Clary, Gregory M.

Haby, Vincent A.

Hillard, J. B.

Leonard, Allen T.

English

Texas A&amp;M Repository

    PUBLICATIONS 1990 DETERMINING FERTILIZER AND LIME RATES FORMAXIMUM PROFITABILITYG. M. Clary, V. A. Haby, A. T. Leonard, and J. B. HillardSUMMARYTechnical or production efficiency is not sufficient for farmers and rancherswho plan to survive in an open-market agricultural economy. Producers must alsoensure that their operations are economically efficient.Decision making aimed at profit maximization is an important element oflong-term business survival. Profit maximization generally occurs at output levelswhich are less than maximum in agricultural production systems. Producers whocan evaluate input and output decisions on the basis of changes in receipts andchanges in costs, and who produce that output for which these changes are equal,are producing at the profit maximizing level.Field research results of fertilizing and liming forage and grain cropscommonly produced in East Texas are subjected to economic analysis. Profitmaximization levels of input use were estimated and compared to input rates formaximum production.In many cases, such as applying Potassium (K) on Coastal bermudagrass,limestone on ryegrass, and Phosphorus (P) on Hard red winter wheat, the profitmaximizing level of input use is very close to input use for maximum production.However, in some scenarios evaluated, differences between these two levels of usewere more dramatic. Results were affected by initial soil conditions, fertilizer andlime prices, and the value of forage or grain being produced.INTRODUCTIONProducers of high quality forages constantly labor over deciding uponfertilizer and lime rates that will result in maximum profitability. These decisionsare complicated since producers face unique situations in terms of availableproduction resources such as soils, rainfall, and temperature, in addition to financialresources such as available capital or credit for operating expenses.Profit is the key factor that hangs in the balance as farmers makemanagement decisions. One key to business success is careful economic analysisof input/output relationships so that inputs will be used at levels as close to thepoint of profit maximization as possible.Three economic principles provide guidance to managers as decisions about1levels of resource use are made. First, input use should be increased as long as thevalue of added output, or income, is greater than added cost of additional units ofinput. For example, additional fertilizer should be applied as long as each dollarexpended generates at least one dollar in income. This implies that the point atwhich profits are maximized is where added income just offsets additional costs.Second, inputs should be substituted, one for another, as long as costs aredecreased with the level of production remaining constant. Producers selectingefficient fertilizer mixes, deciding upon lime products, or choosing feeding programsfor cow herds should closely consider this second principle.Third, agricultural producers generally face diminished marginal returns asadditional levels of inputs are used. For example, yield increases expected fromapplying the first 50 lb of nitrogen to bermudagrass pastures are anticipated to begreater than increased yields attributed to a second 50 lb application shortlythereafter. Figure 1 illustrates this type of production response. The implicationssurrounding this third principle are that producers should target profit maximiza-tion levels of input use rather than maximum production, even though there maynot always be large differences between the two levels.PROCEDURESResults of previous agronomic studies were used to develop economicanalyses of fertilizer and lime applications on Coastal bermudagrass, ryegrass, andHRW wheat in East Texas. Field trials were conducted under the direction of Dr.Vince Haby, Texas Agricultural Experiment Station, Overton and Dr. Leon Young,Stephen F. Austin State University, Nacogdoches. Details concerning experimentaldesign, soil analyses, and other research results can be obtained from either ofthese individuals.The aforementioned economic principles were considered in evaluating theeconomic feasibility of applying fertilizers and other soil amendments in the regionsstudied. The level of application corresponding to the point of maximum profitswas estimated for each experiment evaluated.Fertilizer and lime application recommendations based on profit maximiza-tion result from comparing marginal factor cost (MFC) with marginal value product(MVP). MFC is merely an economic term for "added cost" of using an additionalunit of an input. For example, the added cost of applying an additional unit offertilizer per acre (sayan additional 100 lbs per acre).MVP is the "added return" generated by increased output resulting from2using additional unit of an input. For example, the increased revenue from sellingadditional hay produced when an additional 100 lbs of fertilizer per acre wasapplied.A fundamental principle of farm management is that the profit maximizinglevel of input use occurs when MVP equals MFC. Should MVP be greater thanMFC, then the added value of forage production is greater than the added costsfrom using the next unit of fertilizer. Hence, it makes economic sense to add thenext unit of fertilizer as long as MVP exceeds MFC. By adding more fertilizer,total profits are increased. If the situation were reversed, it would make economicsense to decrease fertilizer use, permitting profits to increase.MFC and MVP estimates were based on current (1989) average prices andcosts provided by industry representatives. Custom rates were used to preventassumptions about equipment components and operating costs. Livestock forageconsumption and rates of gain were supplied by a computerized simulation programdeveloped by research animal scientists.RESULTSWith profit maximization, the goal of the farm manager is to fmd the levelof inputs (and hence outputs) that maximizes the difference between revenues andcosts. One could accomplish this task by calculating the difference between totalincome and total cost. Figures 2 and 3 illustrate these two values from experi-ments which included applying K at various rates on Coastal bermudagrass(Leonard, 1986). However, this method has two disadvantages. First, it concealsthe marginal effects of changes in the input level. Second, it takes more time tofind the new optimum input level if the price of either the input or output changes.Therefore, the preferred method of estimating the profit maximizing level of aninput is to equate MVP and MFC.Three examples of economic applications to forage production situations arepresented. Statistical analysis of field research resulted in estimating a productionfunction with a maximum yield at 304 lbs Klac. However, the profit maximizinglevel of use, determined by equating MFC with MVP, was estimated to be about295 lb Klac when it cost $11 for 50 lbs of K with hay selling for $50/ton (Figure 4).The profit maximizing level of K is directly related to the prices of K andhay. This level decreases as the price of hay decreases or as the price of Kdecreases. It is important to remember that these recommendations andcalculations are based on holding all other factors of production at constant levels.3Annual ryegrass is a very important cool season forage crop in East Texas.The practice of applying limestone to overcome acid soil infertility common to thisregion has been well documented by many researchers including Hillard (1989)whose results were used for economic analysis. Results of research indicated thatryegrass yields more than doubled with the addition of 1 ton limelac on soil withan initial pH of 4.5 (Figure 5).It is interesting to note that limestone was applied in 1983, so that yieldswere effected by the result of residual lime in the soil. This likely accounted fora portion of higher yields at higher lime rates while yields at lower rates droppedoff substantially in 1987.The economic returns from limingryegrass under these experimentalconditions were impressive. An economic value for the additional ryegrass producedas a result of liming was estimated with the aid of a computerized animal nutritionand gain model. The assumption for the economic evaluations was that ryegrasswould be grazed by 450 lb stocker animals and that lime cost $24/ac spread.Results indicated that there were economic benefits to applying more than1.5 tons limelac as MVP remained above MFC (Figure 6). The profit maximizingpoint was not readily calculated as it was beyond the range of the experimentaldata. However, it appears to be near 2 tons limelac under these conditions.Lime, nitrogen (N), and K are all important soil amendments for main-tenance of high quality Coastal bermudagrass pastures in East Texas. Makingrecommendations of application rates based on economics can be confusing wheninteractions between nutrients are considered. Varying application rates of othersoil amendments mayor may not have an affect on the optimum economic level oflimestone.Research results present six different scenarios for economic analysis(Leonard, 1986). Only one, where 249 lb Klac and 250 lb N/ac were applied,resulted in a profit maximizing level at 2 tons limelac (Figure 7). All three caseswith 500 lb N applied/ac resulted in an economic optimum level of lime at 1.6tons/ac (Figure 8).Hard red winter (HRW) wheat is important to East Texas both for its abilityto produce forage for grazing as well as grain for commercial sale. The final twocases, analyzed independent of each other with all other factors held constant, arephosphorous (in the form of phosphate fertilizer) and limestone applications onHRW wheat. Initial soil conditions included a pH of 5.3 and soil test P level of 3.0ppm.4Production responses of HRW wheat to P represented typical diminishingreturns to input use (Figure 9). Maximum production occurred at a fertilizerphosphorus rate of about 100 lbs/ac. The profit maximizing rate was only slightlyless at nearly 98 lbslac (Figure 10).HRW wheat also exhibited typical diminishing returns to lime application onthe soils described above. Maximum production occurred at a rate of 1 ton lime/acwhile the profit maximizing level was estimated to be close to 1.6 tons limelac(Figures 11 and 12).REFERENCESHillard, J. B. 1989. Coastal bermudagrass and Marshall ryegrass response tosurface-applied kunestibe and phosphorus on an acid, sandy East Texas soil.Ph.D. Thesis, Texas Agricultural Experiment Station, Texas A&M University,Overton.Leonard, A. T. 1986. The effects of lime and K on Coastal bermudagrass yield andnutrient concentrations at two N rates. M.S. Thesis, Stephen F. AustinState University, Nacogdoches.5Figure 1. Example of DiminishingReturns to Use of an Input...........•.............................................................................................................................................................•... ............................................................................................................................................................................... ........................................................................................................................................................................... .......... ... , .............................................................................................................................................................................. ...... ........ ............. ............................ , ................................................................ ....................................................... ............ .. .. ..... ...................................•.....•....•....•••••••...........•••••......•••••.•....•.••..........•..................•• .................................... ..................................................•.....................................................................................................................................................................................................................................................................................................................................................................................................62481012tons/acre yield1614(]\o000 100 200 300 400 500 600 700 800Ibs of inputFiglI'e 2. Income from Coastal HayResulting from K FertilizationDollarsFigure 4. Determining Profit MaximizingRate of K Applied to Coastal.400+·· ·.... ·· .. ·· ·.. ················· ···· .. ·· ..·..·.. ··'.:01._-----+ISIO+·· ·.. ·· ·.. ········ .. ·· juoot ····· j"1017- Mara Input Coet , .....-+- Mara Value Prod ................................................................ , ............................................................... ,. ...........SIOSClO.40+······································~···················································1110+········.. ···························································~;···················I'10Dollars110 I 1Figu'e 3. Total Cost of K Applied toCoastal Hay'100 I I I I I I I10 100 1llO 100 110K Applicaton (Ib/ao)1.8 to.- lime/ee: $e01T hay: 250 Ib NtacD-eo -ncly Io-Ill; NacoQClochU CO:8teptlen F. Auatln 8ta18 UnlV.350Dollars$eo$60$40$30$20$10$0-$10160 200 260 300K Applicaton (lb/ac)1.6 tons lime/aci $50/T haYi 250 Ib N/ac$.22/lb Ki Darco sandy loami NacogdochesStephen F. Austin State Univ.-...J11010010 I I I I I I I10 100 80 100 noK Applicaton (Ib/ao)1.8 IlOna llme/ee: $.22/1b K: 250 Ib NteeD-eo _ncly Io-Ill; NacoQCloehe. Co.Stephlll'l F. Au.tln 8ta18 UnlV.Figure 5. Production Response, ApplyingLime to Ryegrass with pH 4.5 Soil in 1983Figure 6. Determining Profit MaximizingLevel, Lime Applied to Ryegrass, pH 4.5 Soil00Lime Rate(Ib/ac)o1000200030001986 Yield(Ib/ac)32335148650372981987 Yield(Ib/ac)551122024947371Lime Apo!. 1966 MFC(Ib/ac)0-1000 $121000-2000 $122000-3000 $121986 MVP$186$132$77112 Ib P/ac; Lllbert Loamy Fine Sandi TAES. Overton 112 Ib P/aci Lllbert loamy fine sandi TAES. OvertonFigure 7. Profit Maximizing Rates of Lime Figure 8. Profit Maximizing Rates of LimeApplied to Coastal with 250 Ib N/ac Applied to Coastal with 500 Ib N/acK Lime Rates K I:J!m(Ib/ac) (tons/ac) (Ib/ac) (tons/ac)125 11.6 248 125 1 1.6 2 4 8\0 -249 11.6 g 4 8 249 1 1.6 2 4 8373 11.6 248 373 11.6 2 4 8Sandy Loam; $60fT hay; $24fT Lime; Nacogdoches; SFA Sandy loam; $60fT hay; $24fT lime; Nacogdoches; SFA..................................- ...,. Input Coet.. .............. .............. - ...,. Valu. Prod ..................................... .........................................................................................................................................................Figure 10. Profit Maximizing Level ofPhosphate Applied to HRW Wheat with$.28/lb Phosphate and $3.50/bu WheatDollars'80'211'20'111'10'IIfa-,II~+ / ··············································1Figure 9. HRW Wheat Yield Response toPhosphate Fertilizer with .5 ton Lime/acWheat yield (bu/ac)110 +. ~ :::::::;:::::j811411 + -/- ,.....o80 I I I I I I I I I I I , I Io ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 00 ~Phosphate rate (Ib/ac)211 110 711 100Phosphate rate (Ib/ac)1000 Ib IIme/ae; Initial pH 6.3:3.0 ppm P: Burleson heavy clay:Red River Co.1211........Figure 11. HRW Wheat Yield Responseto Limestone Applications with 94 IbPhosphate/acWheat yield (bu/ac)112+···········································~······· ~Figure 12. Profit Maximizing Level ofLime Applied to HRW Wheat with $24/TLime and $3.50/bu WheatDollars.111~ I 1 ·1.10t.... ···························~···················· ..1 ... - .. _ .. .-- I'11+ ········?'"··s:::::;::······························.. ······1'0 I .............. I211001100 1000 11100 2000LIme Applicaton (Ib/ac)941b phosphate/ac; Initial pH 6.3Burleson heavy clay; P 3.0 ppm;Red River Co.82.1142 I I I I I I 'o 0.11 1 til 2Lime rate (1000 Ib/ac)Burleson heavy clay; Red River Co.Initial pH 6.3; 3.0 ppm P

Determining Fertilizer and Lime Rates for Maximum Profitability

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Determining Fertilizer and Lime Rates for Maximum Profitability

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Determining Fertilizer and Lime Rates for Maximum Profitability

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