# Section 1: An introduction to models

 The aim of this section is to overview what economic and business studies models are, in particular, the terminology used in describing models and how an economic model is solved. The aim is to introduce some of the concepts at the broad level and to help contextualise the other sections.

The section is divided as follows:

## Section 1.1: What constitutes a model?

Models are the bedrock of economics and business studies as they are used to explain or predict the behaviour of the economy or a business.

The models which are commonly used in teaching introductory Economics or Business Studies are those that show a simplified relationship between various factors. This simplification of the complex interactions between individuals, groups and institutions relies on the ceteris paribus assumption. In other words, other things being equal or unchanged. An example of the ceteris paribus assumption is the demand and supply model. Within the simplified model it is assumed that when solving for quantity (demanded and supplied) the determinant is price.

The major appeal of using models in teaching is the predictive power they offer. For instance, the supply and demand model can be used to predict what should occur to the price and quantity in a given market from a change in the market determinants. A computer based model will allow students to experiment in a safe environment.

Models are expressed in a variety of ways. These include, verbal, algebraic, graphical and statistical. It does not matter which way they are expressed as long as the model is:

1. Internally consistent - possesses a logical argument which is correct and contains no mathematical errors
2. Elegant - possesses a simple structure

The different methods of expressing models can be illustrated using the consumption function.

 Verbal a person will consume more goods and services if their income increases Algebraic C = a + bYd Graphical

## Section 1.2: What is the common terminology used in modelling?

The concept of a model has been introduced, the next step is to flesh out further meaning by discussing some of the common terminology associated with modelling. This will be achieved through comparing opposites, for instance, exogenous and endogenous, static and dynamic, equilibrium and dis-equilibrium and deterministic and stochastic.

### Section 1.2.1: Exogenous and Endogenous

The exogenous variables are those which are determined or set outside the model. These are contrasted by the endogenous variables which are determined inside the model. Therefore, the value of the endogenous variable will change when the exogenous variable changes. For instance, applying the previous example of the consumption function

C = a + bYd

Where C is the endogenous variable (consumption) and Yd is the exogenous variable (disposable income). If Yd = 100, a = 50, b = 0.8, then the endogenous variable is

C = 50 + 0.8 * 100
C = 130

However, if the Yd (exogenous variable) increased to 200, then the endogenous variable will change

C = 50 + 0.8 * 200
C = 210

The exogenous and endogenous variables can also be termed as the independent (exogenous) and dependent (endogenous) variables.

### Section 1.2.2: Static and Dynamic

A static model is one that does not account for time. It identifies the before and after outcomes but does not trace the path that the model takes to move from one equilibrium position to another. The supply and demand model (price determination) is an example of a static model in that it identifies the two equilibrium positions, but it does not trace how the model moved between the two positions.

In contrast, a dynamic model contains time as a variable, that can be used to trace how the model moves from one equilibrium position to the next. An example of a dynamic model is the cobweb theorem.

The discussion to date has assumed that the model is stable, in other words, the model will reach a new equilibrium position. The concept of stability can be introduced through the use of equilibrium and dis-equilibrium models.

### Section 1.2.3: Equilibrium and Dis-equilibrium Models

Static models (by their nature) are equilibrium models as they analyse the before and after equilibrium positions. However, dynamic models can be either equilibrium or dis-equilibrium models. For instance, the cobweb theorem can be either divergent (dis-equilibrium) or convergent (equilibrium). The convergent model will tend, over time, to reach a stable equilibrium position. This is in contrast to the dis-equilibrium model where there is no tendency to equilibrium.

### Section 1.2.4: Deterministic and Stochastic Models

Models can also be distinguished by whether they are deterministic or stochastic. A deterministic model assumes that an outcome is certain. Therefore, a change to an exogenous variable will have a certain impact on the endogenous (dependent) variable.

However, a stochastic model includes an unknown factor that will influence the endogenous variable. It is common for a stochastic model to include a random element. It can be argued that the stochastic model is more realistic as it can account for behavioural factors, for instance, a person's consumption is not solely dependent on their income, it can also be influenced by factors, such as age (demographics), the time of year and tastes / fashions. It can be observed that these variables are difficult to measure, therefore, a more realistic consumption model would include a random variable to account for these issues. The consumption function would be:

C = a + bYd + U

Where U is the stochastic element

## Section 1.3: An example of solving an economic model

For a model to be used in a spreadsheet it needs to be solved. This requires converting the structural equations into their reduced form and then solving for the exogenous variable.

The structure (structural equations) illustrate the relationship between the variables based on the theory. The structural equations are the starting point of the model. The reduced form equations are the solutions to the model based on the structural equations. In many cases the reduced form equations can be solved to give a value of the endogenous variable.

The following example of a supply and demand model illustrates the principle:

Structural Equation 1: The Demand Curve

Qd = a - bP + cY

Structural Equation 2: The Supply Curve

Qs = d + eP

Structural Equation 3: The Equilibrium

Qd = Qs

The consumer demand (Qd) is influenced by the price of the good (P) and their income (Y). The higher the price then the lower the demand, while the higher their income the higher the demand.

A determinant of the quantity supplied (Qs) is the price (P). The higher the price then the more firms will be willing to supply.

The structural equations identify the relationship between the endogenous and exogenous variables. The following procedure will calculate the reduced form equations which are used within the spreadsheet model.

Qd = Qs
a - bP + cY = d + eP

re-arranging the formula will give

a + cY - d = eP + b

solving for P (price) gives

P = (a + cY - d) / (e + b)

The equilibrium quantity can be calculated by substituting the value of price into one of the equations. The reduced form to calculate the quantity would be:

Q = d + e((a + cY - d) / (e + b))

If we assume that; a = 50, b = 0.8, c = 1.2, Y = 100, d = 10 and e = 0.5, then

P = (50 + (1.2 * 100) - 10) / (0.5 + 0.8)
P = 123.1

Therefore,

Q = 10 + 0.5 * ((50 + (1.2 * 100) - 10) / (0.5 + 0.8))
Q = 71.5

The reduced form equations can be used within the spreadsheet.

The above example included a walk through exercise. The walk through exercise uses example data to create a value for the endogenous variables. This exercise can be repeated in the spreadsheet model as a means of checking for errors.

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