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An aggregate in economics is a summary measure describing a market or economy. The aggregation problem refers to the difficulty of treating an empirical or theoretical aggregate as if it reacted like a less-aggregated measure, say, about behavior of an individual agent as described in general microeconomic theory. Examples of aggregates in micro- and macroeconomics relative to less aggregated counterparts are:
- food vs. apples
- the price level and real GDP vs. the price and quantity of apples
- the capital stock for the economy vs. the value of computers of a certain type and the value of steam shovels
- the money supply vs. paper currency
- the general unemployment rate vs. the unemployment rate of civil engineers.
Standard theory uses simple assumptions to derive general, and commonly accepted, results such as the law of demand to explain market behavior. An example is the abstraction of a composite good. It considers the price of one good changing proportionately to the composite good, that is, all other goods. If this assumption is violated and the agents are subject to aggregated utility functions, restrictions on the latter are necessary to yield the law of demand. The aggregation problem emphasizes:
- how broad such restrictions are in microeconomics
- that use of broad factor inputs ('labor' and 'capital'), real 'output', and 'investment', as if there was only a single such aggregate is without a solid foundation for rigorously deriving analytical results.
Aggregate consumer demand curve 
The aggregate consumer demand curve is the summation of the individual consumer demand curves. The aggregation process preserves only two characteristics of individual consumer preference theory - continuity and homogeneity. Aggregation introduces three additional non price determinants of demand - (1) the number of consumers (2) "the distribution of tastes among the consumers" and (3) "the distribution of incomes among consumers of different taste." Thus if the population of consumers increases ceteris paribus the demand curve will shift out. If the proportion of consumers with a strong preference for a good increases ceteris paribus the demand for the good will change. Finally if the distribution of income changes in favor of those consumer with a strong preference for the good in question the demand will shift out. It is important to remember that factors that affect individual demand can also affect aggregate demand. However, net effects must be considered. For example, a good that is a complement for one person is not necessarily a complement for another. Further the strength of the relationship would vary among persons.
Aggregating individual consumer demand curves presents several problems. 
Independence assumption 
First to sum the demand functions it must be assumed that they are independent - that is that one consumer's demand decisions are not influenced by the decisions of another consumer. Example, A is asked how many pairs of shoes he would buy at a certain price. A says at that price I would be willing and able to buy 2 pairs of shoes. B is asked the same question and says 4 pairs. Questioner goes back to A and says B is willing to buy four pairs of shoes, what do you think about that? A says if B has any interest in those shoes then I have none. Or A, not to be outdone by B says then I'll buy five pairs. And on and on. This problem can be eliminated by assuming that the consumers' tastes are fixed in the short run. This assumption can be expressed as assuming that each consumer is an independent idiosyncratic decision maker.
No interesting properties 
This second problem is the most serious. As David Kreps notes is his text, A Course in Microeconomic Theory (Princeton 1990), “...total demand will shift about as a function of how individual incomes are distributed even holding total (societal) income fixed. So it makes no sense to speak of aggregate demand as a function of price and societal income." Since any change in relative prices affects a redistribution of real income the result is that there is a separate demand curve for every relative price. Kreps goes on to say, "So what can we say about aggregate demand based on the hypothesis that individuals are preference/utility maximizers? Unless we are able to make strong assumptions about the distribution of preferences or income throughout the economy (everyone has the same homothetic preferences for example) there is little we can say. ..” The strong assumptions are that everyone has the same tastes and that each person’s taste remain the same as income changes so each additional income is spent exactly the same way as all previous dollars. As Keen notes the first assumption amounts to assuming that there is a single consumer the second that there is a single good. Keen further states that because of the aggregation problem you cannot draw conclusions about social welfare, there is no invisible hand and Adam Smith was wrong. Varian, a leading expert on microeconomic analysis reaches a more muted conclusion, "The aggregate demand function will in general possess no interesting properties..." However Varian went on to say," the neoclassical theory of the consumer places no restriction on aggregate behavior in general." Among other things this means the preference conditions (with the possible exception of continuity) simply don't apply to the aggregate function.
See also 
- Franklin M. Fisher (1987). "aggregation problem," The New Palgrave: A Dictionary of Economics, v. 1, p. 54. [Pp. 53-55.]
- Franklin M. Fisher (1987). "aggregation problem," The New Palgrave: A Dictionary of Economics, v. 1, p. 55.
- Besanko and Braeutigam, (2005) p. 169.
- Kreps (1990) p. 63.
- Kreps (1990) p. 63.
- Keen, Steve (2001). Debunking Economics.
- Varian (1992) p. 153.
- Varian (1992) p. 153.
- Franklin M. Fisher (1987). "aggregation problem," The New Palgrave: A Dictionary of Economics, v. 1, pp. 53–55.
- Jesus Felipe and Franklin M. Fisher (2008). "aggregation (production)," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
- John R. Hicks (1939, 2nd ed. 1946). Value and Capital.
- Werner Hildenbrand (2008). "aggregation (theory)," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
- Thomas M. Stoker (2008). "aggregation (econometrics)," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
- Douglas W. Blackburn and Andrey D. Ukhov (2008) "Individual vs. Aggregate Preferences: The Case of a Small Fish in a Big Pond," Abstract.