UNCWilmington
ECN 321
Department of Economics and Finance
Dr. Chris Dumas
Calculus Review
Calculus
Calculus is the study of the
rates of change
of interrelated variables.
It turns out that just about
all of economics is about the rates of change of interrelated variables; so, just about all of
economics is about calculus.
There are two main parts of calculus:
differentiation
and
integration
.
We will focus on
differentiation in this handout.
Differentiation
Differentiation
is the process of finding the rate of change of one variable with respect to
changes in another.
Suppose we have two variables, x and y, related together by function f:
y = f(x).
The
derivative
of y with respect to changes in x, denoted
dx
dy
, gives the change in y that results
from a small change in x.
If we graph the relationship of y and x, the change in y that results
from a small change in x is the
slope of the graph
; hence, the derivative
dx
dy
gives the
slope
of
the graph of the relationship between y and x
.
IT TURNS OUT THAT MANY IMPORTANT THINGS IN ECONOMICS ARE SLOPES
OF GRAPHS !!!!
THUS, MANY IMPORTANT THINGS IN ECONOMICS ARE DERIVATIVES !!!!
Amazingly
, marginal cost, marginal revenue, marginal product, marginal utility, marginal
benefit, marginal profit, and even part of the formula for elasticity are all derivatives!!!!!!
1
x
y
y = f(x)
dy/dx is the
slope
of the y = f(x) graph
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UNCWilmington
ECN 321
Department of Economics and Finance
Dr. Chris Dumas
Differentiation Rules for Common Functions of
One Independent Variable
:
In the rules below, dependent variable y is a function of one independent variable x.
In addition,
a, b and c are parameters, e is the base of natural logarithms, and f is a function.
A Constant
(The derivative of a constant is zero.)
If
y
= a,
then
dy/dx = 0
Examples:
If
y = 6,
then dy/dx = 0
If y = 1/2,
then dy/dx = 0
If y = 0,
then dy/dx = 0
Linear Function
If y = ax,
then
dy/dx = a
Examples:
If y = 6x,
then
dy/dx = 6
If y = 4x + 3z,
then dy/dx = 4
Exponent Power Function
If
y = ax
b
,
then
dy/dx = b[ax
(b1)
]
(Note: b can be a negative constant, or a fractional constant.)
Examples:
If y = 3x
5
,
then dy/dx = 5∙[3x
4
] = 15x
4
If y = 20x
3
,
then dy/dx = 3∙[20x
2
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 Fall '08
 Dumas
 Economics, Microeconomics, Derivative, Department of Economics and Finance, Dr. Chris Dumas

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