THE BUDGET CONSTRAINT
Virtually all individuals must face two facts of economic life:
1. They have to pay prices for the goods and services they
buy
2. They have limited funds to spend
These two facts are summarized by the consumer’s budget
constraint:
A consumer’s budget constraint identifies which
combinations of goods and services the consumer can
afford with a limited budget, at given prices.
Max’s consumption possibilities with income of $150
Concerts at $30 each Movies at $10 each
Total Expenditure on Total Expenditure on
Quantity Quantity
Concerts Movies
0 $0 15 $150
1 $30 12 $120
2 $60 9 $90
3 $90 6 $60
4 $120 3 $30
5 $150 0 $0
Consider Max, a devoted fan of both movies and concerts,
who has a total budget of $150 to spend on both, each
month. The price for each movie is $10 and for each
concert it is $30. If Max were to spend his entire $150
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budget on concerts at $30 each, he could attend at most
five each month. If he were to spend it all on movies at $10
each, he could watch 15 of them.
But Max could also choose to spend part of his budget on
concerts and part on movies. In this case, for each number
of concerts, there is some maximum number of movies that
he could watch. For example, if he goes to one concert per
month, it will cost $30 of his $150 budget, leaving $120
available for movies. Thus, if Max were to choose one
concert, the maximum number of films he could choose
would be $120/$10 = 12.
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FIGURE 1.3 Budget Constraint
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Each combination of goods in the table is affordable for
Max, since each will cost him exactly $150. Combination A,
at one extreme, represents no concerts and 15 movies.
Combination F, is the other extreme, represents 5 concerts
and no movies. In each of the combinations between A and
F, Max attends both concerts and movies.
Figure 1.4 shows Max’s budget line. A budget line shows
the combinations of two goods you are able to buy, given
your available income to spend on them and their prices.
Note that any point below or to the left of the budget line
is affordable. For example, 2 concerts and 6 movies,
indicated by point G—would cost only $60 + $60 = $120.
Max could certainly afford this combination. On the other
hand, he cannot afford any combination above and to the
right of this line. Point H, representing 3 concerts and 12
movies, would cost $90 + $120 =$210, which is beyond
Max’s budget. The budget line therefore serves as the
boundary between those combinations that are affordable
and those that are not.
The slope of the budget line indicates the spending trade-
off between one good and another—the amount of one
good that must be sacrificed in order to buy more of
another good. If Py is the price of the good on the vertical
axis and Px is the price of the good on the horizontal axis,
then the slope of the budget line is −Px /Py
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Thus,
the slope of the budget line is equal to 3. The slope tells us
Max’s opportunity cost of attending one more concert. The
opportunity cost of 1 more concert is 3 movies forgone.
There is an important relationship between the prices of
two goods and the opportunity cost of having more of one
or the other. The prices Max faces tell us how many dollars
he must give up to get another unit of each good. If,
however, we divide one money price by another money
price, we get what is called a relative price – the price of
one good relative to the other. Since Pc = $30 and Pm=
$10, the relative price of a concert is the ratio Pc/Pm =
30/10 = 3.
Notice that 3 is the opportunity cost of another concert in
terms of movies, and except for the minus sign it is also the
slope of the budget line. That is, the relative price of a
concert, the opportunity cost of another concert, and the
slope of the budget line have the same absolute value.
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CHANGES IN THE BUDGET LINE
At point Y the To draw the budget line in Figure 1.1, we have assumed
consumer is definitely
given prices for movies and concerts and a given income
better off because
this combination was that Max can spend on them. These “givens”, the prices of
not previously the goods and the consumer’s income, are always assumed
available to him.
constant as we move along a budget line; if any one of
them changes, the budget line will change as well.
Case # 1: Rise in income with prices of the two goods
constant
Before: M = $150, Pc = $30, Pm = $10
Now: M’ = $300, while Pc and Pm remain the same
In this case money income has risen while prices have
remained constant, causing purchasing power or real
income to rise. Max can afford to consume more movies,
more concerts, or more of both, as shown by the change in
his budget line in Figure 1.5. Notice that the old and new
budget lines in Figure 1.5 are parallel – they have the same
slope of -3. This is because we changed Max’s income but
not prices, causing the ratio of prices to remain unchanged.
Since prices are constant, an increase in money income will
also cause an increase in real income. A rise in real income
is associated with a rise in welfare.
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Money Income ↑, Price level , Real Income ↑
FIGURE 1.4 Rise in income
Case #2: A fall in the price of both goods in an equal
proportion with no change in income
Before: M = $150, Pc = $30, Pm = $10
Now: Pc’ = $15, Pm’ = $5, and M remains the same
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-
A reduction in price by 50% for both concerts and movies,
with no change in income results in the slope to stay the
same. At new set of prices, Pc/Pm = 15/5 = 3. This would
mean the graph shows a parallel shift to the right like in
Figure 1.6, as real income has increased causing Max to
buy more of both goods.
Money Income , Price level , Real Income ↑
An Indifference curve
shows all theFIGURE 1.5 Equal proportionate fall in prices
various
possible
combinations of two
goods that given an
equal amount of
utility.
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Case #3: Price of concerts fall by 50% and the price of
movies and money income stay constant
Before: M = $150, Pc = $30, Pm = $10
Now: Pc’ = $15, M and Pm remain the same
Except for Point A in figure 1.7, real income has risen at all
levels. Max can afford to buy more of movies and concerts
both. At Point A, the real income remains unchanged. This
is a pivotal shift, as the slope of the line will change. Now,
the slope = Pc/Pm = 15/10 = 1.5
FIGURE 1.6 Pivotal Shift due to fall in price of one good
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Case #4: Money income and price of movies both
double and the price of concerts stays constant
The marginal rate of
Before: M = $150, Pc = $30, Pm = $10
substitution is the
slope of the
Now: M = $300, Pm’ = $20 and Pc remains the same
indifference curve. It
is the rate at which a
A rise in money income will cause a parallel shift to the
consumer is willing to
substitute one good right as shown in the dotted line in figure 1.7. At the same
for another. time if there is an increase in the price of movies, it will
FIGURE 1.7 Pivotal Shift due to rise in budget and price of one good
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cause a pivotal shift inwards. The new slope is Pc/Pm =
30/20 = 1.5
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Case #5: Relative change in prices with income staying
constant
Before: M = $150, Pc = $30, Pm = $10
Now: M = $150, Pc’ = $15, Pm = $20
The price of concerts halves and the price of movies
doubles which will result in the relative prices to change
and the slope to also change. The new slope = Pc/Pm =
15/20 = -0.75
FIGURE 1.8 Relative change in prices
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Case # 6: Price of concerts stays the same while price of
movies and income rises
Before: M = $150, Pc = $30, Pm = $10
Now: M = $300, Pc = $30, Pm’ = $40
This case has a similar diagram to Case #5, as the slope is
also -0.75. The price of concerts has not changed, but the
relative prices have changed. Also, since the income has
risen, Max can buy more of concerts despite no change in
the price of movies. The new slope = Pc/Pm = 30/40 =
-0.75
FIGURE 1.9 Relative change in prices
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