【正文】
B39。B?x2?A39。 Bill Alf Bill ? B ? A ? A39。 the problem is that ine effects are different for Alf and Bill But in the aggregate WARP does not hold (!!!???) WARNING !! ? B39。amp。 ...prices change the same way. Similarly for Bill. Different resources and preferences, but.... Aamp。 ...prices change. Suppose Alf39。?p) ? For normal goods: CV ? CS ? EV ? For inferior goods: CV CS EV CV and EV some handy facts: Aggregation Optimisation and Comparative Statics Welfare Opportunities and Preferences The Consumer Overview... ? (1) We usually suppose that a many dimensioned modity space can be represented appropriately in very simple form. ? (2) We often assume that there is a representative consumer. ? We can use economic analysis to see whether, and when these two assumptions are appropriate Our use of consumer models is usually rather simplified... The Consumer Opportunities and Preferences Optimisation and Comp. Statics Aggregation Welfare ...over goods ...over consumers Aggregation find an aggregate`x and a function `U(x1,`x ) that yield the same behaviour as U(x1, x2, x3,..., xn ) The result: The issue: is it legitimate to simplify an nmodity problem to, say, a 2modity problem? The model: you can always do this if relative prices of goods 2,3,..,n stay constant. Aggregation over goods The Consumer Opportunities and Preferences Optimisation and Comp. Statics Aggregation Welfare ...over goods ...over consumers Aggregation The issue: will the mass of consumers behave in the same sort of way as a single consumer? The model: find the form of the utility function that permits averaging over consumers. This requires that market demand be independent of the ine distribution. The result: you must have demand that is linear in ine, with the same slope for all. Aggregation over consumers. Aggregatable preferences... but what could happen if this condition were not satisfied? Let