Tools of Economic Analysis
Topic Two

### The Economic Model

An economic model is a theoretical construct that attempts to abstract from complex human behavior in a way that sheds some insight into a particular aspect of that behavior. The formulation of a model can be in the form of words, diagrams or mathematical equations, depending on the purpose of the model. In order for a model to effectively represent reality, assumptions are needed. This will mean that certain factors and variables may need to be held constant. Therefore, some of the variables in the model will be variable while some will be fixed or constant. One of the main assumptions in modeling consumer behavior is that consumers are rational in that there choices are sensible. If consumers do not behavior rational, the model will not be able to effectively represent consumer choice in demanding goods and services. Another possible assumption is that consumers will seek to maximize their incomes. This will mean that, with few exceptions, they will want to purchase goods and services that are lower in price assuming that these goods and services are of good quality. Therefore, in modeling consumer demand under these circumstances, one expects that when income rises, the demand for goods that are normal will rise.

### Variables and Constants

A variable is a number that changes over time or can take on other values in different situations. There are two types variables: (1) an independent variable (also called exogenous variable) which can take different values and can result in changes in other variables and (2) a dependent variable (also called endogenous) which can take different values only in response to changes in the independent variable; therefore, the dependent variable depends on the independent variables. On the other hand, a constant can be defined as a unit of measurement that does not change or vary such as fixed cost. When quantity increases or decreases, fixed cost remain the same. The constant is the y-intercept. It cuts the y-axis.

### Equations

Economic theory is a verbal expression of the functional relationships between economic variables. When the verbal expressions are transformed into algebraic form we get equations. Equations are used to calculate the value of an unknown variable. An equation specifies the relationship between the dependent and independent variables. For example, the functional relationship between consumption (C) and income (Y) can take different forms. The most simple equation, C = a (Y) states that consumption (C) is related to income (Y). Here ‘a’ is constant and it has a value greater than zero but less than one (0<a<1). Thus the equation shows that C is a constant proportion of income. For instance, if ‘a’ is ¼ then the consumer will always spend 25 percent of the income on consumption. We can see that C is the dependent or endogenous variable while Y is the independent or exogenous variable. This is a simple linear function.

C = a + b Y is yet another form of consumption function. Here the value of “a’ is positive and b is 0<b<1.

Another example of a simple linear equation is total cost which can take the form of:

TC= a + bY

where:

TC – which is the dependent variable,

Y – income or output which is the independent variable,

a - is the constant or intercept (in this case it is the fixed cost) and,

b - is the coefficient to be estimated and it is also the slope - it is also the marginal cost which is the extra cost (variable cost) incurred as a result of the production of one additional unit of output.

### Lines Graphs

A graph presents the relationship between two or more sets of data or variables that are related to each other. Graphs are the most commonly used tool in modern economics. The common method of constructing a graph or a diagram is described below. The TC or total cost equation is a model which can be represented as a line graph such as follows:

In this line graph, the rate of change of cost, b, is constant at all levels of output. This is what is meant by a linear function (the slope remains constant or the same whatever the level of output or production); “b” can be determined by dividing the change in TC by the change in Y. In this graph, “a” is the constant term and cuts the TC -axis. In this example, TC represents total cost and Y income or output. Therefore, “a” is the constant and it is total fixed cost. Notice that one of the lines in the graph is rising which states that as income rises, so too will cost rise; this is the variable cost. Also notice that the other line in the graph is a horizontal line which states that as income rises, this particular cost will be fixed which represents the fixed cost. A linear function is a straight line as in the above graph. In a linear function, the graph has a constant slope. According to this graph, as income (Y) or output rises, so too will variable and total cost which is why the total cost line which includes variable cost is rising but fixed cost will remain the same and this is why this line is horizontal.

### Scatter Graphs

A scatter graph or plot is a type of graph or plot that shows the relationship between two variables such as between price and quantity supplied as in the following graph. We can see that this relationship is a positive, linear one in that the pattern of the plots follows a straight line in an upward direction. This will mean that as price increases, quantity supplied by suppliers will also increase because they will be able to earn higher profits.

A scatter graph can also show a negative relationship between two variables such as in the following graph where when price rises, quantity demanded falls. .

There may also be cases when a scatter graph will be able to show that no relationship exists between two variables as can be seen in the following graph. This could be the case for the relationship between price and quantity supplied of water. Water as a resource is fixed and does not really depend on price.

### Minimum and Maximum Value Models

Graphs showing maximum and minimum values are also useful tools used in order to illustrate and make effective economic decisions. In terms of showing the maximum output, the total product curve can be used which shows that total output or total product increases with increases in the number of workers. Total product then reaches a maximum which is at point Y then starts to fall as more and more employees have to work with the fixed space and capital.

The following graph shows the case of minimum values which is for the case of minimum total average costs. As can be seen, as output rises, costs falls, reaches a minimum which is at an output level of 4 units, then starts to rise.

### Marginal Analysis

Most times in economic decision-making, total revenue or total cost is used. However, marginal analysis using marginal revenue and marginal cost may be a more effective method. For instance, a bicycle manufacturer should only produce bicycles up to the point where marginal cost is equal to marginal benefit. By breaking down decisions into measurable, smaller pieces, the bicycle manufacturer can optimize profits.

We now know that the aim of marginal analysis is to determine the change in net revenue or benefits so we can now state the formula for marginal analysis:

Marginal revenue also known as marginal benefit is the increase in total revenue or benefit as a result of a change in the output of a good by one unit. The equation for marginal benefit is:

where,

MR - marginal benefit or revenue TR - total revenue Q – output delta symbol (triangle) - the change in units

Marginal cost is the increase in total cost as a result of a change in the output of a good by one unit. It is represented by the following equation:

where,

MC - marginal costTC - total cost

Q – output delta symbol (triangle) - the change in units

From the marginal analysis formula, we can see that if the marginal revenue is greater than the marginal cost, then there will be a positive change in net revenue or benefits. In this case, additional units of output should be produced. However, if the marginal cost is higher than the marginal revenue leading to no change or a negative change in net benefits, then it would not be wise to increase output. In general, net benefits increase when marginal revenue is higher than marginal cost. Therefore, marginal analysis helps to determine if the change is profitable to the business.