Chapter 5Chapter 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 6Chapter 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 curve

s 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.