Unformatted text preview: ned as
B( Px , PY , I ) = {( x, y) : Px x + Py y I }
(2)
The budget line is the set of goods that exactly exhaust all of the consumer’s income: the set of basket
( x, y) such that
Px x + Py y = I
(3) 1 to rearrange the expression as:
The budget line is the boundary of the budget constraint. For graphical purposes, it is useful to rearrange
I
PX
Y=
X
Equation (3) as
PY
PY
Px
I
y=
(4)
Notice that this has a slope of PX , a horizontalx +
intercept of PIX and a vertical intercept of
PY
Py
Py
I
PY . Px
I
For slope of
10. We graph and a vertical intercept
Notice that this has a example, set PX = 1, PY = 2 and I = intercept Py the budget line and budget
Py with a horizontal
constraint in Figure 1.1
Figure 1 shows the budget line and the budget set when Px = 1, Py = 2, and I = 10: I
Px . For example !"#$%&'( )*)+,.'/)012' ! "#$!%&'
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! Figure 1: A budget line and set Figure 1: A Budget Line and Budget Set 2.1 1.1 change in change and price affect the budget
How does a How does a incomein income aect the budget lineline? Recall the formula for the budget line
Recall the formula for the budget line Px x + Py y = I . Now suppose we increase I and hold Px and Py
constant. To maintain this equation, we have to increase either x or y or both: since the right hand side is
PX X + PY Y = I.
higher, we must make the left hand side higher. Thus, in the space of goods ( x, y) the graph of the budget
x
line must shift out. suppose we increase I and hold PX Py has not changed, the new budget line must be parallel
Now Moreover since the slope
and PY constant. To maintain this equation, we
P
to the old one. have to increase eitherseeor Y or both:notice that both the vertical we must make the intercepts of the
Another way to X this is to since the right hand side is higher, and horizontal
graph rise with left hand side higher.The left panel ofof goods (X, Y ) the graph of the budget line must budget line in our
an increase in I . Thus, in the space Figure 2 illustrates what happens to the
example when income increase fromthe= 10 to PI = 12. changed, the new budget line is parallel
shift out; moreover, since I slope PX has not
Y
What does a change in income I mean for the consumer’s budget constraint? As you can see in the
1
All ﬁgures are courtesy of Irene Trela.
to an one. Another way
see this is in a that both the of bundles of
ﬁgure,the old increase in Itoresults to noticelarger set vertical and horizontal goods to choose from (and vice versa for a
intercepts
decrease inofIthe In that case, we say thatFigure consumer’shappens to
). graph increase with an increase in I . the 2 illustrates what purchasing power has increased.
2
the budget line in our example when income increase from 10 to 12.
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 Summer '13
 Microeconomics, py, Corner Solutions

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