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.