B-I653
February i990

TDOC
Z TA245.7

B873

NO.1653

 



 

        

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Yield Response oncl
Profil Implications,
Texos High Plains

The Texas Agricultural Experiment Station, Charles J. Arntzen, Director, The Texas A&M University System, College Station, Texas

Contents

Research Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Sugarbeet Production Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Producer Yields and Research Yield Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Stages of Production and Range of Economically
Rational Irrigated Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Optimal Irrigation Level and Nitrogen Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Economic Analysis of Returns to Management and Risk . . . . . . . . . . . . . . . . . . . . . . . . 4

Sensitivity of Profit-Maximizing Input Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Limitations of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

AppendixA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . ._ . . . . . . . . . . . . . . . . . . . . . 10

Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Irrigated Sugarbeets: Yield Response and Profit Implications,
Texas High Plains

Vernon D. Lansford, S.R. Winter, and W.L. Harman*

Sugarbeets (Beta vulgaris L.) in Texas are grown solely
in the High Plains. In 1985, four counties (Castro, Deaf
Smith, Parmer, and Randall) contributed 98 percent of the
37,000 acres of sugarbeets harvested in Texas (Texas
Agricultural Statistics Service, 1958-1985). Acreage in-
creased dramatically in 1964, when Holly Sugar Corpora-
tion opened a processing plant at Hereford, Texas.
Harvested acreage increased from the 2,000-acre range in
1958-1963 to 25,900 acres in 1964. Acreage continued to
increase to a peak in 1969 of 37,000 acres but then declined
to the lower 20,0()0-acre range in the early 1970’s. By 1985,

"Yreage again reached 37,000 acres, equal to the late 1960’s

.evel. Sugarbeet root yields averaged 19.2 tons per acre
from 1958' to 1985 and ranged from a low of 13.1 tons per
acre in 1975 to 22.8 tons per acre in 1981 (Texas Agricul-
tural Statistics Service, 1958-1985).

Sugarbeets are typically grown in 5-year crop rotations
to minimize the incidence of diseases. Thus, not more than
one-fifth of a producer’s acreage should be planted to
sugarbeets in any one year. Sugarbeets typically follow
wheat in the northern counties and cotton in the southern
producing area but may also follow corn, sorghum, and
other crops to a lesser extent.

The growing season for sugarbeets in the Texas High
Plains extends from April through October, which includes
the 6 months with the highest potential evapotranspiration
(ET). The semi-arid climate, having an annual rainfall of

I only 18 inches and high summer temperatures and winds,

necessitates irrigation for consistent production. Eighty-
three percent of the annual rainfall occurs during the
6-month growing season. However, rain frequently occurs
in high-intensity storms. Sugarbeets are typically grown on

6

‘Rcspectively, research associate, agricultural economist; professor,
agronomist; professor, agricultural economist, Texas Agricultural Ex-

f\periment Station, Amarillo, Texas

Keywords: Beta vulgaris L., production function, irrigation,
nitrogen, economics

graded furrows, where the high soil moisture levels after
irrigation can increase storm runoff. As a result, irrigation
requirements are higher than may be expected. Emergence
irrigation is a common practice to help ensure a stand.
Sugarbeet leaves typically shade the soil effectively before
the evaporation potential reaches its peak in July of slightly
more than 0.30 inches per day (Schneider and Mathers,
1969).

Sugarbeets have traditionally received full irrigation in
the Texas High Plains to produce high yields and to maxi-
mize profits. Fully irrigating beets was common when un-
derground water supplies were abundant and energy costs
for pumping were relatively low. However, as water sup--
plies diminished and energy costs increased over the past
decade, producers tended to reduce water applications.

Researchers have evaluated sugarbeets under water
stress conditions and have found them to be stress tolerant
but also highly responsive to irrigation up to the amount
needed to totally satisfy evapotranspiration (Haddock,
1955; Hobbs et al., 1963; Carter et al., 1980a; Carter et al.,
1980b; Winter, 1980).

The effects of irrigation and nitrogen on root quality
have also been studied (Brewbaker, 1934; Haddock and
Kelly, 1948; Archibald and Haddock, 1952; Haddock,
1959; Erie and French, 1968; Parashar and Dastane, 1973;
Carter, 1980b; Barbieri, 1982; Winter, 1989). Research
indicates that excessively high levels of nitrogen lowers
sugar content.

Nicholson et al. (1974), in Colorado, developed a mul-
tivariate production function that predicted sugarbeet root
yields as related to available nitrogen, consumptive use of
water, and percentage of stand. The function explained
only 52 percent of the observed variation in yield. In 1978,
Hexem and Heady, using experimental data from Arizona,
Colorado, and Texas, developed production functions
reflecting the yield-water-nitrogen relationships for sugar-
beets. The ability to explain these relationships varied from
site to site and year to year. A range of approximately from

40% to 93% of the yield variation was explained. The
quadratic function developed at Plainview, Texas, for 1971
explained only 41 percent of the observed variation in
yields. Hoyt (1984) developed a single variate production
function, which predicted sugarbeet sucrose in pounds per
acre relative to irrigation water applied plus rainfall. Al-
though this relationship explained 92 percent of the varia-
tion in sucrose yields, it was based on only 1 year of data.
Solomon et al. (1985) reviewed other sugarbeet functional
forms relating evapotranspiration to yields.

Limitations of these yield relationships point to the need
for an improved sugarbeet production function to assess
causal factors of yield response in the Texas High Plains
and to evaluate the profitability of production. The objec-
tives of this research were to (1) develop a production
function relating irrigation levels, nitrogen rates, and rain-
fall to root yields, and (2) assess the economic implications
to gross sales, production costs, and profits.

Research Methods

The sugarbeet research was conducted at Bushland,
Texas, on Pullman clay loam soil (fine, mixed Thermic
Torrertic Paleustoll). This soil has a moderately permeable
surface of about 10 inches thick. The subsoil, extending to
21 inches, is a very slowly permeable clay. Because of the
very low permeability of this soil, loss of water or nitrate-
nitrogen (NO3-N) to deep percolation would have been
negligible during these studies (Winter, 1981).

The cultivars Mono-Hy D2 (1976-79) and Mono-Hy
TX9 (1982-87) were seeded on 30-inch beds in late March
or early April. Over the years of research (1976, 1977, 1978,
1979, 1982, 1984, 1986, and 1987), seeding rates were held
constant at 6 to 7 seeds/ft, and the resulting stands were
thinned to 8 inches between plants, resulting in 26,000
plants/acre. Irrigation plots each year included eight 30-
inch-wide rows that varied over the years from 35 to 90 feet
in length. The Plots were relatively disease free compared
with typical producer fields. Two or more of the center
rows from each plot were harvested for yield in November.
Sugarbeets were produced each year in level borders to
improve the accuracy of measuring irrigation water applied
to the plots and rainfall received on the plots. The amount
of water applied was measured with an in-line flow meter.
All treatments were uniformly watered for emergence in
the spring. In most years, seasonal irrigations of three
different levels were applied during the period of about
June 10 to September 10.

Total available nitrate-nitrogen in the root zone was
measured from 0 to 6 feet deep each year before planting.
In some years, varying rates of fertilizer nitrogen were

applied according to expected root yield (which depended
mainly on irrigation) and residual nitrogen levels. This
research negated the interaction between high nitrogen
rates and sugar content by avoiding excessive rates of
nitrogen that could lower sugar content. Other inputs ex-
cept irrigation and nitrogen were the same for all irrigation
treatments.

Sugarbeet root yields were determined for each of the 8
years (Appendix Table 1, Appendix A). During this period,
2 to 6 replications of each treatment were evaluated, giving
a total of 246 observations (Appendix Table 1, Appendix
A). Available nitrogen (residual + applied) ranged from
40 pounds to 458 pounds, and total irrigation water
(preplant + seasonal) ranged from 3.0 inches to 30.5 in-
ches.

Sugarbeet Production Function

From the aforementioned research data, a production
function predicting root yields was developed. A multi-
variate regression analysis using the Reg Procedures (SAS)
resulted in the following predictive equation:

[1] Y = 6.8723 + 0.032813 T12 - 0000607113 + 0.063821 TN - 0.000112 1N2 + 0.000454'ITI'N

[1084] [00031] [0.0001] [00085] [0000014] [.00011]
(8482) (2.835) (5.445) (9.181) (8142) (2594)
+ 0.018088 M13 - 1.144391 SEP + 1.143803 ocrz - 0.339019 0013
[00023] [038198] [02894] [0.0188]
(8025) (-3.110) (3.952) (4.301)

R2 = 0.868, F = 111.121, df = 245

Brackets include the corresponding standard error of
the estimate of each regression coefficient. The cor-
responding t-values are given in parentheses. All regres-
sion coefficients were significant at the 1 percent level.

Variables in the equation are as follows:

Y = yield of sugarbeets in tons of roots per acre,
TI = total irrigation (in.) applied, including pre-
plant or emergence,
TN = total nitrogen (residual + applied) in pounds,
TITN = cross product of total irrigation x total
nitrogen,
MJ = May, June rainfall in inches,
SEP = September rainfall in inches, and
OCT = October rainfall in inches.

The negative signs of the exogenous variables SEP and
OCT3 reflect harvesting losses caused by untimely rainfall. 3°

  

Although a more desirable functional form would have 
included a rainfall-irrigation interaction term, the nature 28 _ 
of the research (being on level borders) prevented statisti- 26 _ 
‘pal sigmficance. 
24 ~ 
Producer Yields and 
Research Yield Adjustment 22 ' 
Ten sugarbeet producers were selected from a list of 2O p 
producers, two from each of five counties in the Texas High 7 8 L 
Plains. Nine of the 10 producers were using furrow irriga- 
tion practices and were the basis for evaluating current ,6 —- = 
production practices. F ive-year average root yields of sur- LU UJ 
veyed producers ranged from 18 to 34 tons/ac, an average 14 0 (D 
yield being 23.3 tons/ac, which were much lower than If E 
research yields. Producer yields may from research 12 — (n U) I
yields for a number of reasons: lack of timeliness of disease L 7 7

and insect control, soil variability, stand variability, weeds,
harvest losses, severe weather incidents, and other factors
such as lower water use efficiency in graded furrows com-
pared with level borders. For these reasons, after evaluat-
ing three adjustment alternatives, the production function
fields estimated by Equation 1 were reduced by 3O percent
.1 reflect producer yields (see Appendix B for adjustment
procedure).

0.8 1- 

Root Yields (tons/ac)

0.6 -

[21 Y = [@8123 + 0.032013 T12- 0.0011007 113 + 0.0638211»: - 0.000112 "m2 + 00004s41rm
+ 0.0100013 M13 - 1.144391 SEP + 1.143603 ocrz - 0.339019 ocr‘ 1 x 0.10

Stages of Production and Range of
Economically Rational Irrigated Production

Given the production response function (Equation 2),
the stages of production and the range over which
economically rational production would occur can be
defined. Irrigation levels outside this rational production

 

region are considered irrational given the assumption of ‘0-2 0 7o 20 30 40
maximizing net returns. Figure 1 shows the yield response
_. function related to varying irrigation amounts based on 300 Tgta] “Tigafign (inc hes)

pounds of total nitrogen.

A 40-year-average monthly rainfall period was used to
depict a long-term weather history using data from Amaril- , , _
lo’ Tgxas (1941 1986), the nearest N O AA reporting Sta-  Sugarbeet production function with 300 pounds of total
tion, where May‘ = 2.76 inches, June = 3.51 inches,

"eptember = 1.89 inches, and October = 1.51 inches
(NOAA). As a result, Equation 2 can be reduced to a

_ _ _ _ 7 _ In Stage I (Figure 1), additional units of input (irrigation
fkmpler equation by entering the average precipitation.

water) increases the productivity of all other inputs; i.e.,
777 = 2015007 + 00,2000, 7.7; 0000424 773 + 00440747770 _ 0000078 7702 average yield is increasing. The greatest efficiency in the
+ °-°°°3178TTIN use of variable inputs is at the boundary of Stage I and Stage

II (Figure 1); i.e., average physical product (APP) of irriga-
tion water is maximum at this point. However, net returns
are not necessarily maximized at this point and can be
increased with additional units of the input, moving into
Stage II. In Stage II, each additional unit of input increases
yield (total physical product, TPP), but yield per unit of
water (APP) decreases. Thus, output increases at a
decreasing rate until TPP reaches a maximum at the
boundary of Stage II and Stage III. In Stage III, additional
inputs cause production to decline. Stage II, therefore, is
the economically rational production region given the as-
sumption of maximizing net returns with respect to the
variable input.

Thebeginning of Stage II is defined as the point at which
APP is maximum and equal to marginal physical product
(MPP) (Figure 1). One can solve for maximum APP (MPP
= APP) by setting the first derivative of APP with respect
to TI equal to zero.

d APP
= 0.0229691 -0.000848TI = 0

d Tl
-0.0229691

= ——--i = 27 inches

-0.0008498

Thus, the beginning of Stage II is at 27 inches of irriga-
tion water.

After determining the beginning of Stage II at 27 inches,
the end of Stage II, or the maximum yield (TPP), can be
determined by setting the first derivative of Equation 3
equal to zero and solving for TI. However, in this function-
al form, total nitrogen (TN) is an implicit variable. In the
following example, nitrogen was assumed to be 300 pounds.

a Y
= 000127411’ + 0045933211 + 00003178119
a 11
a Y
= 0.001274 '11’ + 0045938211 + 0.000317s(300) = 0
a TI

By the quadratic equationl, yield is maximum when TI
equals 38 inches.

0.0459382 - M(0.04593s2)2 - 4(0.0012747)(0.09534)
TI =

(2 * -0.001274)
TI = 38 inches

lThe quadratic equation equals:

-b 1-\/(b2-4ac) whereY = axz + bx + c = 0
2a

Thus, the economically rational production region
(Stage II) for irrigation is defined as being between 27 and
38 inches, given 300 pounds of total nitrogen (Figure 1).
The end of Stage II varies with the level of nitrogen. For
example, with 100 pounds TN, yield is maximum at 36.7
inches irrigation water compared with 38.6 inches with 400
pounds TN. Figure 2 indicates a family of alternative
production functions with 100, 200, 300, and 400 pounds
TN. As TN increases, yields generally increase at a
decreasing rate for each production relationship. How-
ever, a high level of 500 pounds TN reduces yields at all
levels of irrigation below those of 300 and 400 pounds TN
(not shown).

Optimal Irrigation Level and Nitrogen Rate

Although the aforementioned mathematical analyses
determined the stages of production, no determination was
made of the most profitable levels of inputs (TI and TN).
To determine the optimal input levels to maximize profits
with all other inputs held constant, the first derivatives of
the production function with respect to the inputs are set
equal to the ratio of the input cost and the product price
($/ton of sugarbeets) and are solved simultaneously (see
Appendix C). A product price of $37.01/ton (P513) reflects
the 1986 price received by producers for beets yielding 14
percent sugar. The cost of applying irrigation water was
$4.01/ac inch (P1), which includes a $0.45/ac-inch cost of
irrigation labor (Texas Agricultural Extension Service,
1987). The cost of nitrogen (including application) was
$0.11/pound (PN). The optimal input levels that maximized
profits (given P513 = $31.07, P1 = $4.01, PN = 0.11) were
35 inches of irrigation water and 333 pounds of total
nitrogen. Deviation from these levels will result in sub-
optimal profits.

Economic Analysis 0f Returns t0
Management and Risk

Development of the aforementioned relationship of
yield to water and nitrogen permits an expanded analysis
of the potential profitability of sugarbeet production in the
Texas High Plains. Surveyed growers provided information
on production practices for the analyses. The per acre
returns to management and risk were estimated over a
range of sugar prices and at alternative irrigation levels.

Nine of the 10 producers surveyed using furrow irriga-
tion practices were the basis for evaluating current produc-
tion practices and costs. For each producer surveyed, an
enterprise budget was generated estimating the
individual’s cost of production using the Texas Agricultural
Extension Service MBMS budget generator (McGrann et

30

Root Yields (tons/ac)

1 O I i l i I l l
O 10 20 30 40
Total Irrigation (inches)

Figure 2. Sugarbeet production functions at various levels of total nitrogen.

al., 1986). A comparison between the high-cost and low-
cost producer indicated a difference of over $115/ac in total
costs. There was a $70 difference ($315-$245) in the total
preharvest cost between these two producers. The average
preharvest costs of all producers was $302, ranging from
$245 to $346. The high-cost producer applied 31 inches of
irrigation water, compared with 23 inches for the low-cost
producer. Overall, producers applied an average of 26.5
inches, ranging from a low of 20 inches to a high of 34.8
inches.

Equation 2 (adjusted for producer yields) was used to
estimate yields and profits per acre (Table 1). Through
partial budgeting, yields were estimated at various levels of
irrigation and at the corresponding optimal level of

nitrogen. In addition, profits were estimated using alterna-
tive sugar prices and assuming a sugar content of 14 per-
cent. Production costs except for nitrogen and irrigation
were based on the average costs of the survey. Nitrogen was
$0.11 per pound (including application cost), and irrigation
water cost $4.01/ac inch. Calculated on the basis of 2-inch
increments of irrigation, the budgeting analysis indicated
that 36 inches of water was the most profitable level of
irrigation when the price of sugarbeets was at or above
$33.14/ton ($24/cwt of sugar). When the price of sugar-
beets was from $24.68 through $31.76/ton ($18 - $23lcwt of
sugar), 34 inches was the most profitable irrigation level.
Thereafter, 32 inches was most profitable until negative
returns were realized at and below $22.10/ton.

Table 1. Per acre net returns to management and risk at alternative prices 0f sugar, 14 percent sugar content.

Irrigation level (in./ac), total nitrogen (lbs/ac), and yield (tons/ac)

  

   
 

         
   
 

Price

per ton NSP per 18 in. 20 in. 22 in. 24 in. 26 in. 28 in. 30 in. 32 in. 34 in. 36 in. 38 in.
sugar 100 lb. 299 lb. 303 lb. 307 lb. 311 lb. 315 lb. 319 lb. 323 lb. 327 lb. 331 1b. 335 lb. 339 lb.
beets sugar 20.4 t 21.5 t 22.5 t 23.5 t 24.4 t 25.2 t 26.0 t 26.6 t 27.1 t 27.4 t 27.5 t
$41.42 $30.00 346.78 375.40 403.39 429.98 454.45 476.05 494.04 507.67 516.20 518.89 515.00
$40.04 $29.00 318.56 345.76 372.35 397.60 420.81 441.25 458.22 471.00 478.87 481.12 477.04
$38.66 $28.00 290.34 316.12 341.31 365.22 387.16 406.45 422.40 434.33 441.54 443.35 439.08
$37.28 $27.00 262.12 286.48 310.27 332.84 353.52 371.65 386.58 397.66 404.21 405.58 401.12
$35.90 $26.00 233.90 256.84 279.24 300.46 319.87 336.85 350.77 360.98 366.88 367.81 363.16
$34.52 $25.00 205.68 227.20 248.20 268.07 286.23 302.05 314.95 324.31 329.55 330.04 325.21
$33.14 $24.00 177.46 197.56 217.16 235.69 252.58 267.25 279.13 287.64 292.21 292.27 287.25
$31.76 $23.00 149.25 167.92 186.12 203.31 218.94 232.45 243.31 250.97 254.88 254.50 249.29
$30.38 $22.00 121.03 138.28 155.09 170.93 185.29 197.65 207.49 214.30 217.55 216.73 211.33
$29.00 $21.00 92.81 108.64 124.05 138.55 151.64 162.85 171.67 177.63 180.22 178.96 173.37
$27.62 $20.00 64.59 79.00 93.01 106.17 118.00 128.05 135.85 140.95 142.89 141.19 135.41
$26.24 $19.00 36.37 49.36 61.98 73.78 84.35 93.25 100.03 104.28 105.56 103.42 97.45
$24.86 $18.00 8.15 19.72 30.94 41.40 50.71 58.45 64.22 67.61 68.22 65.65 59.49
$23.48 $17.00 -20.07 -9.92 -0.10 9.02 17.06 23.65 28.40 30.94 30.89 27.88 21.53
$22.10 $16.00 -48.29 -39.56 -31.14 -23.36 -16.58 -11.15 -7.42 -5.73 -6.44 -9.89 -16.43
$20.72 $15.00 -76.51 -69.20 -62.17 -55.74 -50.23 -45.95 -43.24 -42.41 -43.77 -47.66 -54.39
$19.34 $14.00 -104.73 -98.84 -93.21 -88.12 -83.87 -80.76 -79.06 -79.08 -81.10 -85.43 -92.35
$17.96 $13.00 -132.95 -128.48 -124.25 -120.51 -117.52 -115.56 -114.88 -115.75 -118.43 -123.20 -130.31
$16.58 $12.00 -161.17 -158.12 -155.29 -152.89 -151.17 .36 -150.70 -152.42 -155.77 -160.97 -168.27
$15.20 $11.00 -189.39 -187.76 -186.32 .27 .81 -186.51 -189.09 -193.10 -198.74 -206.22
$13.82 $10.00 -217.61 .36 -219.96 -222.33 -225.76 -230.43 -236.51 -244.18
$12.44 $9.00 -245.82 -247.05 -248.40 -250.03 -252.10 -254.76 -258.15 -262.44 -267.76 -274.28 -282.14
$11.06 $8.00 -274.04 -276.69 -279.43 -282.41 -285.75 -289.56 -293.97 -299.11 -305.09 -312.05 -320.10
$9.68 $7.00 -302.26 -306.33 -310.47 -314.80 -319.39 -324.36 -329.79 -335.78 -342.42 -349.82 -358.06
$8.30 $6.00 -330.48 -335.97 -341.51 -347.18 -353.04 -359.16 -365.61 -372.45 -379.76 -387.59 -396.02
$6.92 $5.00 -358.70 -365.61 -372.55 -379.56 -386.68 -393.96 -401.43 -409.12 -417.09 -425.36 -433.98
$5.54 $4.00 -386.92 -395.25 -403.58 -411.94 -420.33 -428.76 -437.25 -445.79 -454.42 -463.13 -471.94
$4.16 $3.00 -415.14 -424.89 -434.62 -444.32 -453.98 -463.56 -473.06 -482.47 -491.75 -500.90 -509.90
$2.78 $2.00 -443.36 -454.53 -465.66 -476.70 -487.62 -498.36 -508.88 -519.14 -529.08 -538.67 -547.86
$1.40 $1.00 -471.58 -484.17 -496.70 -509.09 -521.27 -533.16 -544.70 -555.81 -566.41 -576.44 -585.82

Note: The average selling price for sugar in 1986 was $22.51 per 100 lb. sugar or $31.07 per ton of sugarbeets. The solid heavy line denotes

the boundary of profit maximization (column to the left of the line) or loss minimization (negative returns).

i‘ .

Sensitivity of Profit-Maximizing
Input Levels

When water supplies were abundant and when irriga-
tion energy costs were low, producers highly irrigated

’* sugarbeets. However, as underground water supplies

diminished and energy costs increased sharply during the
past decade, producers recently tended to limit irrigation
amounts. The 1987 survey of producers indicates that two-
thirds were irrigating at levels too low to be in Stage II, the
stage of economically rational production. The level of
irrigation applied by a producer is sensitive to input costs,
sugarbeet prices, and seasonal water availability. The fol-
lowing analysis evaluates the sensitivity of maximum-profit
irrigation levels to sugarbeet prices and variations in pump-
ing costs and nitrogen prices.

Varying the price of sugarbeets from $20/ton to $40/ton
resulted in a narrow range of profit-maximizing irrigation
level of only 0.7 inches (36.4 to 37.1 inches), at an irrigation
cost of $1/ac inch. At $6/ac inch, the range of optimal
irrigation levels was only 4.3 inches (30.0 to 34.3 inches).
As the cost of irrigation water increased from $1/ac inch to
$6/ac inch and the price of sugarbeets held constant at

v,\$31.07/ton (1986 price), the profit-maximizing irrigation

level decreased only 3.7 inches, from 36.9 to 33.2 inches.
Hoyt (1984) also found that profit-maximizing water quan-
tities were not significantly affected by varying sugar prices
at low and medium water costs in Colorado.

The profit-maximizing irrigation level was also relatively
insensitive to varying rates of TN. The optimal irrigation
level changed by only 2.9 inches (33.8 to 36.7 inches) when
nitrogen ranged from 100 to 500 pounds. Furthermore,
ranging the price of nitrogen from $0.05 to $0.20/lb
changed the profit-maximizing amount of TN by only 31
lbs/ac.

Summary

Eight years of sugarbeet production resulted in the
following production function:

Y = @373 + 0032813112 - 00110001113 + 0.0038211»: - 0.000112 m2 + 0.0004s41rm
+ 0.010003 M13 - 1.144391s1z1> + 1.143603 ocrl - 0.330010

with an R2 = 0.87. A reduction from research yields of 30
percent was needed to adjust this function to reflect

r~producer field yields. In the research, total irrigations (in-

cluding prewater) ranged from 3 to 30.5 inches and total
nitrogen (residual + applied) ranged from 40 to 458

r"\pounds for a total of 246 observations. The range over

which economically rational production would occur was
calculated to be 27 to 38 inches of total irrigation given 300

pounds of total nitrogen. The optimal (profit maximizing)
irrigation level was calculated to be 35 inches given the
price of sugarbeets of $31.07/ton and the cost of applying
irrigation water of $4.01/ac inch. A comparison of this level
to those of the surveyed producers indicates that producers
in the Texas High plains on the Pullman clay loam soils are
under-irrigating sugarbeets.

Sugarbeets are relatively drought tolerant where water
supplies are limited. However, in areas of adequate water
supplies, this analysis indicates that producers should ir-
rigate at the higher irrigation levels to maximize profits.
The profit-maximizing irrigation level decreased only 3.7
inches when the cost of irrigation water increased from
$1/ac inch to $6/ac inch. When sugarbeet prices were
varied from $20 to $40/ton and water cost held constant,
the profit-maximizing water level was not significantly af-
fected.

Limitations 0f the Analysis

This economic analysis is limited in that it does not allow
for interactions between nitrogen rates and sugar content
of sugarbeets. Research suggests that high rates of nitrogen
decrease sugar percentage. The research was not designed
to evaluate this interaction because the irrigation treat-
ments were adequately fertilized but not excessively fertil-
ized. Thus, the analysis considers only impacts on root
yields but does not evaluate impacts on sugar quality.

Another limitation of the analysis is that the estimated
irrigation levels to maximize yields and profits were outside
the experimental data range. The irrigation level of 38
inches of total irrigation to maximize yield was 7.5 inches
above the experimental range. The maximum profit level
of irrigation was 4.5 inches above the highest level used in
the research (Appendix Table 1, Appendix A). Higher
irrigation levels in future research efforts may improve the
predictive ability of the production function.

Literature Cited

Archibald, D.B., and J .L. Haddock. 1952. Irrigation prac-
tice as it affects fertilizer requirement, quality and yield
of sugar beets. Am. Soc. Sugar Beet Technol. Proc.
7:229-236.

Barbieri, G. 1982. Effects of irrigation and harvesting dates
on the yield of spring-sown sugar-beet. Agricultural
Water Management, 5:345-357. Elsevier Scientific
Publishing Company, Amsterdam.

Brewbaker, H.E. 1934. Studies of irrigation methods for
sugar beets in northern Colorado. Journal of the
American Society of Agronomy, 26:222-231.

Carter, J .N., M.E. Jensen, and D.J. Traveller. 1980a. Effect
of mid-to-late-season water stress on sugarbeet growth
and yield. Agronomy J ournal,72:806-815.

Carter, J.N., D.J. Traveller, and R.C. Rosenau. 1980b. Root
and sucrose yields of sugarbeets as affected by mid-to-
late-season water stress. Journal of the Am. Soc. Sugar
Beet Technol., 20:583-596.

Erie, L.J., and O.F. French. 1968. Water management of
fall-planted sugar beets in salt river valley of Arizona.
Trans. ASAE 11:792-795.

Haddock, J .L. 1955. The irrigation of sugar beets. Year-
book of Agriculture. pp. 400-405.

Haddock, J .L. 1959. Yield, quality and nutrient content of
sugar beets as affected by irrigation regime and fer-
tilizers. Journal of the Am. Soc. Sugar Beet Technol.,
10:344-355.

Haddock, J .L., and O.J. Kelly. 1948. Interrelation of mois-
ture, spacing, and fertility to sugarbeet production. Am.
Soc. Sugar Beet Technol. Proc. 5:378-396.

Hexem, R.W., and E.O. Heady. 1978. Water production
functions for irrigated agriculture. Iowa State Univer-
sity Press, Ames, Iowa, pp. 136-171.

Hobbs, E.H., K.K. Krogman, and L.G. Sonmor. 1963. Ef-
fects of levels of minimum available soil moisture on
crop yields. Canadian Journal of Plant Science, 43
(4):441-446.

Hoyt, P.G. 1984. Crop-water production functions:
economic implications for Colorado. ERS Staff Report
No. AGES 840427, Natural Resources Economics
Division, Economic Research Service, U.S. Depart-
ment of Agriculture, Washington, D.C. 19 p.

McGrann, J .J ., K.D. Olson, T.A. Powell, and T.R. Nelson.
1986. Microcomputer budget management system user
manual. Department of Agricultural Economics, Texas
A&M University, College Station, Texas. 450 p.

National Oceanic and Atmospheric Administration
(NOAA), National Environmental Satellite, Data and
Information Service. Local climatological data, annual
summary with comparative data, Amarillo, Texas,
Dept. of Commerce, U.S.A.

Nicholson, M.K., T. Kibreab, R.E. Danielson, and R.A.
Young. 1974. Yield and economic implications of
sugarbeet production as influenced by irrigation and
nitrogen fertilizer. Journal of the Am. Soc. Sugar Beet
Technol., 18 :34-44.

Parashar, K.S., and N.G. Dastane. 1973. Studies on the
effect of soil moisture regime, plant population and
nitrogen fertilizer on yield and quality of sugarbeets.
Indian Journal of Agronomy, 18:349-353.

SAS. 1985. SAS/STAT guide for personal computers.
SAS Institute, Inc., Cary, N.C. 378 p.

Schneider, A.D., and A.C. Mathers. 1969. Water use by
irrigated sugar beets in the Texas High Plains. MP-935,
Texas Agri. Exp. Sta., Texas A&M University, College
Station, Texas.

Solomon, K.H. 1985. Typical Crop Production Functions.
ASAE Paper No. 85-2596, presented at the 1985 winter
meetings, ASAE, Chicago, IL, Dec. 17-20, 1985.

Texas Agricultural Extension Service. 1987. Texas crop
enterprise budgets - Texas Panhandle district. B-
1241(C01), Texas A&M University, College Station,
Texas.

Texas Agricultural Statistics Service, Texas Department of
Agriculture. 1958-1985. Texas field crop statistics. Aus-
tin, Texas.

Winter, S.R. 1980. Suitability of sugarbeets for limited
irrigation in a semi-arid climate. Agronomy Journal,
72:118-123.

Winter, S.R. 1981. Nitrogen management for sugarbeets
on Pullman soil with residual nitrate problems. Journal
of the Am. Soc. Sugar Beet Technol. 21:41-49.

Winter, S.R. 1989. Sugarbeet yield and quality response to
irrigation, row width, and stand density. Journal of
Sugar Beet Research. 26:26-33.

APPENDIX A

Research Data

Appendix Table 1. Sugarbeet treatments by irrigation, nitrogen, and precipitation used to formulate the
sugarbeet production function, Bushland, Texas, 1976-87.

Mean Seasonal Pre Appl. Resid. May-June Sept. Oct.
Year Rep’s Yield Irrg. Irrg. N N Precp. Precp. Precp.
(tons/ac) (in) (lb.) (lb.) (in) (in) (in)
87 6 20.7 0.0 3.0 0.0 96 8.21 4.46 1.25
87 6 21.3 0.0 3.0 89.2 96 8.21 4.46 1.25
87 6 23.8 0.0 3.0 178.4 96 8.21 4.46 1.25
87 6 23.7 0.0 3.0 267.6 96 8.21 4.46 1.25
77 2 14.2 0.0 5.0 60.0 120 4.19 0.43 0.28
78 4 24.2 0.0 5.3 40.0 171 9.57 5.34 0.33
76 2 15.6 0.0 6.0 0.0 398 2.60 2.31 1.63
86 6 18.2 0.0 8.7 0.0 40 6.77 1.88 2 49
86 6 20.2 0.0 8.7 53.5 40 6.77 1.88 2 49
86 6 20.5 0.0 8.7 107.0 40 6.77 1.88 2 49
86 6 22.0 0.0 8.7 214.0 40 6.77 1.88 2 49
82 3 15.3 0.0 9.1 0.0 75 5.85 2.15 1 02
82 3 19.6 0.0 9.1 53.5 75 5.85 2.15 1.02
82 3 20.3 0.0 9.1 107.0 75 5.85 2.15 1.02
82 3 23.0 0.0 9.1 160.6 75 5.85 2.15 1.02
87 6 20.4 8.1 3.0 0.0 96 8.21 4.46 1.25
87 6 23.4 8.1 3.0 89.2 96 8.21 4.46 1.25
87 6 24.8 8.1 3.0 178.4 96 8.21 4.46 1.25
87 6 27.1 8.1 3.0 267.6 96 8.21 4.46 1.25
82 3 17.8 3.4 9.1 0.0 75 5.85 2.15 1 02
82 3 22.6 3.4 9.1 53.5 75 5.85 2.15 1 02
82 3 22.2 3.4 9.1 107.0 75 5.85 2.15 1.02
82 3 23 2 3.4 9.1 160.6 75 5.85 2.15 1.02
84 3 20.4 0.0 13.1 0.0 182 4.81 0.74 3.44
84 3 19.7 0.0 13.1 53.5 182 4.81 0.74 3.44
84 3 19.9 0.0 13.1 107.0 182 4.81 0.74 3.44
84 3 20.8 0.0 13.1 214.0 182 4.81 0.74 3.44
77 2 22.8 10.0 5.0 120.0 120 4.19 0.43 0.28
76 2 21 8 12.0 6.0 40.0 398 2.60 2.31 1.63
86 6 24 1 10.3 8.7 0.0 40 6.77 1.88 2.49
86 6 25 7 10.3 8.7 53.5 40 6.77 1.88 2.49
86 6 29.0 10.3 8.7 107.0 40 6.77 1.88 2 49
86 6 32.3 10.3 8.7 214.0 40 6.77 1.88 2.49
87 6 24.6 16.2 3.0 0.0 96 8.21 4.46 1.25
87 6 30.9 16.2 3.0 89.2 96 8.21 4.46 1.25
87 6 33.3 16.2 3.0 178.4 96 8.21 4.46 1.25
87 6 33.2 16.2 3.0 267.6 96 8.21 4.46 1.25
78 4 35.1 14.0 5.3 80.0 171 9.57 5.34 0.33
82 3 18.8 10.4 9.1 0.0 75 5.85 2.15 1.02
82 3 24 3 10.4 9.1 53.5 75 5.85 2.15 1.02
82 3 24 6 10.4 9.1 107.0 75 5.85 2.15 1.02
82 3 27.2 10.4 9.1 160.6 75 5.85 2.15 1 02
84 3 29.2 8.0 13.1 0.0 182 4.81 0.74 3 44
84 3 30.3 8.0 13.1 53.5 182 4.81 0.74 3 44
84 3 29.7 8.0 13.1 107.0 182 4.81 0.74 3.44
84 3 28.6 8.0 13.1 214.0 182 4.81 0.74 3.44
78 4 40.9 19.1 5.3 120.0 171 9.57 5.34 0.33
:77 2 34.2 20.0 5.0 180.0 120 4.19 0.43 0.28
Q86 6 25.6 18.0 8.7 0.0 40 6.77 1.88 2.49
'86 6 30.1 18.0 8.7 53.5 40 6.77 1.88 2 49
86 6 31.5 18.0 8.7 107.0 40 6.77 1.88 2 49
86 6 36.4 18.0 8.7 214.0 40 6.77 1.88 2 49
84 3 32.8 16.0 13.1 0.0 182 4.81 0.74 3 44
84 3 34.2 16.0 13.1 53.5 182 4.81 0.74 3.44
84 3 31.8 16.0 ‘13.1 107.0 182 4.81 0.74 3 44
84 3 32.9 16.0 13.1 214.0 182 4.81 0.74 3.44
76 2 28.9 23.9 6.0 60.0 398 2.60 2.31 1.63
79 6 37.0 22.5 8.0 89.0 218 4.84 0.39 1 82

APPENDIX B

Producer Yield Adjustment Procedure

Three methods of estimating differences between producer yields and those obtained
in the research were evaluated by selecting the method that minimized the average of
the sum of deviations between predicted yields using Equation 1 and the 5-year average
yield of the producers surveyed. The predicted yields, using Equation 1, were based on
the producers’ irrigation levels and nitrogen rates. However, 40-year normal monthly
rainfall for Amarillo, Texas, was used for the rainfall variables.

The first method simply multiplied the predicted yields from Equation 1, using
producer levels of irrigation and nitrogen, by 70 percent; the percentage research yields
varied from the 1976-85 county average yields (Texas Agricultural Statistics Service,
1976-85). These adjusted yields were then compared with reported yields, and the sum
of the deviations was averaged across producers, resulting in an average reduction of 9.2
tons/ac from predicted yields. The next two methods resulted in subtracting a constant
amount from the predicted yields of Equation 1 rather than subtracting a percentage
amount. The second method used 70 percent of the predicted yield of Equation 1 but
was based on the surveyed average producer irrigation level of 26.5 inches irrigation
water and 300 pounds nitrogen. Compared with reported yields, the average of the sum
of deviations was a 10-ton reduction from predicted yields. The final method also
reduced the predicted yield of Equation 1 by 30 percent but was evaluated at the end of
Stage II as being 38 inches irrigation water and 300 pounds nitrogen. This resulted in an
average of the sum of deviations of an 11-ton reduction from the predicted yields. Thus,
the first of the three estimating methods, a 30 percent _reduction from predictions of
Equation 1, minimized the sum of the deviations between predicted and reported yields.

1O

APPENDIX C

Simultaneous Solution of Optimal Irrigation Level and Nitrogen Rate

The simultaneous solution of the optimal irrigation level and nitrogen rate is accomplished by simultaneously solving the
following two general equations:

d Y P] d Y PN
____ = and =
d TI PSB d TI PSB
d Y _
The first derivative d is set equal to the ratio of the water cost and the product price (S/ton of beets).
TI
Ci Y 2 P I
= -0.0012747 TI + 0.0459382 TI + 0.0003178 TN =
d TI PS3
2 4.01
= -0.0012747 TI + 0.0459382 TI + 0.0003178 TN = —————
31.07
[1] = -0.0396049 T12 + 1.427299 TI + 0.0098740 TN = 4.01
d Y
\ The first derivative is set equal to the ratio of the nitrogen cost (including application) and the product price
d TN
($/ton of sugarbeets).
d Y PN
= -0.0001568 TN + 0.0003178 TI + 0.0446747 =
Cl TN PSB
0.11
= -0.0()01568 TN + 0.0003178 TI + 0.0446747 = --——-
31.07
[2] = -0.0048718 TN + 0.0098740 TI + 1.3880429 = 0.11

To simultaneously solve Equations 1 and 2, one must reduce the equations to one unknown. To solve for TI, TN must
be cancelled when adding the two equations. This is accomplished by multiplying Equation 2 by 2.0267663
(0.0098740/0.0048718), which will cancel TN out of the summation of the equations.

[3] -0.0098740 TN + 0.0200123 TI + 2.8132386 = 0.2229443

11

Adding Equations 1 and 3 together results in the following:

-0.0396049 T12 + 1.4272999 TI + 0.0098740 TN = 4.01
0.0200123 TI - 0.0098740 TN + 2.1832386 = 0.2229443
0.0396049 T12 + 1.4473113 TI + 2.1832386 = 4.2329443

0.0396049 T12 + 1.4473113 TI = 1.4197057
Solving for TI using the quadratic equation results in the following:

-0.0396049 T12 + 1.4473113 TI - 1.4197057 = 0

- 1.4473113 - \/ (-1.4473113)2-4(-0.0396049)01.419705?)

2(-0.0396049)

TI = 35 inches

To determine optimal TN, substitute (TI = 35) into Equation 2 as follows, and solve for TN:

—0.0048718 TN + 0.0098740 (35) + 1.3880429 = 0.11
-0.0048718 TN = -1.6236329

TN = 333 pounds

12

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