Functional Relationship

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A functional relationship is a connects two or more variables such that a change in one variable causes a change in the other variables. These relationships are particularly significant in Economics owing to their wide applicability. This is because Economics is essentially a behavioral science in which cause and effect phenomena are systematically studied. Observed results are evaluated in terms of both the factors that cause them and the relative importance of each factor to the final observed result. Ultimately, the primary objective is to develop a model for potential prediction of certain behavior.

The general format of a functional relationship is y=f(x) where y is the dependent variable while x represents the independent variable. It should be noted that for any dependent variable, there can be multiple independent variables.  This paper shall use the voting pattern observed across the Northern region of the United States for its illustration. Specifically the relationship between the age of voters and the number of voters is examined with a view to presenting the key features of a functional relationship. Therefore, in this example the number of people who vote is a function of their age.

Figure 1: Voters per Age Group in Northern United States.

The x-axis shows the age of voters divided into 4 groups. Group 1 represents ages 18-24years; Group 2 represents ages 25-44 years; Group 3 represents ages 45-64 years while Group 4 represents 65 years and above. The y-axis indicates the number of registered voters who turned up on Election Day to vote. It is important to note that the age of voters determines the number of voters, assuming all other factors remain constant, hence the functional relationship between the two variables. It can be observed that the number of voters slowly but steadily rises as the age of voters rises from 18 to 24 years. This is possibly due to an increasing awareness and understanding of the issues discussed during the election campaigns. The slope of the graph at this point is therefore gentle and positive.

However, between 25 and 44 years of age, the number of voters sharply increases. The slope of the graph therefore increases rapidly, indicating that a positive change in age causes