Aggregation problem

In economics, an aggregate is a summary measure. It replaces a vector that is composed of many real numbers by a single real number, or a scalar. Consequently, there occur various problems that are inherent in the formulations that use aggregated variables. The aggregation problem is the difficult problem of finding a valid way to treat 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 (see Representative agent, Heterogeneity 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 the aggregate production function. Another famous problem is Sonnenschein-Mantel-Debreu theorem. Most of macroeconomic statements comprise this problem. Examples of aggregates in micro- and macroeconomics relative to less aggregated counterparts are: Food vs. apples Price level and real GDP vs. the price and quantity of apples Capital stock vs. the value of computers of a certain type and the value of steam shovels Money supply vs. paper currency 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 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.