In economics, characteristics or elements such as prices, outputs, income, etc., are measured by numerical values. Some of these will always remain the same, and some will change. The characteristic or element that remains the same is called a constant. For example, the number of donuts in a dozen is always 12. That means the number of donuts in a dozen is a constant.
While some of these characteristics or elements remain the same, some of these values can vary (e.g., the price of a dozen donuts can change from $2.50 to $3.00), we call these characteristics or elements variables. Variable is the generic term for any characteristic or element that changes. You should be able to determine which characteristics or elements are constants and which are variables.
Which of the following are variables and which are constants?
We express a relationship between two variables, which we will refer to as x and y, by stating the following: The value of the variable y depends upon the value of the variable x. We can write the relationship between variables in an equation. For instance:
is an example of a relationship between x and y variables. The equation also has an "a" and "b" in it. These are constants that help define the relationship between the two variables.
The following example illustrates how these equations are constructed.
Throughout this book we will use an example of a pizza shop that charges 7 dollars for a plain pizza with no toppings and 75 cents for each additional topping. The total price of a pizza (y) depends upon the number of toppings (x) you order. So, the price of a pizza is a dependent variable and the number of toppings is the independent variable. In this example both the price and the number of toppings can change, therefore both are variables. The total price of the pizza also depends on the price of a plain pizza and the price per topping. In our example, the price of a plain pizza and the price per topping do not change, therefore these are constants. The relationship between the price of a pizza and the number of toppings can be expressed as an equation of the form:
If we know that x (the number of toppings) and y (the total price) represent variables, what are a and b? In our pizza example, "a" is the price of a plain pizza with no toppings and "b" is the price of each topping. They are constant. In other words, they are fixed values which specify how x relates to y.
We can set up an equation to show how the total price of pizza relates to the number of toppings ordered.
If we create a table of this particular relationship between x and y, well see all the combinations of x and y that fit the equation. For example, if plain pizza (a) is $7.00 and price of each topping (b) is $.75, we get:
|y =||a +||b||x|
|$ 7.00||$ 7.00||$.75||0|