BUDGET CONSTRAINT
Budget Constraint
 Economists assume that consumers choose the best




bundle that they can afford (Rationality
assumption)
Suppose there are two goods
.Notation : Bundle (x1, x2 ); prices (p1, p2 ); income m
Budget Constraint: p1x1  p2 x2  m
Budget Set shows all the affordable bundles

Budget Set and Line
x
2
m /p2
Budget line is
p1x1 + p2x2 = m.
Not affordable
Just affordable
Affordable
m /p1
x1
Budget Set and Line
x
2
m /p2
Budget line is
p1x1 + p2x2 = m.
the collection
of all affordable bundles.
Budget
Set
m /p1
x1
Budget Set and Line
x
2
m /p2
p1x1 + p2x2 = m is
x2 = -(p1/p2)x1 + m/p2
so slope is -p1/p2.
Budget
Set
m /p1
x1
Slope of Budget Line
 For x1 on the horizontal axis, the budget line’s
slope is -p1/p2. What does it mean?
p1
m
x 2   x1 
p2
p2
 With the given income, to increase the
consumption of x1 by 1, p1/p2 units of x2 should
be given up. ( i.e. opportunity cost of good 1 in
term
 of good 2)
Slope of Budget Line
x2
Opportunity cost of an extra unit of
good 1 is p1/p2 units
foregone of good 2.
-p1/p2
+1
x1
Budget Sets & Lines; Income and Price Changes
 The budget line and budget set depend upon prices
and income. What happens as prices or income
change?
How do the budget set and budget line change
as income m increases?
x2
New affordable consumption
choices
Original and
new budget
lines are
parallel (same
slope).
Original
budget set
x1
How do the budget set and budget line change as income
m decreases?
x2
Consumption bundles
that are no longer
affordable.
New, smaller
budget set
Old and new
lines are
parallel.
x1
Budget Lines - Income Changes
 Increases in income m shift the line outward in
a parallel manner, thereby enlarging the budget
set and improving choice.
 Decreases in income m shift the line inward in a
parallel manner, thereby shrinking the budget
set and reducing choice.
Budget Lines - Price Changes
 What happens if just one price decreases?
 Suppose p1 decreases.
How do the budget set and budget line change as p1
decreases from p1’ to p1”?
x2
m/p2
New affordable choices
-p1’/p2
Original
budget set
Budget line pivots;
slope flattens
from -p1’/p2 to
-p1”/p2
-p ”/p
1
m/p1’
2
m/p1
”
x1
Budget Line - Price Changes
 Reducing the price of one commodity pivots the
constraint outward.
 Similarly, increasing one price pivots the constraint
inwards
Examples of Budget Lines
1.


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Uniform Ad Valorem Sales Taxes:
Ad Valorem tax is a tax on value (i.e. the price) of a
good.
An uniform ad valorem sales tax levied at a rate of
5% increases all prices by 5%, from p to (1+0×05)p
= 1×05p.
An uniform ad valorem sales tax levied at a rate of
t increases all prices by tp from p to (1+t)p.
Uniform Ad Valorem Sales Taxes
 A uniform sales tax levied at rate t changes the
line from
to
i.e.
p1x1 + p2x2 = m
(1+t)p1x1 + (1+t)p2x2 = m
p1x1 + p2x2 = m/(1+t).
Uniform Ad Valorem Sales Taxes
x2
m
p2
m
(1  t ) p2
p1x1 + p2x2 = m
p1x1 + p2x2 = m/(1+t)
m
(1  t ) p1
m
p1
x1
Examples of Budget Lines
2. Coupons: (ex: Food Stamps)
 Food stamps are coupons that can be legally
exchanged only for food.
The Food Stamp Program
 Suppose m = $100, pF = $1 and the price of “other
goods” is pG = $1.
 The budget line is then
F + G =100.
 How does 40 food stamps alter the budget line?
(assuming that with each food stamp, consumer can
get 1 unit of food)
The Food Stamp Program
G
F + G = 100: before stamps.
100
100
F
The Food Stamp Program
G
F + G = 100: before stamps.
100
Budget set after 40 food
stamps issued.
The budget
set is enlarged.
40
100 140
F
Examples of Budget Lines
3. Quantity Discount:

Suppose p2 is constant at $1 but that p1=$2 for 0 
x1  20 and p1=$1 for x1>20 (i.e. each additional
unit of good 1 purchased after 20 units). Then the
line’s slope is
{
-p1/p2 =
- 2, for 0  x1  20
- 1, for x1 > 20
Quantity Discount
x2
100
m = $100
Slope = - 2 / 1 = - 2
(p1=2, p2=1)
Slope = - 1/ 1 = - 1
(p1=1, p2=1)
20
50
80
x1
Quantity Discount
x2
100
m = $100
Slope = - 2 / 1 = - 2
(p1=2, p2=1)
Slope = - 1/ 1 = - 1
(p1=1, p2=1)
20
50
80
x1
Quantity Discount
x2
m = $100
100
Budget Line
Budget Set
20
50
80
x1
Examples of Budget Lines
4. Other Examples: (Will be discussed in class)

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Per unit tax
Per unit tax after certain amount
Rationing