Aggregation problem

Aggregation problem

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An aggregate in economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 is a summary measure describing a market or economy. The aggregation problem refers to the difficulty of treating an empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 or theoretical aggregate as if it reacted like a less-aggregated measure, say, about behavior of an individual agent
Agent (economics)
In economics, an agent is an actor and decision maker in a model. Typically, every agent makes decisions by solving a well or ill defined optimization/choice problem. The term agent can also be seen as equivalent to player in game theory....

 as described in general microeconomic theory. Examples of aggregates in micro- and macroeconomics
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...

 relative to less aggregated counterparts are:
  • food vs. apples
  • the price level
    Price level
    A price level is a hypothetical measure of overall prices for some set of goods and services, in a given region during a given interval, normalized relative to some base set...

     and real GDP
    Real GDP
    Real Gross Domestic Product is a macroeconomic measure of the value of output economy adjusted for price changes . The adjustment transforms the money-value measure, called nominal GDP, into an index for quantity of total output...

     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 shovel
    Steam shovel
    A steam shovel is a large steam-powered excavating machine designed for lifting and moving material such as rock and soil. It is the earliest type of power shovel or excavator. They played a major role in public works in the 19th and early 20th century, being key to the construction of railroads...

  • the money supply
    Money supply
    In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...

     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
Law of demand
In economics, the law of demand is an economic law that states that consumers buy more of a good when its price decreases and less when its price increases ....

 to explain market behavior. An example is the abstraction of a composite good
Composite good
In economics, demand for a good is often the focus as to a change in its price. A composite good is an abstraction used in economics that represents all goods in the relevant budget besides the one in question.-Purpose:...

. 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.

Franklin Fisher notes that this has not dissuaded macroeconomists from continuing to use such concepts.

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.

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), “ 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
Homothetic preferences
Homothetic preferences is a subset of preferences used in economics when analyzing the demand for consumption of various goods and services.In mathematics, a function of two or more arguments is homothetic if all ratios of its first partial derivatives depend only on the ratios of the arguments,...

 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
Steve Keen
Steve Keen is a Professor in economics and finance at the University of Western Sydney. He classes himself as a post-Keynesian, criticizing both modern neoclassical economics and Marxian economics as inconsistent, unscientific and empirically unsupported...

 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

  • Aggregate demand
    Aggregate demand
    In macroeconomics, aggregate demand is the total demand for final goods and services in the economy at a given time and price level. It is the amount of goods and services in the economy that will be purchased at all possible price levels. This is the demand for the gross domestic product of a...

  • Aggregate supply
    Aggregate supply
    In economics, aggregate supply is the total supply of goods and services that firms in a national economy plan on selling during a specific time period...

  • Cambridge capital controversy
    Cambridge capital controversy
    The Cambridge capital controversy – sometimes simply called "the capital controversy" – refers to a theoretical and mathematical debate during the 1960s among economists concerning the nature and role of capital goods and the critique of the dominant neoclassical vision of aggregate...

  • Price index
    Price index
    A price index is a normalized average of prices for a given class of goods or services in a given region, during a given interval of time...

  • Representative agent
    Representative agent
    Economists use the term representative agent to refer to the typical decision-maker of a certain type ....

  • Social choice theory
    Social choice theory
    Social choice theory is a theoretical framework for measuring individual interests, values, or welfares as an aggregate towards collective decision. A non-theoretical example of a collective decision is passing a set of laws under a constitution. Social choice theory dates from Condorcet's...