Use of Models in Economics!

The method of economic enquiry most popular today is that of building economic models. A model is any theoretical construction which attempts to analyse and explain a phenomenon. These are various types of problems in Economics which call for power explanation before a solution can be thought of the attempts at clarification of the issues, the analysis of the relationships between different factors acting on the phenomenon are called economic models.

Reality as we observe it is the result of the working of a number of factors—systematic, seasonal, cyclical and random and is too complex to be explained as such. We need to considerably simplify reality before it can be explained. This is done by making simplifying assumptions about the nature and behaviour of the relationships between the factors influencing the phenomenon. Judged this way, economic models are simplification of reality.

#### Type of Models:

Economic models can be simple or complex according as they involve relationships between a few or a large number of factors called “variables”. According to Gardener Ackley, “An economic model consists simply of a group or a set of economic relationships, each one of which involves at least one variable which also appears in at least one other relationship which is part of the model.”

A model can be constructed at different levels of aggregation, detail and sophistication depending on its purpose. The lowest level is that of a firm. We study a monopoly firm or a firm under oligopoly. The second level of analysis is the industry and the third level is that of the economy. There are two main purposes for which models are built analysis and prediction. The familiar Marshallian Supply-Demand Cross is a simple model seldom stated as such but often used.

It combines supply and demand relationships to determine the price and amounts exchanged of a single commodity. On the other side are the models of an economy containing hundreds of equations and variables. But the basic form and salient features of all economic models remain the same. This is mainly because the inspiration behind all of them is to establish relationships between economic variables through mathematical logic.

#### Validity of a Model:

The validity of a model may be judged on several criteria:

(1) Its predictive power.

(2) The consistency and realism of its assumptions,

(3) The extent of information it provides,

(4) Its generality (that is the range of cases to which it applies) and

(5) Its simplicity. However, the most important attribute of a model depends upon its purpose.

#### Variables, Parameters and Relationships:

A model must clearly lay down the various relationships between different variables in the form of mathematical equations. A variable is any measurable magnitude which varies and in whose change we are interested either because of its direct importance or because of its effect on other variables. Variables may be stock variables like the number of cars or flow variables like production, consumption per period of time. Or variables may be ratios between stocks and flows such as price and saving rate.

To write down the structure of a model is to spell out the relationships between our variables conceitedly. These relationships are called functional relationships. “The existence of a functional relationship among two or more variables simply means that the values or magnitudes of the variables are somehow uniquely related. A change in one variable is associated in some regular and predictable way with a change in another.” The relationship may be direct as between price and quantity supplied or inverse as between price and quantity demanded.

The relationships may be between a dependent variable written on the left-hand side of the equation and one or more independent variables are written on the right-hand side. It is often the case that only one or more variables are written on the right hand side of the equation and others are left out of the model relationships, being assumed as ‘given’. These variables which are assumed as given and which do not occur in the working of the functional relationships in the model are called parameters. These are generally summed up in the phrase ‘other things equal’ or external circumstances—subject to change to be sure but not of interest to the problem at hand.

Economic relationships spelling out the model are classified as:

(1) ‘behavioural’ relationships which reflect the voluntary choices of economic subjects i.e., individuals and firms;

(2) ‘institutional restraints’ which show the operations of laws or rules of behaviour;

(3) ‘technical’ relationships reflecting technical choice; and

(4) ‘identities’ or ‘definitions’.

Examples of institutional restraints are required bank reserves-deposit ratio, lax collection as a function of income, etc. Technical relationships are represented through the production function. Identities or definitions are merely accounting relationships or simple truisms. An example of an identity is that in a market, the amount of a commodity sold the previous day must equal to the amount bought.

If the relationships are precise and put in a mathematical form, we can solve the model to find out the equilibrium values of the variables involved. This is possible only if the model is complete. Mathematically, it means that there must be as many equations as there are unknowns. If the unknowns are less than the number of relationships (equations), the model is ‘over determined’. Once the values of the variables are determined, we can use these to make specific predictions.

#### Use of Mathematics:

Economists have come to use increasingly the language of mathematics to build economic theories in the form of models. In fact the course of development of economics is one of increasing rigour and precision of theories. The tendency has led to the building of sophisticated, mathematical (and now econometric) models.

Classical economists used to discuss “tendencies” or “causes.” The neoclassical started making use of mathematics but the Cambridge University tradition has till date remained one of verbal statements relegating mathematical notes to appendices. But it is well known that this verbal tradition has caused lot of confusion and unnecessary controversy particularly about Keynes’ General Theory.

The use of mathematics in Economics is growing day by day. Besides the universality of mathematical language, mathematical models afford exactness to economic theories saving them from ambiguity. In the mathematical form, economic models are succinct statements of economic theory.