The Budget Constraint

A. The budget constraint defines the set of
baskets that a consumer can purchase with
a limited amount of income.

For convenience, we will consider only the
case of 2 goods (x and y), since we can graph
the budget constraint in this case.

B. Budget set is the set of all baskets that
are affordable, i.e., all (x, y) such that Pxx +
Py y ≤ I, with x ≥ 0, y ≥ 0.

C. Budget line is the set of baskets that cost
exactly the consumer’s income I, i.e., the set
of (x, y) such that
Pxx + Py y = I.

D. Example: Suppose a consumer, Eric, purchases only two goods: food and clothing.
Let x be the number of units of food he
purchases each month and y the number of
units of clothing.

The price of a unit of food is Px, and the
price of a unit of clothing is Py . Assume
that Eric has a fixed income of I dollars per
month.

Eric’s total monthly expenditure on food will
be Px · x (the price of a unit of food times
the amount of food purchased).
Similarly his total monthly expenditure on
clothing will be Py · y.

The budget line indicates all of the combinations of food (x) and clothing (y) that Eric
can purchase if he spends all of his available
income on the two goods. It can expressed
as
Px x + Py y = I

Figure shows the graph of a budget line
for Eric based on he following assumptions:
I = $800, Px = $20 and Py = $40. The
equation of the budget line is
20x + 40y = 800.
Eric can buy any basket on or inside the budget line (A, C, F etc.), but he cannot afford
a basket outside the budget line (G).

Figure 2.1 Eric’s Budget Constraint

How Does the Budget Line Change?

When prices and/or income change, the budget constraint also changes, so do the budget line, budget set, and some of the intercepts

How Does a Change in Income Affect
the Budget Line?

Suppose that Eric’s income increases from
$800 to $1000, while Px and Py stay the
same (See Figure 2.2).
When Eric has I1 = $800, the budget line
is BL1 with a vertical intercept of y = 20, a
horizontal intercept of x = 40, and a slope
of −1/2.
When Eric’s income grows to I2 = $1000,
the budget line is BL2 with a vertical intercept of y = 25, a horizontal intercept of
x = 50, and the same slope of −1/2.


In general, an increase (decrease) in income
causes a parallel shift outward (inward) of
the budget line.
The slope of the budget line −Px/Py does
not change, when only income changes.
Both the horizontal and the vertical intercept
increase or decrease at the same ratio.

How Does a Change in Price Affect
the Budget Line?

Consider for example, only Px increases from
$20 to $25. Py and I do not change. The
budget line rotates in toward the origin, from
BL1 to BL2 (see Figure 2.3).

The horizontal intercept shifts from 40 to
32 units. The vertical intercept does not
change because income and the price of clothing are unchanged.
In general, an increase in the price of one
good moves the intercept on that good’s
axis toward the origin.
Conversely, a decrease in the price of one
good would move the intercept on that good’s
axis away from the origin.
In either case, the slope of the budget line
would change, reflecting the new trade-off
between the two goods.