Farming a Flat Function
AAE 320
Overview of Lecture

“Farming a Flat Function”




What is it? (Give Examples)
What does it mean? (Implications)
In my opinion, this problem underlies a lot
of complaints about farmers and the
environment
It’s not a simple problem to fix
Farming a Flat Function
For many crop production processes, yield
becomes relatively unresponsive to inputs
when they are used at near optimal levels
Yield

Input
Farming a Flat Function
As a result, profit also has a “flat”
response to the input
Profit

Input
Mitchell (2004)





Assembled data from experiments
examining corn response to nitrogen
Most from late 1980’s and early 1990’s
Seven states (IA, IL, IN, MN, NE, PN, WI)
Almost 6,000 individual observations
Analyzed to see if could statistically
observe effect of nitrogen on yield when
used at high/near optimal nitrogen rates
One Site-Year from Iowa
Yield (% max)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
50
100
150
200
N Rate (lbs/ac)
250
300
All Site Years from Iowa
Yield (% max)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
50
100
150
200
N Rate (lbs/ac)
2,200 observations
250
300
Avg Yield (% max)
Average Yield by N Rate
1.2
1.0
IN
IA
PN
Waseca
Morris
0.8
0.6
0.4
0.2
0.0
0
50
100 150 200 250 300
N rate (lbs/ac)
Main Point



Once N rates get above 85-100 lbs/ac,
expected (average) corn yield very flat,
but lots of variability around this average
Makes identifying yield effects of nitrogen
on corn statistically difficult/impossible
Change in yield with changing N rate hard
to see with all the noise from other factors
Online N Tool from Problem Set 1
Current WI Recommendations
Net return to N ($/a)
100
80
60
N:Corn price ratio
0.05
0.10
0.15
0.20
40
20
CC - High Yield Potential Soils
0
0
50
Source: C. Laboski, UW Soil Science
100
150
N rate (lb/a)
200
250
Main Point





WI nitrogen recommendations for corn give the
range of N rates that are within $1/ac of the
maximum return
Notice how wide the range of N rates is
Over the range of application rates the
recommendations give, expected net returns
vary less than $1/ac
Returns from applying nitrogen to corn are
very flat when near optimal levels
See the same thing for corn seeding rates:
very flat returns
What about other inputs?


1) Economic analysis of Seeding Rates
2) Economic analysis of processing and
fresh market sweet corn and the value of
insecticide sprays for controlling European
corn borer (ECB)
 Mitchell et al. (2005)
Corn Returns for Seeding Density
from Problem Set 1 (Lauer)
Soybean Returns for Seeding
Density and Seed Treatments
(Gaspar et al. 2014)
Processing Sweet Corn Insecticides
250
Net Returns
200
Pounce
Mustang
Baythroid
Capture
Warrior
150
100
50
0
0
1
2
3
# Sprays
4
5
Capture on Processing Sweet Corn
(mean with 95% error bars)
350
Average Returns
300
250
200
150
100
50
0
0
1
2
3
# Sprays with Capture
4
5
Capture on Fresh Market Sweet Corn
3000
Average Returns
2500
2000
1500
1000
500
0
0
2
4
6
# Sprays with Capture
8
10
Capture on Fresh Market Sweet Corn
(mean with 95% error bars)
3500
Average Returns
3000
2500
2000
1500
1000
500
0
0
1
2
3
4
5
6
# Sprays with Capture
7
8
9
10
Main Point





Farmers are “Farming a Flat Function” for
several of main inputs
Implications
1) Small profit change over wide input range
2) Impact of inputs on returns is hard to notice
with all the variability from other factors
3) Wide range of input levels will be/seem
consistent with profit maximization
And Another Issue

Under use of inputs is often obvious


See weeds, insects, diseased plants, yellow or purple
crop, wilted crops
Over use of inputs is often invisible

How many farmers leave an untreated check strip?
When Farming on a Flat Function,
How do you know if you put on too much Can’t?
Fertilizer? Fungicide? Insecticide? Water? Costly!
Over use of inputs often an invisible cost

Main Point





Implications of Farming a Flat Function when
under use of inputs is obvious and over use is
invisible
Wide range of input levels consistent with profit
maximization (and risk management)
Some inputs turn out to not be used/needed
afterwards, but cannot tell when put them on
Some of the “extra” inputs end up as pollution
Farmers accused of using too many inputs
In my opinion





This problem underlies a lot of complaints about farmers
and the environment
It’s not a simple problem to explain to the public: Why
do farmer use so much fertilizer, pesticide, water, etc.?
 Would farmers waste money on purpose?
Most farmers make an honest effort to be good stewards
But farming is messy and variable and it is expensive to
find out where you are or will be on some flat function
What’s the answer? More/better technology? Try to
better match “natural” systems? Both? Something else?