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Market Behaviour - Part 2

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Change in relative price alters incomes.
Start with arbitrary price ratio; Keep aggregate income constant; Consider lower price for bananas. Crusoe’s (banana owner) income falls; Friday’s increases. Market demand for bananas falls because of lower price – Crusoe’s income fell. Friday’s income rose – But his preference for bananas less than Crusoe’s.
Hicksian procedure – Keep relative prices constant. Increase income equally. Banana demand rises more than Coconut. Crusoe’s income rises more than Fridays. Cannot compensate for income effect of price change; Uniform increase in income alters income distribution, because varying consumption as income rises favours luxury-producing agent over the other.
Outcome: Market demand curve can have any (polynomial shape at all: Need to obey Law of Demand. Only way to avoid this – Assume all consumers have identical tastes. So thers is only one consumer. And assume that tastes don’t change with income. So there is only one commodity. Contradicts starting assumption. Two consumers with different tastes, Two different commodities. Proof by contradiction that Law of Demand does not apply to market demand curve.

Describe contradiction as stringent conditions for a market demand curve to obey Law of Demand. Decrease in price causes increase in demand. Reflect rules of Revealed Preference. Shafer and Sonnenschien (1982). Market demand curve will obey law of demand. When preferences are homothetic and the distribution of income is independent of prices. Gorman (1953, p. 63) if and only if the personal Engel curves are parallel straight line for different individuals at the same prices.
All good have to be “homothetic or neutral. Relative consumption does not change as income rises. If you consumed 1 pizza, 1 coke and 0 Rolls Royces a day when your income was $100 a day. Then you would consume 100 pizzas, 100 cakes and 0 Rolls Royces a day at an income of $10,000 a day.
Your Engel curve has to be parallel to everyon’s else’s. But there’s even more – Parallel lines that pass through the same point are the same line. All Engel curves must pass through 0, 0 (no income, no consumption of anything). So all individuals have to have identical preferences.
Every individual must have indifference curves that generate Engel curves identical to these.
Hang on a second… If all individuals have the same preferences – Then there’s only one individual and if your relative consumption of goods doesn’t change as income changes then there’s only one good. So market demand curves obey the Law of Demand (be downward sloping) if there is only one consumer and there is only one commodity.
Assume market demand curves slope downwards. Start from condition of many consumers and commodities. Find that can only get downward sloping market demand curve if there is only 1 consumer and 1 commodity. Proof by contradiction that market demand curves can have any shape at all. Even if individual demand curves obey Law of Demand. So though economists draw curves like this.
This is more valid: Proper response to result: Market demand curves can’t be guaranteed to slope downward. Supply- demand equilibrium analysis not sustainable. Have to replace Marshallian micro with something else. And in micoreconomics.
Every individual must have indifference curves that generate Engel curves identical to these.

Can’t model whole economy as a single individual. But could aggregate to classes. Should revive Classical economic class-based analysis. Alan Kirman’s sensible reaction to this result: If wea re to progress further we may well be forced to theorise in terms of groups who have collectively coherent behavior. Thus demand and expenditure functions if they are to be set against reality must be defined at some reasonably high level of aggregation. The idea that we should start at the level of the isolated individual is one which we amy well have to abandon. (Kirman, Economic Jouranl, 1989, p 138). How is this communicated to Students?
Honest statement of this in advanced research book: Shafer and Sonnenschien (Handbook of Mathematical Economics Vol II 1982 pp 671 -2) Market demand functions need not satisfy in any way the classical restrictions which characterize consumer demand functions. The importance of the above results is clear: strong restrictions are needed in order to justify the hypothesis that a market demand function has the characteristics of a consumer demand function. Only in special cases can an economy be expected to act as an idealized consumer. The utility hypothesis tells us nothing about market demand unless it is augmented by additional requirements.
Varian Microencomics Analysis. It is sometimes convenient to think of the aggregate demand as the demand of some representative consumer. The conditions under which this can be done are rather stringent but a discussion of this issue is beyond the scope of this book. (Varian 1987: p268) 2nd Edition – This demand function can in fact be rationalized by a representative consumer.