Basic Functions
In financial mathematics, there are consumers and producers. Generally, consumers demand items and producers supply items.
The price per item that consumers will demand and purchase items is the demand function and is denoted by
Likewise, the price per item that producers will be willing produce and sell items is the supply function and is denoted by
The market equilibrium point is a point where consumers are willing to pay for items at the same time that producers are willing to set a price of for items. In other words:
So the point is the intersection point of the curves and .
The (total) revenue from producing and selling items is related to the demand function and is given by In other words revenue is the product of quantity and price, where the price is the price determined by the demand function.
The (total) cost of producing items is denoted Of note is the value This value is the fixed cost of producing any number of items and does not change as changes.
The average cost per item produced is
The (total) profit generated by producing and selling items is the difference between the revenue and cost
Compound Interest
Compound interest is a type of exponential function which gives the value of an investment over time at a particular interest rate.
Suppose:
then