Management Effects of Spatially Dispersed Land Tracts: A Simulation Analysis

Transcription

1 Management Effects f Spatially Dispersed Land Tracts: A Simulatin Analysis Orlan Buller and Gary Bruning A sequential simulatin mdel is used t test a way t study the relatinship between net farm incme and land tract dispersin, ttal acres, machinery size and rainfall. The mdel simulates the day-t-day sequence f field wrk n a hypthetical farm situatin varying crp acreage, machinery size and fr a wet and dry rainfall situatin. Data generated by this mdel are then analyzed using a regressin equatin estimating the influence f studied variables n net farm incme. ncreases in size, pwer, and mbility f mst types f farm machinery in recent years have enabled farmers t perate mre land at greater distances frm the hme base in rder t increase their farm size. The increase in size and greater machine utilizatin enhances efficiency f peratin thrugh attaining ecnmies f size, and increases the farmer's incme generating capacity. Hwever, mst studies abut firm grwth and increasing farm size have nt explicitly cnsidered the dispersin f land tracts. This study develps and tests a sequential simulatin mdel fr analyzing the relatinships f tract dispersin, crp acres, and machinery size t farm prfits. We limited the effects f dispersin n prfits t tw aspects: (a) the effect f increased travel n csts and (b) the pssible reductin in crp yield per acre resulting frm lst fieldwrk time and, hence, nntimely planting and harvesting. We used the results t evaluate the apprach, the mdel, and data requirements. We cnsidered the simulatin apprach instead f surveying farmers t estimate Orlan Buller is Assciate Agricultural Ecnmist with the Department f Ecnmics, Kansas State University, and Gary Bruning is Assistant Prfessr f Ecnmics, Western llinis University, Macmb, llinis. ntributin number 618-J, Kansas Agricultural Experiment Statin, Manhattan, Kansas. the effect f dispersin and distance n csts and yield per acre in rder t cntrl the range in value f variable factrs. Simulatin, even mre s than a fertilizer r feeding experiment, appraches a ttally cntrlled experiment. The imprtant part f using simulatin is t define and quantify the real situatin studied. Hwever, by hlding sme factrs cnstant, we were able t study a situatin atypical f an actual farm situatin. Prblems with Spatial Dispersin The absence f past research n dispersin f land tracts makes it difficult t evaluate its effects n efficiency f peratin. As a result, ur apprach here is t cite bservatins n the prblem made by ther analysts, t ffer evidence n changing sizes f farms in Kansas, and t characterize sme f the likely prblems assciated with land dispersin. Warren Jhnstn shwed that "... the dispersin f farmed land was mre widespread with increasing farm size." A recent issue f a farm magazine reprts: "f adding t the hme farm was a simple matter f annexing the field acrss the fence, large machinery wuldn't pse such a prblem. But, in many cmmunities yu're lucky t find extra acres in the same cunty - much less right next dr." This article als tuches n the prblem f field time lst because f mves: "... A field-t-field switch that eats up the 129

2 July 1979 Western Jurnal f Agricultural Ecnmics better half f a day instead f the better part f an hur." A Kansas farm management extensin ecnmist suggests that the extent f dispersin f tracts depends n hw aggressively the farmer pursues grwth in land size. f a farmer senses the need t acquire crpland rapidly t achieve firm grwth r t include a sn in the business, then he likely will end up with farm tracts quite widely dispersed. Table 1 uses Nrtheast Kansas farm management assciatin recrds t cmpare farm size reprted in 1973 with size f the same farm in The underlined numbers n the diagnal are the number f farms with crp acreage in the same size grup in bth years. Fifty-ne percent f the farms stayed in the same size grup, 35 percent are in a larger size grup in 1977 than in 1973; and 14 percent are in a smaller size grup in n eastern Kansas, farms with 64 acres r mre are likely nt in ne cntiguus tract because f the terrain and the histry f land wnership with many peple wning relatively small tracts. n 1973, 2 percent f the farms were ver 64 acres whereas by 1977, 4 percent were ver 64 acres. Mst farms in nrtheast Kansas are small enugh s that tracts farmed are likely less dispersed. But many farms are expanding t sizes where dispersin is a prblem. r ) E a U as c. (n z c z E -J c, 1) c r O (D c re.r- N r M O c ) '_ O O ( O T O ' M ) O (D M ' a) (g a u NM 't \ 't T- M 1 )- M N -N N T-- M L. "t M T- ~lt-- - ) T- Ml r- c) r~- 'V* T- a) ) ' ) ) N D M On widely dispersed farmland, an peratr may experience difficulties nt cmmn n a cntiguus tract. A light rain n ne tract may interrupt n-ging field wrk there; anther tract, lcated several miles away but n the dispersed farmland, may nt have received the rain. Determining amunt f rainfall n varius tracts culd require time and quite likely increase travel csts. Althugh devices like tw-way radis can greatly facilitate cmmunicatin amng labrers wrking at different tracts, they are f limited use in a ne-man farm situatin. Narrw bridges with limited lad capacities may als increase farmers' travel time between widely dispersed tracts, as will time spent in preparing equipment fr transprt. Purchasing special equipment t trans- ON O-N-N.T- ) O O t O (D (D t D T- c) 13

3 Buller and Bruning prt large machines wuld further add t equipment cst. Amng sme advantages f spatial dispersin are the pssibility f rain ccurring n tracts ther than the ne f n-ging field wrk and the pssibility f reduced risk f hail lss. Our mdel accunts fr the first pssibility but nt fr the secnd. Mdel Our apprach was t simulate the day-tday sequence f events relating t field preparatin, planting, and harvesting n a representative farm in Nrtheast Kansas. Each situatin studied was based n a different number f land tracts and n alternative machinery sizes, levels f dispersin, and rainfall amunts. We frmulated the study as a discrete system by using a versin f the prgramming language f the General Purpse Simulatin System. We related net farm incme t fur cntrlled, variable factrs and t sme fixed factrs. The experimental design included variables ver a range, with sme ther factrs fixed at specified levels. ntrl Variables Managing Dispersed Land Land, equipment capacity, dispersin, and rainfall were the cntrl variables specified in the simulatin mdel. rpland studied was fr 32, 48, 64, 1,12, and 1,44 acres. Tracts were in increments f 16 acres. Sizes f varius implements fr alternative equipment capacity levels studied are given in Table 2. The pattern f tract dispersin was defined as the lcatin f tracts in relatin t each ther and t the base f peratins. We used a circular pattern with the base tract as the center; added tracts were situated as nearly as pssible in a circle, with equal distances between tracts and frm the base tract. Defining level f dispersin as the distance the circular pattern is frm the base tract, we cnsidered three levels: (1) cntiguus with tracts adjacent t the base tract and t each ther; (2) mderately dispersed, with each tract abut 6 miles frm the base tract and with equal distances between adjacent tracts; and (3) widely dispersed, with each tract abut 16 miles frm the base tract and with nearly equal distances between adjacent TABLE 2. Machine Sizes Fr Each Size f Equipment apacity by Type f Equipment Equipment Equipment Equipment Equipment Machine capacity 4 capacity 5 capacity 6 capacity 7 Plw 4-16" 5-16" 6-16" 7-16" Offset disc 16' 18' 2' 24' Springtth harrw 16' 18' 2' 24' Spiketth harrw 18' 2' 22' 24' Rtary he 4-4" 6-3" 8-3" 12-3" ultivatr 4-4" 6-3" 8-3" 12-3" Planter 4-4" 6-3" 8-3" 12-3" Grain Drill 1.5' 12.2' 12.2' 14.5' NH 4 applicatr 12.5' 12.5' 17.5' 17.5' Bulk spreader 24' 24' 24' 24' mbine 185 bu./hr. 23 bu./hr. 325 bu./hr. 325 bu./hr. rnhead 2-4" 3-3" 4-3" 6-3" Grainhead 12' 14' 16' 16' 131

4 July 1979 tracts. Using the same pattern at each level f dispersin wuld affect variable csts. mbinatins f acreage, machinery capacity, and dispersin level were studied fr tw rainfall amunts: 19.1 inches during a relatively dry grwing seasn and 28.8 inches during a relatively wet grwing seasn. These rainfall extremes were selected t estimate the upper and lwer bunds n net farm incme as affected by rainfall. Eventually we cmbined results frm the dry and wet situatins t present the analysis in a decisin-making framewrk. Farmers wrk in a variety f weather situatins and d nt adjust size, dispersin, and equipment capacity n a year-t-year basis in respnse t anticipated weather cnditins. Therefre the cmbined estimates frm the dry and wet situatins wuld represent mre nearly an average situatin. Assumptins Abut Other Factrs Yield per acre per crp was the same n each tract except as dispersin affected timeliness, which in turn culd affect yields. We did nt cnsider the effect f different rainfall patterns n the physilgical develpment f the crp plant, and cnsequently n yield. A mdel t frmulate this cmplex yield-rainfall relatinship was nt available; thus, it was mitted. nsequently, prfit estimates fr dry cmpared with wet situatins likely differ less in this mdel than in an actual situatin. Sil differences, which inevitably ccur as dispersin increases and which affect yield and tillage practices, were nt cnsidered. Labr available was based n ne full-time peratr; hiring labr and custm harvesting were nt cnsidered. Family labr was assumed available t help during harvest. Planting and harvesting were scheduled t begin n a specified day, if field cnditins wuld permit, fr all equipment capacities, dispersin levels, and acreages. Fr crn and sybeans, tract acreage might vary if crn planting had been s delayed that it became mre prfitable t plant sybeans. 132 Western Jurnal f Agricultural Ecnmics Flw Diagram and Sequence f Field Jbs The day-t-day sequence f field jbs, simulated in a sequence f days, began April 1 and lasted until Nvember 1. Jb assignments and their pririties were made fr each day. Optimum planting and harvest dates were based n recmmended practices and infrmatin btained frm a survey f Kansas farmers published by Kansas rp and Livestck Reprting Service. Figure 1 illustrates the jb assignments and pririties each day fr May, June, and July; the prcedure was the same fr ther mnths. Field jbs were assigned pririties frm 1 t 4, with 1 the highest pririty. Fr example, highest pririty n June 2 was t plant sybeans; then, wheat harvest wuld begin and, when cmpleted, sybeans wuld be hed. Figure 2 is the flw diagram shwing, in general, the decisin prcess in the mdel. Each day, the mdel searched varius tracts t determine field cnditins and any jb t be dne and n which field. nput data included the number f land tracts, size f tract, distance frm dispersed tracts t hme base f peratin, distance between dispersed tracts, crp csts and returns based n expected yields (travel csts excluded), maximum hurs f labr available each day, number and type jbs required n each tract, jb pririties fr each day, and field time f each jb. Simulating Rainfall A cmputer-simulatin-prbabilisitc mdel develped by sn, Feyerhern and Bark was used t estimate the sequence f wet and dry days and the amunt f rainfall ccurring each day frm April 1 t Nvember 1. Each day was divided int fur 6-hur perids with a prbability f a strm beginning fr each perid based n research by hangnn. The prbability that a strm wuld begin during ne f the perids changed as the seasns changed. Even if the prgram specified rain n a given day, field wrk might nt be delayed the entire day,

5 Buller and Bruning Managing Dispersed Land (n c= D Z D D >^ > ) D D -s ), a) cn c > D T- Y) \J - '\ a \j v ṁ -D> D ) L- D L- ) D cn - ), c. >, >m _ ) -4- -,,, Z a - ) - L-, O ) DO,, Z, D _ : Oc Q cn ) - D, <), U) - -\ D O ''~ _- ) O O 'O4 QL m- D Z c , Z - D _. ) - - cn cn c ) ) r ) :~~~~~ 4-3, D 2, c, > l) U co L-4 L. L-.= m -'-)..c a Y) (i) '- e" 133t *' l 1) - O - L a_ Mj t- M T- - M 3D il

6 July 1979 Western Jurnal f Agricultural Ecnmics initialize t alculate distance, - d... rd,\ -- 1 ct nf tr l and '--Uy = y-t time V L spent. Lv A time spent. Figure 2: A Flw Diagram Shwing the General Nature f the Decisins. 134

7 Buller and Bruning because rainstrms culd be initiated at the beginning f any f the fur perids. The mdel first determined, fr each tract whether r nt rain wuld ccur n each day and at what time f day. f the weather check revealed that the amunt f rain was sufficient t stp field wrk at a particular lcatin, then the search fr a dry field wuld begin. Delay in Field Wrk The length f delays in field wrk attributed t rainfall depends n the amunt f rain. During field preparatin and planting time, the expsed bare sil wuld dry relatively fast; a mature crp wuld shade the sil s that less evapratin wuld ccur, and hence the sil wuld dry mre slwly. Hwever, fr summer and fall harvest, the sil culd be mre mist than fr tillage peratins - just dry enugh t supprt harvesting equipment. Because f lack f data, we assumed that precipitatin during harvest time wuld cause the same delay as during field preparatin and planting time. Table 3 gives the estimate f the delay in field wrk fr specified amunts f precipitatin in nrtheastern Kansas prvided by William Pwers. Rainstrm Patterns Rainstrm patterns fr nrtheastern Kansas were estimated using rainfall data fr Hrtn, Kansas and a mdel develped by F. A. Huff and are assumed apprpriate fr nrtheastern Kansas. Thugh mst strms in that regin mve suthwest t nrtheast, fr simplicity Managing Dispersed Land we simulated their mvement frm west t east. We als assumed that rainstrms riginate utside the area f the dispersed tracts, and then pass thrugh it. Amunt f rainfall decreases as distance frm the strm center increases. nsequently, it was imprtant t determine the strm center in relatin t the lcatin f dispersed tracts. The nrth-suth lcatin f the strm center was determined, by using a pseud-randm number technique, s that fr each simulatin run the same lcatin f strm centers wuld be repeated. The relatinship between amunt f rainfall at the strm center and amunt at varius distances frm the center is: lg R = P½ +.33 lg D, where R is the average difference between ttal rainfall at the strm center and at pints lcated at distance D (miles) frm the center, when rainfall (inches) at the strm is P. This relatin is fr warm seasns f spring, summer, and fall. Thus, whether r nt dispersed tracts wuld receive the same amunt f rainfall depends n their nrth-suth distances frm the strm center and the amunt f rainfall at the strm center. nterrupting Field Wrk Hw lng field wrk shuld be delayed depends n the amunt f rain n the tract where field wrk is in prgress and n ther dispersed fields. The mdel was designed s that after a rainfall, if a field was judged t wet fr wrk, a dry field wuld be sught. TABLE 3. Field-Wrk Delays by Precipitatin Level, Nrtheastern Kansas Amunts f precipitatin (inches) Days field wrk is delayed.5 r less.5 t t t t t

8 July 1979 Based n the equatin abve, if precipitatin at ne tract shuld exceed.5 inch, a farmer culd expect t travel mre than 2 miles t find a dry field. Fr sme field peratins several trips wuld be required t mve all equipment (planter, spring tth harrw, seed, fertilizer, and herbicide applicatr) frm ne lcatin t anther. n ur mdel, if less than.5 inch rain shuld fall n a field being planted, a mve is made t a dry field, if within 2 miles. Shuld rainfall exceed.5 inch at the field being planted, hwever, n mve wuld be scheduled that day because there culd be n dry fields within 2 miles. The decisin wuld be reevaluated the next day. st f Travel rp budgets include the usual variable csts fr seed, fertilizer, fuel, il, repairs assciated with field wrk, herbicides, and hauling. Fr dispersed farmland, variable travel csts estimated at $.13 per mile fr tractr fuel, il, and repairs are added. With Western Jurnal f Agricultural Ecnmics distance between fields prvided in the initial input data, travel csts are determined as the prduct f the number f trips times distance times cst per mile. Thus, as distance r number f trips increased, because f rainfall interrupting wrk and requiring added travel t cmplete field wrk, ttal variable csts wuld als increase. rp Penalties When rainfall frequently interrupts field wrk r equipment capacity is t small relative t crp acreage, crp planting r harvesting may be extended beynd the recmmended perid. nsequently, crp penalties wuld ccur if planting is delayed past the ptimum planting perid, r if harvest is delayed past ptimum harvest time. n the mdel the csts f these penalties are reductins in yields estimated frm studies by per, Laude, Pauli, Stickler and Luchele. Penalties resulting frm bth delayed planting and delayed harvest were specified in the mdel n the basis f relatinships shwn in 9-7- a) - - grain srghum crn cr, n sybeans wheat - - ' April June August Octber Planting Date Figure 3: Expected yield per acre by planting dates fr crn, sybeans, grain srghum, and wheat. 136

9 Buller and Bruning Managing Dispersed Land ā) K\ wheat -, crn July August September Octber Harvest Date grain srghum Nvember s ' sybeans a N- 2-1 December Figure 4: Percent f expected yield per acre harvested by harvest date fr crn, sybeans, grain srghum, and wheat. Figures 3 and 4. The cmputer was prgrammed t begin as thugh planting and harvesting wuld ccur t give the highest yield. Then, if delays caused by rainfall r lack f field wrk time shuld reduce yield, the estimated yields culd be adjusted accrdingly. rp Distributin and Decisins rp acreages were based n an average calculated frm farm recrds f Nrtheastern Kansas farmers shwing that in 1972, 12 percent f the crpland was planted t winter wheat and 88 percent t spring crps. That same allcatin f crpland was used fr each tract. Pririty f land use amng spring crps was based n net return per acre. n this regin crn has higher expected average peracre returns than des either grain srghum r sybeans if it is planted befre the end f May; thus, crn was given highest pririty. f rainfall r size f equipment in relatin t acreage shuld delay planting past May 3, then many farmers replace crn with grain srghum and sybeans as mst prfitable crps fr land-use changes. But t simplify the mdel, we did nt include grain srghum, because there are nly three t five calendar days when planting grain srghum wuld have pririty ver planting crn r sybeans. Thus, acreages in crn and sybeans were determined by number f field wrk days, size f equipment, and acres f crpland. alculating Net Farm ncme Explaining hw we calculated net farm incme prbably can best summarize hw the varius variables interacted. The input data prvided cst and return data fr each crp. Variable csts included thse fr seed, fertilizer, herbicides, insecticide, fuel and il fr field wrk time, and repairs, as well as cst related t field wrk time and marketing r hauling. As the simulatin run prgressed thrugh the sequence f day-t-day events, travel csts t and frm fields - which included thse fr fuel, il, and repairs assciated with distance traveled- were added t the variable csts. As interruptins caused by rain increased r as distances t fields increased, the mre cstly the travel cmpnent becmes. Als prvided as input data was the maximum number f hurs f field time available each day. Subtracting the time required fr travel and time t allw a field t dry frm the maximum time specified fr each day determined hw many days wuld be required t plant r harvest a specified number f acres. f the time required indicated there wuld be delays sufficient t cause a penalty in yield, the expected yield per acre wuld be reduced t make the apprpriate calculatin f grss incme. Depreciatin, taxes, and insurance f equipment were included in calculating cst t shw the increased wnership cst f large-sized equipment. Labr cst and cst f 137

10 July 1979 wning land were nt included. Thus, grss incme initially calculated culd be adjusted by subtracting the usual variable csts, as well as csts fr travel, equipment wnership, and any lss in incme frm crp penalties. Validating the Mdel Western Jurnal f Agricultural Ecnmics The net returns fr the simulatin run f 32 acres and equipment capacity 4 ranged (at 1972 prices) frm $15,269 t $17,766, depending n dispersin level and weather. Based n Farm Management Assciatin recrds fr 1972, the average size cash-crp farm in Brwn unty, Kansas was 365 acres. Net incme f that average farm fr 1972, if adjusted t a 32-acre basis, wuld be $16,271. The estimated prfit f the actual farm then wuld lie within the prfit range f the simulated farm. n the simulatin the range in farm size that minimizes ttal csts with equipment capacity 4 wuld be 565 t 645 acres, depending n the dispersin level and weather. The average Brwn unty cash-crp farm, hwever, might be smaller than that f the simulated situatin because mst crp farmers in that cunty als have livestck, thugh their main surce f incme is frm crps. Thus, labr availability culd reduce the number f acres the farmer culd till. Als, Brwn unty farmers culd have limitatins n credit and capital available, which wuld limit the acres farmed. Results Tables 4 and 5 reprt the calculated prfits fr varius cmbinatins f acreage, dispersin level, and equipment capacity fr the dry and wet years, withut regard t higher yields prbable with the wet year. Thugh rainfall usually increases yields and prfits, we ignred that respnse t study nly hw rainfall wuld affect csts assciated with increased travel and lsses due t timeliness f wrk. Prfits are greatly influenced by the prduct prices and input csts, which remained cnstant in varius situatins studied. We believe that the general character r relatinship amng variables wuld hld fr a reasnable price range. TABLE 4. Estimated Ttal Prfits fr Alternative Farm Sizes, Dispersin Levels, and Equipment apacities, During Dry Weather Farm size (acres) Disp. Equip. level capacity Prfits (dllars) A 4 17,463 27,117 31,81 31, ,975 26,774 31,84 32,195-18, ,299 26,354 3,858 31,775 32,416 29, ,558 24,94 29,561 3,438 31,756 32,16 B 4 17,766 26,559 3,795 29, ,148 26,82 3,581 3,65-16, ,462 25,493 29,514 3,998 29,432 18, ,19 24, 28,59 28,815 28,842 27, ,336 24,222 27,932 25, ,934 24,224 28,583 27, ,46 23,869 27,915 28,975 2,222 9, ,82 22,55 25,998 26,792 25,75 18,64 adispersin level A, cntiguus tracts; B, mderately dispersed tracts apprximately 6 miles frm base; and, widely dispersed tracts apprximately 16 miles frm base. 138

11 Buller and Bruning Managing Dispersed Land TABLE 5. Estimated Ttal Prfits fr Alternative Farm Sizes Dispersin Levels, and Equipment apacities, During Wet Weather Farm size (acres) Disp. Equip. level capacity Prfits (dllars) A 4 17,446 27,33 31,793 3, ,81 26,74 31,781 31,998-15, ,194 26,197 3,721 31,76 32,9 7 17,696 24,713 29,438 3,167 31,192 31,464 B 4 17,753 26,536 3,631 29, ,6 26,24 3,532 3,391-12, ,365 25,362 29,482 3,812 27,22 13, ,935 23,841 28,2 28,616 28,195 25, ,269 24,29 27,434 24, ,95 24,25 28,453 26, ,39 23,849 27,736 28,444 17,25 5, ,58 22,426 25,82 26,564 23,589 12,735 asee ftnte Table 4. Data frm Tables 4 and 5 were cmbined and a quadratic equatin fitted because farmers d nt knw at planting time whether the year will be wet r dry. Thus, the fllwing equatin based n cmbined data wuld prbably be better than using equatins based n the dry and wet situatin fr evaluating the effect f different cmbinatins f sizes, acres, and dispersin: (1) NF = S D S (S) (D) (S) * () R 2 =.89, F(6,116) = 15, where NF is net farm incme, S is size in acres, D is dispersin in miles, and is equipment capacity expressed as mldbard plw size. Variables allwing fr diminishing prfits t dispersin and capacity were tested, but estimates frm the equatins were less satisfactry than estimates using equatin 1. The relatin shws that prfit increased at a decreasing rate as size increased. Hwever, increases in dispersin level and equipment capacity culd be assciated with increases in size. The relatinship f size, dispersin, and machinery capacity is evaluated by differentiating equatin 1 with respect t each variable: (2) dnf = S - ds.817d (3) dnf = S dd (4) dnf = S d Equatin 3 shws that increasing dispersin wuld decrease NF fr size exceeding 275 acres. With the machine capacity cnsidered in the study, the effect f tract dispersin wuld be relatively unimprtant n small acreages. Equatin 4 shws that increasing machine capacity abve capacity level 4 wuld increase NF nly fr sizes larger than 665 acres. NF wuld be larger if tract dispersin were less; hwever, NF wuld be the same fr all machinery capacities at the 665 acreage. 139

12 July 1979 The mst prfitable farm size fr varius dispersin levels and equipment capacities can be calculated by using equatin 2. The results are shwn in Table 6. The mst prfitable size can be estimated by specifying alternative sizes f equipment and dispersin distances, and then finding the value fr the acreage. The interactin f size with dispersin and equipment capacity shws that the benefits frm large equipment can ffset csts f dispersin as size increases. Table 6 indicates that an increase in equipment capacity f ne plw wuld be needed t ffset a 6.5 mile increase in dispersin. Hwever, if size is increased (and cnsequently dispersin), the effect f increasing equipment capacity t ffset csts wuld be much greater. f farm size is increased by 16 acres, and that increase als increases the dispersin level by ne mile, then equipment capacity must increase by 1.6. The mst prfitable size in crp acres increases abut 59 acres with each unit increase in machinery capacity. That increase held fr all dispersin distances studied. Prfits increased at an increasing rate f abut $3 fr each increase f 59 acres and each unit increase in machinery capacity. Mst prfitable size decreases abut 8 acres fr each mile f increase in dispersin; that decrease held fr all dispersin distances studied. Western Jurnal f Agricultural Ecnmics NF decreases as dispersin increases; NF increases as machinery capacity increases. The decrease in mst prfitable size mre than ffset the effect f larger equipment. Hwever, with a given machinery capacity, the decrease in prfits was cnstant fr each mile increase in dispersin. Sme f these relatinships were based n characteristics f a quadratic equatin, and s the statistical fit f the equatin t the data was imprtant here. The statistical measures f R-squared and F were reasnably gd. Thus, we believe the equatin described the data at an acceptable level f reliability. mplicatins Farm management researchers shuld be explicit abut the extent f crpland dispersin that is assumed when studying ecnmies f farm size. ncreased travel csts, less time fr field wrk and the effect f nn-timely field wrk n crp yields are several f the prblems that may cause per unit variable csts t increase r per unit net incme t decline if land tracts are widely dispersed. Studies f ecnmies f size fcus n per unit csts in relatin t utput, but the effect f nntimely field wrk reducing crp prductin is t reduce grss incme and nt t increase cst. Thus, the ttal effect f in- TABLE 6. Mst Prfitable Farm Size fr Dispersin Distances and Equipment apacities Net Size, Equipment Dispersin Farm acres capacity (miles) incme (dllars) , , , , , , , , , , , ,839 14

13 Buller and Bruning creasing utput by increasing acreage that is widely dispersed will nt be included if the study relates nly t cst. The reductin in incme caused by dispersin may be ffset, within limits, by machinery f greater capacity. The mdel estimates that an increase in plw capacity f 1 unit is needed t ffset the effect f 6.5 mile increase in dispersin. Thus, tw farms with the same crp acreage but ne with acreage dispersed an average f 6.5 miles mre wuld need 1 plw capacity larger t get the same amunt f field wrk dne in the same number f days. f crp acreage increases 16 and cnsequently dispersin increases an average f 1 mile, the estimate is that an additinal 1.6 plw capacity is needed. n general, the results agree with the bservatins f the authrs and f farm management extensin ecnmists: relatively small farms can be widely dispersed withut greatly affecting net incme; farmers with many widely dispersed tracts have truble getting their field wrk dne n time during critical perids and need larger equipment. The parameters f the equatin develped seem reasnable, althugh the results shw a bias in the mdel in the amunt f field wrk that can be dne at each capacity level, and cnsequently farm size and net farm incme fr equipment capacity studied are t high. Hwever, all cases studied have the same bias; thus, differences amng situatins studied culd still be crrect. Althugh this study was f a nrtheast Kansas farm situatin, the prblem exists in western regins f the Great Plains as well. Althugh many farms may be f a size s that the tracts need nt be widely dispersed, increasing numbers f farmers face the management prblems assciated with widely dispersed tracts. Results estimate that increasing dispersin may decrease net farm incme if crp acreage exceeds 275. Nrtheast Kansas farm management assciatin recrds shw 64 percent f farms larger than 32 acres. Thus, based n the results, mst farmers in nrtheast Kansas are f the size that land dispersin may have an ecnmic effect. Managing Dispersed Land n evaluating the mdel, we believe the apprach used t be very useful. Hwever, prgramming rainfall events fr each f fur daily perids was prbably the mst difficult aspect f the mdel. Althugh the time f day when rain strms begin varies frm April thrugh Octber, it is dubtful that the truble f adding that degree f realism wuld have been wrth the increased accuracy. We believe it was well t simulate the rain event as thugh it wuld ccur at the beginning f each day and calculate the delay frm that time. Since this mdel was develped, imprved methds f estimating sil misture have been develped. t is difficult t evaluate accurately hw well the mdel wuld have depicted the delay in field wrk caused by rainfall. Results simulated fr a dry and a wet situatin did nt shw as much difference as anticipated. Thus, using a sil-mistureestimatr prgram as a subrutine in the mdel t estimate the sil misture at each tract each day might have imprved results. Develping a discrete sequential simulatin mdel fr the type f prblem studied requires data in frm and type nt nw readily available r btainable. Such mdeling, hwever, can specify types f data that might be useful t a farmer and ften are needed by researchers. Since we began ur study, mre infrmatin n weather, sils and equipment is becming available fr use in imprving this type f a mdel. References hangnn, Stanley., Jr. "Precipitatin in a 55-square mile area f Suthern llinis," Reprint frm Transactins f the llinis State Academy f Science, 56(1963): per, Richard L. "nfluence f Sybean Prductin Practices n Ldging and Seed Yield in Highly Prductive Envirnment," Agrnmy Jurnal, 63(1971):

14 July 1979 Western Jurnal f Agricultural Ecnmics Greenberg, Stanley. General Purpse Simulatin System Primer. New Yrk: Wiley-nterscience Divisin f Wiley and Sns, nc Huff, F. A. "Rainfall Gradients in Warm Seasn Rainfall," Jurnal f Applied Meterlgy, 6(1967): sn, N. T., A. M. Feyerherm and Dean Bark. "Wet Perid Precipitatin and the Gamma Distributin," Jurnal f Applied Meterlgy, 1(1971): Jhnstn, Warren E. "Ecnmies f Size and the Spatial Distributin f Land in Farm Units," American Jurnal f Agricultural Ecnmies, 1(1972): Laude, et. al. Grwing Wheat in Kansas, Kansas Agricultural Experiment Statin Bulletin, 37(1955.):21. Luchele, W. F., M. Farrell, H. Waelti. "Prgress Reprt n Lsses Assciated With rn Harvesting in wa," Jurnal f Agricultural Engineering Research, 14(1969): Pauli, A. W. and F. L. Stickler, Yield and Yield mpnents f Grain Srghum as nfluenced by Date f Planting, Kansas Agricultural Experiment Statin Technical Bulletin, 13, August Pwers, William. Department f Agrnmy, Kansas State University, Manhattan, Kansas. Stickler, F.., R. F. Slan and M. A. Yunis, Kansas rps, Planting t Harvest, Kansas rp and Livestck Reprting Service, Tpeka, Kansas, Respnse f Grain Srghum Hybrids f Varying Maturity t Planting Date, Kansas Agricultural Experiment Statin Reprt f Prgress 19, June 1965, Figure 2. "Planting rps in Kansas." perative Extensin Service, Kansas State University, 197. Successful Farming, "New Machines That Wrk Wider - Fld Narrwer," February, 1978, p