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Mathematics in Business and Economics
Equations
An equation consists of two parts - the left hand side and the right hand side of the equals sign. An equation simply means that whatever value you have or is implied on the left hand side is the same value as that implied or given on the right hand side. 2χ - 3 = 14 - y therefore simply means that whatever value χ and y have the resulting sums must be the same. So if χ = 7, then the left hand side simplifies to (2 x 7) - 3 = 11. To make the right hand side equal to 11, y must equal 3. Rules for working with equations are:
- To maintain the balance of the equation, whatever you do to the right hand side you must also do to the left and vice versa.
- You can add, subtract, divide, multiply any number/s to one side provided you do the same thing to the other side. This is often used to help make the equation more manageable but the whole process is not always obvious!
Algebra
Much of what you will come across in economics will be relationships between different variables. These 'variables' as their name suggests can take on many different values. Algebra merely uses symbols to represent those numbers. Numbers used with these symbols tell us something about the nature of the change in the variable.
Take the example of a typical production function: Q = ƒ (4K + 3L). What this tells us is that the quantity of output produced (signified by the letter Q) is dependent on (or is a function of ƒ) a number of units of capital equipment (signified by the letter K) and a number of units of labour (signified by the letter L).
Exogenous and Endogenous Variables
These are two terms that are regularly used to describe variables in functions. Exogenous variables are the independent variables. They are not influenced or determined by the other factors in the equation - they are independent of those other variables. The 'ex' in the term implies the value is determined from outside. Endogenous variables are dependent and are determined from within. In the production function, the output level is dependent on the number of units of capital and labour employed. If the amount of capital and labour is increased or decreased, it will directly affect the amount that can be produced. The output level is the endogenous variable, the capital and labour the exogenous variables.
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