Types of equations of economic models

In economics, a distinction is made between different types of equations in economic models according to different points of view . A classic division takes place in behavior, definition and identity equations . The purpose of these distinctions is to avoid confusion between definitions and derivation results. These basic types of equations must not be confused with special laws or theories, such as the Euler equation of consumption , Fisher equation or quantity equation (also called traffic equation ). The distinction between different equations takes place in both microeconomics and macroeconomics .

Economic models can exist as systems of in / equations and contain variables and parameters as components . Equations can be sorted according to whether they make statements about a model (definition equations and equilibrium conditions) or whether they contain hypotheses about functional relationships between variables or other statements about reality (behavioral equations, technical equations, institutional equations, expectation functions). The behavioral, technological and institutional equations are sometimes summarized as structural equations .

The mathematical division of equations according to their validity into identity equations , determining equations and defining equations does not always coincide with the terminology used in economics.

Behavior equation

The behavior of a feature is described in relation to another feature. From a mathematical point of view , behavior equations thus describe simple equations . Sometimes, however, a finer distinction is made with an emphasis on the behavioral aspect. A production function (a relationship between output and input) can be viewed more as a technical equation , whereas behavioral equations provide information on how the relationship between different economic variables is established through human behavior. This distinction becomes particularly clear in the concept of the reaction function , which describes an optimal strategy given the strategy of the opponent.

The investment function is a typical behavioral equation that describes the investment planning of the company (investments depending on the interest). It is thanks to John Maynard Keynes to have explained the investment function not only as a deterministic equation of a production-related relationship, but as a behavioral equation for the future-oriented and risk-conscious action of economic subjects.

The consumption function (consumption depending on income) is also a behavioral equation.

Definition equation

Definition equations (also called determining equations ) define a fixed relationship between different features and are not derived from other equations. The income utilization equation ( ) and income generation equation ( ) are defining equations. But the formula for the direct price elasticity of demand with respect to price also corresponds to a defining equation: ${\displaystyle Y=C+S}$ ${\displaystyle Y_{1}=C+I}$

${\displaystyle \eta _{x,p}\colon ={\frac {\frac {\mathrm {d} x}{x}}{\frac {\mathrm {d} p}{p}}}={\frac {\mathrm {d} x}{\mathrm {d} p}}\cdot {\frac {p}{x}}}$.

Identity equation

→ Main article : Identity equation

Identity equations are combined definition equations that make an equivalent statement based on various characteristics. Examples of economic identities are say's theorem or change in wealth .

Invest and save

A well-known example is the consideration of national income . This can be viewed ex post under the aspects of origin, use and distribution. An identity can be derived from these defining equations of national income, the income utilization equation and the income generation equation:

${\displaystyle Y_{1}=C+I}$

${\displaystyle Y_{2}=C+S}$

Both equations apparently describe the same national income, so that:

${\displaystyle Y_{1}\equiv Y_{2}}$,

and from this identity it also follows:

${\displaystyle I\equiv S}$,

so that the level of savings ex-post corresponds to the level of investment in the economy. Care must be taken to ensure that the ex-post identity (or equality) of investment and saving, which is valid by definition , must not be confused with the concept of equilibrium . The economic cycle assumes equality of investment and savings not only ex post, but also ex ante (in planning). However, macroeconomic theory regards and as mutually independent quantities that are usually of different sizes ex ante . ${\displaystyle S}$ ${\displaystyle I}$

Individual evidence

1. ^ Artur Woll: Economics. 16th edition. Vahlen, 2011, ISBN 978-3-8006-3835-2 , pp. 14/15.
2. ↑ Stobbe, Alfred. Microeconomics. Springer-Verlag, 2013. pp. 35/36.
3. ↑ Müller, Udo. General Economics: Introduction and Microeconomics. Vol. 1. Springer-Verlag, 2013. p. 58.
4. ^ Jürgen Faik: Wiley crash course in economics . Wiley-VCH Verlag GmbH & Co. KGaA. 2014. ISBN 978-3527530052 . P. 58.
5. ↑ Heertje, Arnold. Basic concepts of economics. Vol. 78. Springer-Verlag, 2013. p. 17.
6. ^ Brunner, Sibylle, and Karl Kehrle. Economics. Vahlen, 2012. p. 525.
7. ↑ Stobbe, Alfred. Microeconomics. Springer-Verlag, 2013. p. 114.
8. ↑ Heertje, Arnold, and Heinz-Dieter Wenzel. Fundamentals of Economics. Springer-Verlag, 2013. pp. 185/186
9. ^ Artur Woll: Economics . 16th edition. Vahlen, 2011, ISBN 978-3-8006-3835-2 , pp. 14/15.
10. ^ Michael Frenkel, Klaus Dieter John: National Accounts. 7th edition. Munich 2011, p. 24 f.
11. ^ Behrens, Christian-Uwe, and Matthias Kirspel. Fundamentals of Economics: Introduction. Oldenbourg Verlag, 2003. p. 241.
12. ^ Artur Woll: Economics. 16th edition. Vahlen, 2011, ISBN 978-3-8006-3835-2 , p. 293.

Web links

• 1.1.9 Methods of Economics II - Section in the part textbook General Economics