~In elementary or introductory courses, derivatives are primarily used to find rates of change associated with various quantities.  These rates are instantaneous describing the function in concern at a specified instant or point.

 

~When applied to Revenue, Cost, & Profit functions, they are called Marginal rates. By taking the derivatives of these functions and substituting the value in question (usually the number of units of production), we have a good idea how these quantities are changing at that level of production.  Decisions can then be made to promote more efficient production.

 

~The most popular applications in basic courses would be Optimization problems. These involve finding maximum or minimum values for given functions. When applied to business, finding production levels that yield maximum revenue or profit would be of major concern. Also, we certainly would like to minimize the total cost of production.

 

~All of the above require an equation or function for the quantities in question.  So, modeling becomes an important feature. In many cases, data points are used to construct such a model by the use of curve fitting. This is usually introduced in lower levels.  Computers or advanced calculators make many problems very convenient & less laborous to complete.

See Curve Fitting

 

~Derivatives can also be applied to find any rate of increase or decrease in other quantities.  Popular quantities include depreciation, drug absorption, growth/decay (population growth/radioactive decay) & investment banking problems.

 

~In much more advanced courses, derivatives are involved in differential equations defining more advance business terms. Also, partial derivatives (knowledge of calculus III) are also used in other more advanced fields of economics.

 

~The other main process in calculus is Integration.  This process is the reverse of finding derivatives. Usually covered in the later stages of calculus I & most of calculus II.  It is also referred to as anti-differentiation. 

 

~In basic courses, we deal mainly with given rates.  We then proceed to find the value of the original function.  For example, given marginal revenue, marginal cost, or marginal profit, we can find the total revenue, cost, or profit function.  In such problems an extra or initial condition needs to be know in order to achieve a numerical answer.  

 

~Many such problems involve Definite Integrals which are easily handled by a computer or an advanced calculator such as the TI-83.

 

~Other popular applications of integration are finding the Producers' & Consumers' surplus dealing with supply & demand curves.  These also involve evaluating a definite integral in part of the solution.

 

~In more advance phases of economics & business, it is not unusual to see multiple integrals which are used to calculate various advanced quantities defined by these integrals.  Select groups of individuals would ever reach this level, since this would involve proficiency in calculus I, II, & III along with a good knowledge of differential equations.

See a more mathematical & detailed description of many of the concepts mentioned in this article on the web page Calculus Concepts