Front Cover

Group Title: Research report - North Florida Research and Education Center ; 90-9
Title: Maximum economic yield a mathematical definition
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00066081/00001
 Material Information
Title: Maximum economic yield a mathematical definition
Series Title: Research paper (North Florida Research and Education Center (Quincy, Fla.))
Physical Description: 6 leaves : ill. ; 28 cm.
Language: English
Creator: Rhoads, Fred ( Frederick Milton )
North Florida Research and Education Center (Quincy, Fla.)
Publisher: North Florida Research and Education Center
Place of Publication: Quincy Fla
Publication Date: 1990
Subject: Crops -- Economic aspects   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Bibliography: Includes bibliographical references.
Statement of Responsibility: F. M. Rhoads.
General Note: Cover title.
 Record Information
Bibliographic ID: UF00066081
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 71152156

Table of Contents
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        Front Cover
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        Page 4
        Page 5
Full Text

NFREC, Quincy Research Report 90-9

Maximum Economic Yield

A Mathematical Definition

Florida Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville

610 1

|^^^^^^^ *^^^ ^^

Maximum Economic Yield: A Mathematical Definition

Maximum economic yield (MEY) of a crop results in maximum

profit per acre. Profit is determined by yield response to

production inputs, cost of inputs, and price of output. It has

been suggested that maximum economic yield is about 95% of maximum

yield, however, high input-costs and low commodity prices may

reduce MEY further. Therefore, a mathematical definition of MEY

would be helpful in setting yield goals for specific cost-price

situations. When maximum yield is reached an increase of

production inputs does not increase yield. Furthermore, the ratio

of change in output/change of input becomes less as maximum yield

is approached and is equal to zero at maximum yield.

It is not economical to add more production inputs when the

cost of added inputs is greater than the value of the increase in

output. Therefore, MEY occurs when the cost of added input is

equal to the value of the yield increase produced. This can be

expressed mathematically as follows:

(AY)(Yp) = (AX)(Xc)

where AY = yield increase

AX = increase of production input

Yp = commodity price

Xc = production cost per unit of input.

Making use of calculus the above equation can be expressed as dy/dx

= Xc/Yp

where dy/dx = slope of the yield versus input

function and

Xc/Yp = cost/price ratio.

A mathematical definition of MEY is illustrated for grain

yield of irrigated corn in figure 1 where the production input is

nitrogen (N). Maximum yield and MEY for a cost/price ratio of 0.58

are shown. Nitrogen rate and MEY for a cost/price ratio of 0.58

are 150 lb/A and 203 bu/A, respectively. The MEY for a cost/price

ratio of 1.0 is 120 bu/A and nitrogen rate is 45 lb/A. To

determine MEY for any cost/price ratio, construct a horizontal line

from the cost/price axis to the curve representing the cost/price

function, then construct a vertical line from the C/P curve to the

yield curve, finally construct a horizontal line from the yield

curve to the yield axis, the resulting value is the MEY. Nitrogen

rate is equal to the distance between the yield axis and the

vertical line connecting the two response curves.

Some input costs remain fixed regardless of yield goal. These

costs include equipment, land, pesticide, etc. Variable costs such

as nitrogen, phosphorus, potassium, seed, and irrigation change

with yield goal. Nitrogen is usually the factor that limits yield

of corn most. Therefore, when N rate is reduced other inputs can

be reduced in proportion to the N reduction. Consequently, all

variable input costs can be expressed in terms of cost per pound of


Magnitude of profit margin, which may be positive or negative,

depends on the difference between total input costs and total

output returns. Remember, when profit is negative low or high

input agriculture is not sustainable. The effect of increasing N

cost on profit from irrigated corn at $2.00/bu is shown in table 1.

As expected, the cost/price ratio increased as the cost of N

Yield (bu/acre)

Cost/Price (ratio)

Maximum Yield 244 bu/A N 294 Ib/A

0 50 100 150 200 250 300









Ib N/acre
Figure 1. Grain yield of corn as a function of nitrogen rate. The cost/price
ratio is equal to the slope of the yield function. Equations were
derived from yield data obtained at the North Florida Research and
Education Center, Quincy.


increased, while profit and MEY decreased. Profit also decreased

as N rate decreased. Zero profit occurred with 120 lb of N/A and

a fixed cost of $200/A. However, a net loss of $58/A was the

result of zero N rate and $200/A fixed cost. The break even corn

price with zero N and $200/A fixed cost is $2.82/bu or the fixed

cost would have to be reduced to $142/A in order to break even with

zero N at $2.00/bu. Fixed costs can vary between locations due to

pest control and land cost differences. A higher N rate was

required to break even with a $300/A fixed cost than with a $200/A

fixed cost (198 vs. 120 lb/A). The influence of corn price on

profit and MEY of irrigated corn is shown in table 2. At $3.00/bu

MEY is equal to maximum yield which requires about 270 lb N/A.

However, further increases in corn price do not justify additional

production inputs because maximum yield has occurred and additional

inputs only decrease profit.

Table 1. Influence of N cost on MEY and net profit for corn
production at two levels of fixed input costs.
Calculations are based on functions shown in figure 1.
Corn price is $2.00 per bushel.

N Rate Cost of N Cost/price MEYt Fixed Input Costs
lb/acre $/lb ratio bu/acre $200/acre $300/acre

---profit $/acre---

261 0.25 0.13 242 218.75 118.75
232 0.50 0.25 237 158.00 58.00
199 0.75 0.38 226 102.75 2.75
169 1.00 0.50 213 57.00 43.00
107 1.50 0.75 174 -12.50 -112.50
45 2.00 1.00 120 -50.00 -159.00

tUnder certain cost structures MEY represents the minimum loss.
iProfit = (bu/acre x $/bu) (lb N/acre x $/lb N + other input

Table 2. Influence of corn price on MEY and net profit at two
levels of fixed input costs. Calculations are based on
functions shown in figure 1. Price of N is $0.30 per lb.

N Rate Corn price Cost/price MEYt Fixed Input Costs
lb/acre $/bu ratio bu/acre $200/acre $300/acre

---profit $/acre---

219 1.00 0.30 233 -32.70 -132.70
244 1.50 0.20 239 85.30 14.70
256 2.00 0.15 241 205.20 105.20
269 3.00 0.10 243 448.30 348.30
269 4.00 0.08 243 691.30 591.30

tUnder certain price structures MEY represents the minimum loss.
Profit = (bu/acre x $/bu) (lb N/acre x $/lb N + other input

This report shows conclusively that MEY is inversely proportional

to the cost/price ratio for production of irrigated corn.

Furthermore, in production systems adequately described by the

function in figure 1, it is not profitable to add variable inputs

when the cost/price ratio is greater than 1.18 regardless of fixed

costs. Data are needed to develop regression models of yield as a

function of pesticide rates in order to define low input

sustainable agriculture (LISA).

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