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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 = – p 1 / p 2 . Fig. Basic equations: MU 1 / p 1 = MU 2 / p 2 and

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chapter 5
Chapter 5

Choice of consumption

slide2
Optimal choice is at the point in the budget line with highest utility.
  • Thetangencysolution of an indifferent curve and the budget line:

MRS = – p1 / p2.

Fig.

slide3
Basic equations:
  • MU1 / p1 = MU2 / p2and
  • p1 x1 + p2 x2 = m.

Figs.

  • ( How if negative solutions.)
slide4
Interiorsolutions, and
  • Boundary (Corner) solutions.
  • Kinky tastes.

Figs.

slide5
Three approaches to

the basic equations:

  • Graphically;
  • As-one-variable;
  • *Lagrangian.
slide7
Examples:
  • perfect substitutes,
  • perfect complements,
  • neutrals and bads,
  • concave preferences.

Figs.

slide8
Cobb-Douglas demand functions.
  • * Choosing taxes.

(By *Slutsky decomposition.)

Figs.

slide10
Demand functions:
  • x1 = x1 (p1, p2, m),
  • x2 = x2 (p1, p2, m).
slide11
Normaland inferiorgoods (by income); Fig.
  • Luxury and necessarygoods (by income). Fig.
  • Ordinary and Giffen goods (by price). Fig.
slide12
The income expansion path

or the income offer curves,

  • and the Engel curve.

Figs.

slide13
The price offer curve
  • and the Demand curve.

Figs.

slide14
Substitutes and complements.
  • Cobb-Douglas preferences.
  • Quasilinear preferences.
slide15
* 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.
slide16
Example:
  • Quasilinear preferences

lead to

vertical (horizontal) income offer curves and

vertical (horizontal) Engel curves.