Microeconomics is a branch of economics that focuses on the behaviour of individual agents as opposed to macroeconomics, which studies the behaviour of aggregates. The object of the study of microeconomics is, in general, individuals, families and companies. Microeconomics is considered to be the study of the allocation of scarce resources among alternative purposes.
One of the purposes of microeconomics is to analyze the mechanisms that establish the relative price of goods and factors and to study the effects that different institutions have on key variables such as market price, quantities traded and benefits for the companies and utility for consumers. The institutions analyzed by microeconomics can be different market structures (perfect competition, monopoly, oligopoly, etc.), the effects of varying types of taxes, etc.
A few major contributors to microeconomics have been Marshall, Walras, Jevons and Menger.
Microeconomics and how it relates to other areas: logic, mathematics and macroeconomics
Microeconomics uses formal models to explain the behaviour of producers and consumers. These microeconomics models part from assumptions to come to conclusions using a deductive method. The analytical method of microeconomics is based in logical reasoning. Mathematical language helps to clearly express the reasoning and increases the stringency level. This is why microeconomics tends to use mathematical language.
In the last few decades, microeconomics has narrowed its ties with macroeconomics because the modern aggregate models include microeconomic fundamentals which allow for increased solidity in formal terms. For example, the aggregate consumption function (which explains the behaviour of many individuals) in macroeconomic models must be consistent with the microeconomic behaviour function (which explains the behaviour of a single individual).