And the impossibility of utility maximisation From indifference Concept of subjective utility dates back at least to Aristotle made central tenet of economics and philosophy by Jeremy Bentham ID: 513919
Download Presentation The PPT/PDF document "The “curse of dimensionality”" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
The “curse of dimensionality”
And the impossibility of utility maximisationSlide2
From indifference…
Concept of subjective utility dates back at least to Aristotle; made central tenet of economics and philosophy by Jeremy Bentham (
not
Adam Smith!)
Formalised into concept of “indifference curves” by neoclassical economists (see Chapter 2,
Debunking Economics
)
Many different combinations of goods capable of giving consumer same level of subjective utility
Line linking points akin to “isoquant” on map, linking points of equivalent altitude
Christened “indifference curves”:Slide3
Bananas
Biscuits
A
B
C
D
Combinations A and B give same level of satisfaction
Combination C gives higher level than A or B
Combination D gives lower level than A or B
From indifference…
Just one wee problem…
Indifference curves no more observable than angels dancing on heads of medieval pins…Slide4
To revealed preference…
Samuelson proposed solution: “revealed preference”
Indifference curves could be inferred from behaviour of consumer, provided 4 postulates of rationality met:
Completeness: consumer knows own subjective ranking of all combinations of goods
Transitivity: If combination A preferred to combination B, and B to C, then A preferred to C
Non-satiation: More is always preferred to less.
Convexity: additional utility a consumer gets from extra units of each commodity fallsPreferences and budget completely independentApplying this:Slide5
Bananas
Biscuits
A
To revealed preference…
All points in rectangle necessarily preferred to A (“non-satiation”)
Bananas
Biscuits
B
A
C
If A purchased when both B and C affordable, then A necessarily on higher indifference curve than B and C
Move budget line around, see responses, can eventually infer indifference map from observed behaviour
Appears scientific, but problems when verification attempted…Slide6
To experimental testing…
Bananas
Biscuits
In theory, consumer starts with
complete
preference set
Imposes budget line
Works out point of tangency
Buys this combination
In experiment, easy to decide whether someone is rational or irrational according to theory:
(Preferences and budget completely independent)Slide7
The neoclassical expectation…
Bananas
Biscuits
X Initial budget line
Consumer chooses A when A & B both affordable
A must lie on higher indifference curve
Rational consumer “should” always prefer A to B
But in experiments they don’t do this! Sometimes, they choose B instead of A
A
X
B
Budget Y: A no longer best, but “clearly” better than B
YSlide8
Consumers “irrational”
But in reality, economists definition of “rational” is irrational
Many weaknesses
but key one the unwitting assumption that consumers have near infinite information processing ability: the “curse of dimensionality”
issue easily illustrated by putting numbers on axes of economists’ graphs:
The neoclassical explanation…Slide9
Putting some numbers on the graph…
Bananas
Biscuits
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
121 combinations
Some you ignore
Others you can’t…
10 pairs
10 additions
10 comparisons
Easy!
But…Slide10
Putting some numbers on the graph…
Every additional commodity considered adds another dimension. With no more than 10 units of each:
2 commodities, ~100 combinations
(actually 121)
3 commodities, ~1,000 combinations
4 commodities, 10,000 combinations
30 commodities…
how many combinations?Slide11
Putting some numbers on the graph…
10,000,000,000,000,000,000,000,000,000,000!
If budget obviously ruled out 99.9% of these;
If each evaluation took 1 billionth of a second…
Process would complete after
32 billion years
Maximum (est.) age of universe 20 billion yearsIndividual would take 1.6 times age of known universe to make “utility maximising” choice of just 30 commoditiesMaximising utility in typical supermarket (1,000+ different items) doesn’t bear contemplationlet alone millions of products in modern economyInstead, intelligent partitioning of commodity space vital…Slide12
Utility maximising individuals?
Sources of partitioning
Culture
some commodities not even contemplated (sea slugs, anyone?)
Income & Needs
Fulfil hierarchy of wants from basic to ethereal (Maslow’s concepts)
Rolls Royce’s not part of “utility set” of poorBaked beans not part of “utility set” of richHabitBuy mainly what you bought yesterdayChange in consumptionEvolutionary rather than “rational” processSlide13
Utility maximising individuals?
Individual tastes no longer a “given” but vital economic issue
Explains individual partitioning of commodity space
Selling new products requires movement of this space
Marketing, advertising thus essential “economic” activities if new products are to be sold
Co-evolution of products and tastes an essential aspect of economic development
Consumers do not “utility maximise” but instead “satisfice” (as per Herbert Simon)Demand curve for individual consumer becomes meaningless, let alone neoclassical idea of market demand curve (see Debunking Economics, Chapter 2)