Ineconomics, anaggregate is a summarymeasure. It replaces avector that is composed of manyreal numbers by a single real number, or ascalar. Consequently, there occur various problems that are inherent in the formulations that use aggregated variables.[1]
Theaggregation problem is the problem of finding a valid way to treat anempirical or theoretical aggregate as if it reacted like a less-aggregated measure, say, about behavior of an individualagent as described in generalmicroeconomic theory[1] (seerepresentative agent andheterogeneity in economics).
The second meaning of "aggregation problem" is the theoretical difficulty in using and treating laws and theorems that include aggregate variables. A typical example is theaggregate production function.[2] Another famous problem isSonnenschein-Mantel-Debreu theorem. Most of macroeconomic statements comprise this problem.
Disaggregation is the decomposition of an aggregate to variables closer to empirical data.[3] Examples of aggregates in micro- andmacroeconomics relative to disaggregated counterparts are:
| Aggregate variable | Disaggregated components |
|---|---|
| Food basket | Apples, coffee |
| Price level (of basket) | Price level of apples, coffee |
| Price level of apples | Price level of green apples, red apples |
| Gross output of a nation | Total sales of a nation's apples,steel coils |
| A firm'scapital stock | Value of a firm's buildings,steam shovels |
| Money supply | Savings deposits,vault cash,paper money |
| Generalunemployment rate | the unemployment rate of civil engineers,waiting staff |
Standard theory uses simple assumptions to derive general, and commonly accepted, results such as thelaw of demand to explain market behavior. An example is the abstraction of acomposite 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 aggregatedutility functions, restrictions on the latter are necessary to yield the law of demand. The aggregation problem emphasizes:
Franklin Fisher notes that this has not dissuaded macroeconomists from continuing to use such concepts.[1]
The aggregate consumerdemand curve is the summation of the individual consumer demand curves. The aggregation process preserves only two characteristics of individualconsumer preference theory—continuity and homogeneity. Aggregation introduces three additional non-price determinants of demand:
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 that good will change. Finally, if thedistribution of income changes in favor of consumers who prefer 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. The most important problem for micro- and macro-economics is theSonnenschein–Mantel–Debreu theorem, which shows that almost no properties of the individual preference are inherited to the aggregate demand functions.[4][5][6]
Sonnenschein-Mantel-Debreu theorem (SMD theorem) is a theorem for exchange economy that can be expressed in the following way:
for a function that is continuous, homogeneous of degree zero, and in accord with Walras's law,there is an economy with at least as many agents as goods such that, for prices bounded away from zero, the function is the aggregate demandfunction for this economy.[5]
First, to sum the demand functions without other strong assumptions 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.[7] For 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 two pairs of shoes. B is asked the same question and says four 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.
This second problem is more serious. AsDavid M. Kreps notes, “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 ofaggregate demand as a function of price and societal income".[8] Since any change inrelative price brings about a redistribution of real income, there is a separate demand curve for every relative price. Kreps continues, "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 samehomothetic preferences for example) there is little we can say”.[8] The strong assumptions are that everyone has the same tastes and that each person's tastes remain the same as income changes so additional income is spent in exactly the same way as before.
MicroeconomistHal Varian reached a more muted conclusion: "The aggregate demand function will in general possess no interesting properties".[9] However, Varian continued: "theneoclassical theory of the consumer places no restriction onaggregate behavior in general".[9] This means the preference conditions (with the possible exception of continuity) simply do not apply to the aggregate function.
Disaggregation is the breakdown of observations, usually within a common branch of a hierarchy, to a more detailed level to that at which detailed observations are taken.
| Supply and demand | |
|---|---|
| Markets andFirms | |
| Decision theory andbehavioural economics | |
| Welfare economics | |
| Econometrics andmathematical economics | |
| Other subfields | |
| See also | |
