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Chapter 2
NAME
Budget Constraint
Introduction.
These workouts are designed to build your skills in de
scribing economic situations with graphs and algebra. Budget sets are a
good place to start, because both the algebra and the graphing are very
easy. Where there are just two goods, a consumer who consumes
x
1
units
of good 1 and
x
2
units of good 2 is said to consume the
consumption bun
dle
,(
x
1
,x
2
). Any consumption bundle can be represented by a point on
a twodimensional graph with quantities of good 1 on the horizontal axis
and quantities of good 2 on the vertical axis. If the prices are
p
1
for good 1
and
p
2
for good 2, and if the consumer has income
m
, then she can aFord
any consumption bundle, (
x
1
2
), such that
p
1
x
1
+
p
2
x
2
≤
m
. On a graph,
the
budget line
is just the line segment with equation
p
1
x
1
+
p
2
x
2
=
m
and with
x
1
and
x
2
both nonnegative. The budget line is the boundary
of the
budget set
. All of the points that the consumer can aFord lie on
one side of the line and all of the points that the consumer cannot aFord
lie on the other.
If you know prices and income, you can construct a consumer’s bud
get line by ±nding two commodity bundles that she can “just aFord” and
drawing the straight line that runs through both points.
Example:
Myrtle has 50 dollars to spend. She consumes only apples and
bananas. Apples cost 2 dollars each and bananas cost 1 dollar each. You
are to graph her budget line, where apples are measured on the horizontal
axis and bananas on the vertical axis. Notice that if she spends all of her
income on apples, she can aFord 25 apples and no bananas. Therefore
her budget line goes through the point (25
,
0) on the horizontal axis. If
she spends all of her income on bananas, she can aFord 50 bananas and
no apples. Therfore her budget line also passes throught the point (0
,
50)
on the vertical axis. Mark these two points on your graph. Then draw a
straight line between them. This is Myrtle’s budget line.
What if you are not told prices or income, but you know two com
modity bundles that the consumer can just aFord? Then, if there are just
two commodities, you know that a unique line can be drawn through two
points, so you have enough information to draw the budget line.
Example:
Laurel consumes only ale and bread. If she spends all of her
income, she can just aFord 20 bottles of ale and 5 loaves of bread. Another
commodity bundle that she can aFord if she spends her entire income is
10 bottles of ale and 10 loaves of bread. If the price of ale is 1 dollar per
bottle, how much money does she have to spend? You could solve this
problem graphically. Measure ale on the horizontal axis and bread on the
vertical axis. Plot the two points, (20
,
5) and (10
,
10), that you know to
be on the budget line. Draw the straight line between these points and
extend the line to the horizontal axis. This point denotes the amount of
6
BUDGET CONSTRAINT
(Ch. 2)
ale Laurel can aFord if she spends all of her money on ale. Since ale costs
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 Winter '08
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