+ ~ ~ ")

The principal thrust of Gorman's aggregation theorem is that aggregate demand systems are consistent with individual utili tv maximization (individual "rationality") and simple aggregation if and only if individual preferences have the structure (8) with interpersonal commonality of the function n. but more can be said. The total expenditure of the II optimizing consumers is

(20)

(p),

(21)

has the structure of an expenditure function in aggregate utility nand A have the requisite homogeneity, monotonicity, and curvature properties); indeed, ) has the same (GPF) structure as the individual expenditure functions in (8). Corresponding to (21) is the aggregate indirect utility function

y A(p) y y) = - - -- =: -~

which, of course, has the same structure as the individual utility functions (9). Finally, the application of Roy's Identity to (22) yields the aggregate demand system

which,withy=Lhyh,isidenticaltotheaggregatedemandsystem(ll),obtained bydirectaggregationoftheindividualdemandsystems.Thus,theaggregatedemand systemisrationalizedbyautilityfunctiondefinedonaggregatecommodityquantities,x=Lhxh.Inotherwords,theaggregatedemandsystemisgeneratedbyan optimizing"representativeagent,"withutilityu=Lhuhandaggregateincome y=Lhyh.Thus,theeconometricestimationofanyaggregatedemandsystemwith theshucture(23)isconsistentwithindividualoptimizationandaggregationofthe individualdemandsystems.