Flat-earth economics

Far-reaching consequences of flat payoff functions

David PannellUniversity of Western Australia

Starting point

1983

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

Monopolist’s pricing decision

Price

Pay

off

.

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

Implications

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

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

90% range

Externality doesn’t change story

0 20 40 60 80 100

Input

$

Private payoff

Externality

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

www.davidpannell.net

Pannell, D.J. (2006). Flat-earth economics: The far-reaching consequences of flat payoff functions in economic decision making, Review of Agricultural Economics 28(4): 553-566.