David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

5.1 Demand by a single consumer
where PH is the price of the good on the horizontal axis and Pv is the price of the good on the vertical axis.
In our example, the price of meals PH = £5 and the price of films Pv = £10. The formula confirms that the
slope of the budget line is - 1 I2• The minus sign reminds us that there is a trade-off. We have to give up one
good to get more of the other good.
The two end-points of the budget line (here, A and F) show how much of each good the budget buys if the
other good is not bought at all. The slope of the budget line joining these end-points depends only on the
relative prices of the two goods.
Any point above the budget line (such as G in Figure 5.1) is unaffordable. The budget line shows
the maximum quantity of one good that is affordable, given the quantity of the other good purchased and
the budget available to spend. With an income of £50, G is out of reach: it would need £25 to buy 5 meals
and £50 to buy 5 cinema tickets. Points such as K, which lie inside the budget line, leave some income
unspent. Only on the budget line is there a trade-off where the student must choose between films and
meals.
II i ;.lpt eeh: e nf xr !hbetf c:tr =thacal way. A consumer
faces different bundles containing different quantities of two goods, call them X and Y. The
consumer takes the prices of the two goods as given. Define by Px the price of good X and by py the price of
good Y. Define by x the quantity of good X and by y the quantity of good Y. Define by M the income available
to the consumer. Then the budget constraint of the consumer can be written as:
Pxx +pyy =M (1)
The left-hand side of the expression above is the total expenditure of the consumer who buys quantities x and
y of the two goods at the given prices. The expenditure of the consumer must be equal to her income M.
From the budget constraint in (1) we can derive the corresponding budget line using simple algebra:
Equation (2) is the budget line. The slope of
the budget line is given by -pxlpy, that is,
the price ratio.
Since the budget line is a straight line, the
slope is constant along the line. The term
M/py is the vertical intercept of the budget
line. It tells you how much the consumer
can buy of good Y when she spends all her
income on good Y.
The term Mlpx is the horizontal intercept of
the budget line; it tells you the amount of
good X that the consumer can buy if she
spends all the income on good X. Bundle a
on the graph contains an amount xa of good
X and an amount Ya of good Y. In moving
M
Px
y = ---x
py
y
py
Y a
y : I
I
Yb - - - - - - - - -·- - - - - - - -
I
I
I
x
(2)
Slope of the budget
line = -p.fp r
x
0
99