DEMAND FUNCTIONS
In principle it will usually be possible to solve
the necessary conditions of a utility maximum
for the optimal levels of x1, x2, xn (and , the
Lagrangian multiplier) as functions of all prices
and income. Mathematically, this can be
expr
Effects of Price Changes for Inferior Goods
So far we have shown that substitution and income
effects tend to reinforce one another. For a price
decline, both cause more of the good to be demanded,
whereas for a price increase, both cause less to be
deman
THE INDIVIDUALS DEMAND CURVE
Economists frequently wish to graph demand
functions. It will come as no surprise to you that
these graphs are called demand curves.
Understanding how such widely used curves relate to
underlying demand functions provides addi
COMPENSATED DEMAND CURVES
In Figure 5.5, the level of utility this person gets
varies along the demand curve. As px falls, he or she
is made increasingly better-off, as shown by the
increase in utility from U1 to U2 to U3. The reason
this happens is that
Shifts in the Demand Curve
Three factors were held constant in deriving this
demand curve: (1) income; (2) prices of
other goods (say, py ); and (3) the individuals
preferences. If any of these were to change, the
entire demand curve might shift to a new
CHANGES IN A GOODS PRICE
The effect of a price change on the quantity of a good
demanded is more complex to analyze than is the
effect of a change in income. Geometrically, this is
because changing a price involves changing not only
the intercepts of the
CHANGES IN INCOME
As a persons purchasing power rises, it is
natural to expect that the quantity of each good
purchased will also increase. This situation is
illustrated in Figure 5.1. As expenditures
increase from I1 to I2 to I3, the quantity of x
demand
DEMAND FUNCTIONS
In principle it will usually be possible to solve
the necessary conditions of a utility maximum
for the optimal levels of x1, x2, xn (and , the
Lagrangian multiplier) as functions of all prices
and income. Mathematically, this can be
expr
Homogeneity
A first property of demand functions requires little
mathematics. If we were to double all prices and
income (indeed, if we were to multiply them all by
any positive constant), then the optimal quantities
demanded would remain unchanged.
Doubl
Graphical Analysis of an Increase in Price
If the price of good x were to increase, a similar
analysis would be used. In Figure 5.4, the budget
line has been shifted inward because of an
increase in the price of x from p1x to p2x.The
movement from the ini
SUMMARY
Hence, our graphical analysis leads to the following
conclusions.
O P T IM I Z A T I O N
PRINCIPLE
Substitution and income effects. The utilitymaximization hypothesis suggests that, for
normal goods, a fall in the price of a good leads to an
incre