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The “curse of dimensionality” 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 (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”: From indifference… Biscuits • 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 • Just one wee problem… A C B D Bananas • Indifference curves no more observable than angels dancing on heads of medieval pins… 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 falls – Preferences and budget completely independent • Applying this: To revealed preference… Biscuits • All points in rectangle necessarily preferred to A (“non-satiation”) A Bananas Biscuits C A B Bananas • 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… • In theory, consumer starts with complete preference set • Imposes budget line • Works out point of tangency • Buys this combination Bananas To experimental testing… • (Preferences and budget completely independent) Biscuits • In experiment, easy to decide whether someone is rational or irrational according to theory: • X Initial budget line • Consumer chooses A when A & B both affordable • Rational consumer “should” always prefer A to B Bananas The neoclassical expectation… Budget Y: A no longer best, but “clearly” better than B X • A must lie on higher indifference curve A B Y Biscuits • But in experiments they don’t do this! Sometimes, they choose B instead of A The neoclassical explanation… • 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: • 121 combinations • Some you 10 ignore 9 • Others 8 you can’t… 7 • 10 pairs 6 • 10 additions 5 4 • 10 comparisons 3 2 • Easy! 1 • But… 0 Bananas Putting some numbers on the graph… Biscuits 0 1 2 3 4 5 6 7 8 9 10 Putting some numbers on the graph… • Every additional commodity considered adds another dimension. With no more than 10 units of each: • 2 commodities, • 3 commodities, ~1,000 ~100 combinations combinations (actually 121) • 4 commodities, 10,000 combinations • 30 commodities… • how many combinations? 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 years – Individual would take 1.6 times age of known universe to make “utility maximising” choice of just 30 commodities – Maximising utility in typical supermarket (1,000+ different items) doesn’t bear contemplation • let alone millions of products in modern economy • Instead, intelligent partitioning of commodity space vital… 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 poor – Baked beans not part of “utility set” of rich – Habit • Buy mainly what you bought yesterday – Change in consumption • Evolutionary rather than “rational” process 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)