[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

As we learned in Chapter 2, a budget constraint diagram has two important features.
First, although any point in the shaded area of Figure 5.1A is feasible, only the
points on the line BC are really relevant, because Fran is not consuming her entire
budget if she is inside her budget constraint. Second, by looking along the budget
constraint, we can see her trade-offs—how many candy bars she has to give up to
get 1 more CD, and vice versa. Look at points F and A, a part of the budget constraint
that is blown up in panel B. At point A, Fran has 10 CDs; at F, she has 11. At F, she has
135 candy bars; at A, 150. To get 1 more CD, she has to give up 15 candy bars.
These are her trade-offs, and they are determined by the relative prices of the
two goods. If one good costs twice as much as another and we went 1 more unit of
the costly good, we have to give up 2 units of the cheaper good. If, as here, one good
costs fifteen times as much as another, and we want 1 more unit of the costly good,
we have to give up 15 units of the less costly good.
The slope of the budget constraint, which measures how steep it is, also tells us
what the trade-off is. As we move 1 unit along the horizontal axis (from 10 to 11 CDs),
the slope represents the size of the change along the vertical axis. It is the rise (the
movement up or down on the vertical axis) divided by the run (the corresponding horizontal
movement). The slope of this budget constraint is thus 15. 1 It tells us how
much of one good, at a given price, we need to give up if we want 1 more unit of the
other good: it tells us, in other words, what the trade-off is.
Note that the relative price of CDs to candy bars is 15; that is, a CD costs fifteen
times as much as a candy bar. But we have just seen that the slope of the budget
constraint is 15, and that the trade-off (the number of candy bars Fran has to give
up to get 1 more CD) is 15. It is no accident that these three numbers—relative price,
slope, and trade-off—are the same.
This two-product example was chosen because it is easy to illustrate with a
graph. But the same logic applies to any number of products. Income can be spent
on one item or a combination of items. The budget constraint defines what a certain
amount of income can buy, a balance that depends on the prices of the items.
Giving up some of one item would allow the purchase of more of another item
or items.
Economists represent these choices by putting the purchases of the good to
which they are paying attention, say CDs, on the horizontal axis and “all other goods”
on the vertical axis. By definition, what is not spent on CDs is available to be spent
on all other goods. Fran has $300 to spend altogether. A more realistic budget constraint
for her is shown in Figure 5.2. The intersection of the budget constraint with
the vertical axis, point B—where purchases of CDs are zero—is $300. If Fran spends
nothing on CDs, she has $300 to spend on other goods. The budget constraint intersects
the horizontal axis at 20 CDs (point C); if she spends all her income on CDs
and CDs cost $15 each, she can buy 20. If Fran chooses a point such a F, she will buy
11 CDs, costing $165, and she will have $135 to spend on other goods ($300–$165).
The distance 0D on the vertical axis measures what she spends on other goods; the
distance BD measures what she spends on CDs.
1 We ignore the negative sign. See the appendix to Chapter 2 for a more detailed explanation of the slope of a line.
THE BASIC PROBLEM OF CONSUMER CHOICE ∂ 103