flat-earth economics far-reaching consequences of flat payoff functions david pannell university of...
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Flat-earth economics
Far-reaching consequences of flat payoff functions
David PannellUniversity of Western Australia
Payoffs
profit expected value of profit expected utility any other objective function that
has an internal optimal solution
Example: whole farm plan
-10000
0
10000
20000
30000
40000
50000
60000
0% 20% 40% 60% 80% 100%
Percentage of farm land in crop
Wh
ole
-far
m a
nn
ual
pro
fit
(A$)
90% of maximum
51% 92%
Example: herbicide dose
0
20
40
60
80
100
120
140
160
0 0.1 0.2 0.3 0.4 0.5
Herbicide dose (kg/ha)
Pro
fit
(A$
/ha
)
95% of maximum
0.440.15
Jardine (1975):
“On presenting information to agronomists about flat profit curves for fertlizers, I observed such reactions as complete disbelief, blank incomprehension, incipient terror, and others less readily categorized.”
Flat payoff functions are:
A consistent empirical finding (almost universal)
Very important Rarely acknowledged
Debated in 1975, but apparently not since
What is behind it?
0
20
40
60
80
100
120
140
160
180
0 0.1 0.2 0.3 0.4 0.5
Herbicide dose (kg/ha)
Be
ne
fit
or
co
st
(A$
/ha
) Benefit
Cost
What is behind it?
Diversified portfolios e.g. because of
risk aversion variable resource quality resource constraints complementarity between enterprises
Implication 1:Margin for error
Decisions without careful analysis Can consider extra factors
Risk Personal preference
DSSs focus on plateau, not optimum
Implication 2: The value of monitoring
Sustainability indicators/EMS The value of information
decision theory framework What difference to the decision?
• information decision What difference then to payoff?
decision payoff Weighted by probabilities
Value often low
Implication 2: The value of monitoring
If payoff function is flat: Info may change decision But not change payoff by much
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 40 80 120 160 200 240 280
Area of trees (ha)
NP
V (
m$
)
Implication 2: The value of monitoring
If payoff function steep Optimal solution obvious More info doesn’t change it
0.8
0.9
1.0
1.1
1.2
0 40 80 120 160 200 240 280
Area of trees (ha)
NP
V (
m$
)
Either way, low info value
Implication 3: Precision farming
Jock Anderson (1975): "In pursuing optimal levels of
decision variables, precision is pretence and great accuracy is absurdity."
Implication 3: Precision farming
Example: lime application for acidity Very low precision: same low rate for all Low precision: rate set for each soil type for each
region Moderate precision: paddock by paddock (High: adjust within paddock)
Example: liming acidic soils
0
10
20
30
40
50
60
70
0 1 2 3 4 5
Lime rate (T/ha/year)
Gro
ss m
arg
in (
A$/
ha/
year
)Typical payoff function
Implication 3: Precision farming
Rainfall zone Change fromvery low tolow
Change fromlow tomoderate
Low 148
42
High 721
30
Value of information $/ha from greater precision of info
Change frommoderate tohigh
0
0
Implication 4:Value of research
Consider two types of research increases the yield of a crop by 20%
(increases yield directly) provides info that yield will be 20% higher than
previously believed (increases yield indirectly through adjustments to input levels)
Which is more valuable?
Implication 4:Value of research
Input level
Pa
yo
ff (
e.g
. ex
pe
cte
d p
rofi
t)
Perceived payoff without research
Perceived payoff with research
I1 I2
P1,1
P1,2
P2,2
Value of improving technology = P2,2 - P1,1Value of improving information = P2,2 - P1,2
Implication 5:Risk
Accounting for risk aversion makes a small difference to payoffs (CE or U)
Example: herbicides againFarmer’s relativerisk aversion
Cost of using risk-neutral model
(%)0.0 0.00.8 0.0381.6 0.182.4 0.463.2 0.95
Example: herbicide dose
0
20
40
60
80
100
120
140
160
0 0.1 0.2 0.3 0.4 0.5
Herbicide dose (kg/ha)
Pro
fit
(A$
/ha
)
95% of maximum
R=0R=3.2
A non-implication:Externalities
“Surely, if you consider externalities, the point breaks down!” payoff function stops being flat input level starts to really matter
Externality doesn’t change story
0 20 40 60 80 100
Input
$
Private payoff
Payoff - externality
Externality
Conclusion
Flatness far more important than optimum
Should emphasise flatness and its implications to our students to our clients to ourselves
Conclusion
Implications include Margin for error/Flexibility Low value of monitoring Diminishing marginal value of precision Research: value of new technology greater than
value of new information Risk aversion not very important in normative
studies
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