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

CHAPTER 5 Consumer choice and demand decisions
0 from bundle a to bundle b, the consumer increases her consumption of good X, from xa to xb, but she has to
reduce the consumption of good Y from Ya to Yb· This shows the trade-off between the two goods implied by the
budget constraint. Since the budget line is linear, we can find the slope of the budget line analytically in a simple
way. Notice that both bundles (a and b) satisfy the budget constraint, therefore it must be true that:
and
M Px
Ya = ---Xa
py py
M Px
Yb =---xb
py py
By taking the difference between (4) and (3), we obtain:
(3)
(4)
M M Px Px
Yb -Ya = -----xb +-Xa
PY PY PY Pr
(5)
Call y =Yb - Ya the change in the quantity of Y between bundle b and bundle a, and similarly for good X
define = xb - xa. Then (5) can be written as:
Or, written differently:
that is, exactly the slope of the budget line.
y = -Px
Pr
y Px
-=--
x py
Utility maximization and choice
The budget line shows affordable bundles given a consumer's market environment (her budget and the
price of different goods). The indifference map shows her tastes. We put the two
The chosen bundle will concepts together in order to see how the consumer chooses among different
be the point at which an bundles. We assume that the consumer is rational, implying that she chooses the
indifference curve just touches affordable bundle that maximizes her utility. She cannot afford points above the
the budget line. The budget
budget line and will never choose points below the budget line (it is then possible
line is a tangent to the
indifference curve at this point.
to buy more of one good without sacrificing any of the other good). She will select
a point on the budget line - her chosen bundle.
To find which point on the budget line maximizes utility, we examine the consumer's tastes. Our glutton
should pick a point with more meals and fewer films than the point our film buff selects. We first show how
to use indifference curves to find the bundle the consumer chooses. Then we confirm that our model of
consumer choice captures the different behaviour of the glutton and the film buff.
Figure 5.7 shows the budget line AF for the student who had £50 to spend on films (£10 each) and meals
(£5 each). The indifference curves 1/1 UI> U2U2 and U 3 U 3 are part of the indifference map describing her tastes.
All points on U3 U3 are unattainable since it lies entirely above the budget line AF. The student would like
this high level of utility but cannot afford it. Next, suppose she considers the attainable point B on the
indifference curve 1/11/1• She prefers this to point A, which must lie on a lower indifference curve (since
indifference curves cannot intersect, the indifference curve through A lies entirely below the indifference
curve U1 U1). Similarly, F must lie on a lower indifference curve than E and she prefers E to F.
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