# Aggregation problem

While in microeconomics the individual behavior of companies and households is examined and described using microeconomic functions, in macroeconomics functional relationships are assumed between the variables aggregated from microeconomic variables to macroeconomic variables . The aggregation problem consists in the question of whether and how microeconomic and macroeconomic functions are compatible with one another.

## example

If, for example, at the microeconomic level it is assumed that the monetary consumption demand of every consumer i is a linear function of his income , the macroeconomic consumer demand C is defined as the sum of all and the national income Y as the sum of all individual incomes , the question arises whether it is gives a function F such that ${\ displaystyle c_ {i}}$${\ displaystyle y_ {i}}$${\ displaystyle c_ {i}}$${\ displaystyle y_ {i}}$

(i) for all i = 1, ... n, and ${\ displaystyle c_ {i} = a_ {i} + b_ {i} y_ {i}}$

(ii) C = F (Y)

apply simultaneously. In general, this is not the case, as a given value of Y can be divided among the n consumers in very different ways, which would lead to correspondingly different values ​​of the aggregated consumption C. If there are only two consumers with individual consumption functions and , the aggregated consumption C for a given aggregated income Y can assume any value between 0.4Y and 0.6Y if nothing is known about the distribution of Y between the two consumers. ${\ displaystyle c_ {1} = 0,4y_ {1}}$${\ displaystyle c_ {2} = 0.6y_ {2}}$