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1
Introduction to
Microeconomics
Lecture 4
Maths: Lines and Graphs
Simon Cowan
Outline
z
Lines and slopes
z
Drawing nonlinear curves
z
Solving quadratic equations graphically
z
(We’ll draw indifference curves in Lecture 8 on Functions)
z
Applications:
z
demand and supply
z
budget lines
Drawing lines
Take the demand function used in Lecture 3
q
=
A
−
Bp
,
q
is the number of units bought,
p
is the price and
A >
0
and
B
> 0
.
This holds when
0
≤
p
≤
A B
If
p
>
A B
then
q
= 0
This holds when
0
A
/
B
.
If
>
A
/
B
then
0
.
First, we shall follow the convention in economics of inverting the
demand function to obtain price in terms of quantity. To do this
add
Bp
to both sides, subtract
q
, and divide both sides by
B
:
(Inverse) demand:
()
A
q
p
B
−
=
Graph of the (inverse) demand
line:
p
= (
A
–
q
)/
B
p
A
/
B
Quantity is on the horizontal axis and price
is on the vertical axis.
We are only interested in nonnegative
values of
p
and
q
.
When
q
= 0
we have
p
=
A
/
B.
This is the
vertical intercept of the function
q
A
vertical intercept of the function.
When
q = A
,
p
= 0
. Thus
q
=
A
is the
horizontal intercept of the function.
The inverse demand function is the straight
line between these two points.
0
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 Spring '10
 Vines
 Economics, Microeconomics

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