  The growth of the herd size in future years is driven by changes in meat demand at both the national and global levels, changes in meat stocks at both the national and global levels, and changes in grazing land at the national level.
 +  
−   +  
−  At the national level, herd sizes for the next year are first estimated as a function of changes in national meat demand, national meat stocks, national grazing land, and an adjustment factor related to national meat stocks:
 +  
−   +  
−  :<math>LVHERD_{r,t+1}=LVHERD_{r,t}*(AGDEM_{r,f=2,t}/AGDEM_{r,f=2,t1})*(LD_{r,l=2,t}/LD_{r,l=2,t1})*stockadjustmentfactor_{r,f=2}</math>  +  
−   +  
−  The forecasts of meat demand (AGDEM<sub>r,f=2</sub>) and grazing land (LD<sub>r,l=2</sub>) are described in the [http://www.du.edu/ifs/help/understand/agriculture/equations/demand/meat.html Meat Demand] section and the [http://www.du.edu/ifs/help/understand/agriculture/equations/land/grazing.html Changes in Grazing Land] section, respectively. The national stock adjustment factors are calculated using the same ADJSTR function as used to adjust crop yields. In this case, the desired stock level is given as agdstltimes the sum of national meat demand (AGDEM<sub>r,f=2</sub>) and national meat production (AGP<sub>r,f=2</sub>). As mentioned previously, agdstl is set to be 1.5 times '''''dstl'' ''', which is a global parameter that can be adjusted by the user. Also, the two parameters that determine how much of an adjustment there is due to changes in stock levels from the previous years and the difference between the actual and desired stock levels are hard coded with values of 0.05 and 0.1, respectively.
 +  
−   +  
−  At the global level, herd sizes for the next year are estimated as a function of changes in global meat demand, global meat stocks, and an adjustment factor related to global meat stocks:
 +  
−  <div>
 +  
−  :<math>LVHERD_{t+1}=LVHERD_{t}*(AGDEM_{f=2,t}/AGDEM_{f=2,t1})*stockadjustmentfactor_{f=2}</math>  +  
−  </div>
 +  
−  <span>The global stock adjustment factor is calculated in the same manner as the national stock adjustment factors, only using global values for actual and desired stocks.</span>
 +  
−   +  
−  <span>Finally, the herd sizes for the next year are normalized so that the sum of the national values equals the global value:</span>  +  
−   +  
−  :<math>LVHERD_{r,t+1}=LVHERD_{t+1}*(LVHERD_{r,t+1}/\Sigma_{r}LVHERD_{r,t+1}</math>
 +  
−   +  
−  [file:///C:/Users/Ara/Desktop/Agricultural%20Documentation%20v19_AG.docx#_ftnref1 [1]] For details on the base year value of meat production, which is based on historical data related to production, imports, exports, and assumptions about expected meat consumption and production losses, see the description of agricultural data initialization in the preprocessor.
 +  
−   +  
−  == <span style="fontsize:xlarge;">Water Dynamics</span> ==  +  
−   +  
−  <span>Water use begins with data on total water withdrawals from FAO Aquastat. These are divided by the size of the population to get an estimate of water use per capita.</span>[[File:Water dynamics.pngcenterWater dynamics.png]]  +  
−   +  
−  <span>In future years, water use per capita is forecast to increase in parallel with crop production per capita. Specifically, an expected level of water use per capita as a function of crop production per capita (see figure below) is calculated for crop production in the current year (CropPC) and crop production in the first year (CropPCI). The ratio of these values is multiplied by the water use per capita in the first year (WatUsePCI) to get water use per capita in the current year (WatUsePC). This is multiplied by population (POP) to get total water use (WATUSE).</span>
 +  
−   +  
−  :<math>WatUsePC_{r}=WatUsePCI_{r}*\frac{f(CropPC_{r})}{f(CropPCI_{r})}</math>
 +  
−   +  
−  :<math>WATUSE_{r}=WatUsePC_{r}*POP_{r}</math>
 +  
−   +  
−  </div></div></div></div></div></div></div></div>
 +  