Chapter 5
Choice of consumption
Optimal
choice is at the point
in the budget line with highest
utility.
The tangency solution of an
indifferent curve and the
budget line:
MRS = – p1 / p2.
Fig.
Basic
equations:
MU1 / p1 = MU2 / p2 and
 p1 x1 + p2 x2 = m.
Figs.
(
How if negative solutions.)
Interior
solutions, and
Boundary (Corner) solutions.
Kinky tastes.
Figs.
Three
approaches to
the basic equations:
Graphically;
As-one-variable;
*Lagrangian.
The
optimal choice is the
consumer’s demanded bundle.
The
demand function.
Examples:
perfect
substitutes,
perfect complements,
neutrals and bads,
concave preferences.
Figs.
Cobb-Douglas
demand
functions.
*
Choosing taxes.
(By *Slutsky decomposition.)
Figs.
Chapter 6
Demand
Demand
functions:
x1 = x1 (p1, p2, m),
x2 = x2 (p1, p2, m).
Normal
and inferior goods
(by income);
Fig.
Luxury and necessary goods
(by income).
Fig.
Ordinary and Giffen goods
(by price).
Fig.
The
income expansion path
or the income offer curves,
and the Engel curve.
Figs.
The
price offer curve
and
the Demand curve.

Figs.
Substitutes
and complements.
Cobb-Douglas preferences.
Quasilinear preferences.
*
Homothetic preferences:
if (x1, x2) is preferred to (y1, y2),
then (tx1, tx2) is preferred to
(ty1, ty2) for any t > 0.
Thus both the income offer curves
and the Engel curves are all rays
through the origin.
Example:
Quasilinear
preferences
lead to
vertical (horizontal) income
offer curves and
vertical (horizontal) Engel
curves.