[MUSIC] A financial model is essentially a theoretical framework which can become but necessarily be mathematical. If the model is mathematical however, we will need to use a set of equations which have the function of describing the structure of the model. While building up a financial model, we first pose a set of analytical assumptions. The system of the equations by relating a number of a variable to one another in certain ways constitutes the mathematical model, which has the function of giving mathematical form the set of our assumptions. Once we build up the mathematical model, which best fits our assumptions, we focus on deriving the conclusions which logically follow from our assumptions. A variable is an entity whose value can change. In fact, it can take on different values. The most important economic variables are price, profit, revenue, cost, national income, consumption, investment, imports, and exports. Since a variable can assume various values, it is more convenient to represent them by using symbols rather than specific numbers. For example, usually prices are represented by P. Profits are represented by the Greek letter pi, revenues are represented by R, and costs are represented by C, while national income is represented by Y, and so forth. When we write P equal to a specific number like P=5, then we stick a specific value to a variable. We build up an economic model with the aim of finding the solution values of a certain set of variables. Like for example, the profit maximizing level of output. When we try to find the solution of a system from the variables contained into the model, then these variables are said to be endogenous variables which indicates that they originated from within. If the model contains also variables which derived from forces which are external to the model and whose values are accepted as given data only, such variables are called exogenous variables, which indicates that they are originating from without. Notice that even if a variable is endogenous to one model, it might be the case that the same variable is exogenous to a different model. In an analysis of the market determination of weak price, for instance the variable P should definitely be endogenous. But, in the framework of the theory of the consumer expenditure, P would be become instead a datum to the individual consumer, and must therefore be considered exogenous. Variables are often combined with fixed numbers, which are called constants. We can find for example, 9P or 0.4R. A constant is an entity that does not change and therefore is the opposite of a variable. The constant, which is along with the variable, it is indicated as the coefficient of the variable. However, a coefficient may be symbolic rather than numerical. We can indicate the coefficient by using symbols rather than numbers, so that to obtain a higher level of generality. We can for example, let the symbol a stand for a given constant and use the expression aP instead of 7P in a model. Notice that it can take the entirety of the value. This is why it can be said that it is a constant, that is a variable. In order to fix this characteristic, we call it parametric constant or parameter. Normally by convention, parametric constants are represented by the symbol a, or b, or c, or their counterparts in the Greek alphabet alpha, beta and gamma. But of course, other symbols can be used. In order to visually distinguish exogenous variables from their endogenous counterparties, it is usually followed the practice of attaching a subscript zero to the chosen symbol. Therefore, if P symbolizes price, then signifies an exogenously determined price. [MUSIC]
