L02 Preferences

Rationality in Economics u Behavioral Postulate: A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. u Budget set = affordable alternatives u To model choice we must have decisionmaker’s preferences.

Last Week apples oranges x=(2,3) p 1 =2 p 2 =1 M=6

Today: Preferences u Rational agents: can rank any two consumption bundles u We call such ranking preferences –weak preference: x is at least as good as is y. (x y) –strict preference: x is strictly better than is y. (x y) –indifference: x is exactly as preferred as is y. (x y) ~  ~ 

Rational Decisionmaker x2x2x2x2 x1x1x1x1 I)Completeness: either or or both ~  ~  x y y x II) Transitivity: x y and y z x z. ~  ~  ~  y ~  x ~  z ~  ~  ~  u Rationality Axioms (Assumptions)

Indifference Curves u Convenient representation of Indifference Curve Map u The set of all bundles equally preferred to x is the indifference curve containing x;  The collection of all bundles y  x. ~ 

Representation: Indifference Curves x2x2x2x2 x1x1x1x1 x” x”’ x’  x”  x”’ x’ u Indifference curve = a collection of all indifferent bundles.

Indifference Curve Map x2x2x2x2 x1x1x1x1 zxy z x y  x y z

Can Two Indifference Curves Intersect? x2x2x2x2 x1x1x1x1 x y z

u Two goods always consumed in the same proportion u Example: Right and Left Shoes u We like to have more of them but always in pairs Example: Perfect Complements

Example 1: Perfect complements Left Right 1:1

Example: Perfect complements Coffee Sugar (teaspoons) 1:2

u Two goods that are substituted at the constant rate u Example: French and Dutch Cheese (I like cheese but I cannot distinguish between the two kinds) Example: Perfect substitutes

Dutch French

Slopes of Indifference Curves (MRS) u The slope of an indifference curve is its marginal rate-of-substitution (MRS). u Why rate-of-substitution? u Why marginal?

Slope: Marginal Rate of Substitution x2x2x2x2 x1x1x1x1 RS(x) is a slope of the indifference curve at x MRS(x) is a slope of the indifference curve at x x

Slope of Indifference Curves u When more of a commodity is always preferred, the commodity is a good. u Two goods. Sign of MRS? Good 2 Good 1

Slope of Indifference Curves u If less of a commodity is prefered the commodity is a bad. (Spinach) u Two goods. Sign of MRS? Bad 2 Good 1

Preferences Exhibiting Satiation u Many commodities become bads after some threshold of consumption (salt and pepper) u Bundle consisting of threshold quantities is called a satiation point or a bliss point. u A satiation point is strictly preferred to any other bundle.

Preferences Exhibiting Satiation x2x2x2x2 x 1 (salt) Satiation point x* 1 x* 2 (pepper)

Well-Behaved Preferences u We will typically assume that preferences are well-behaved: 1)monotonic (all goods) 2)weakly convex

Convexity. x2x2x2x2 y2y2y2y2 x1x1x1x1 y1y1y1y1 x=(1,3) y=(3,1) z =(2,2) Preferences are convex if mixtures “z” are (weakly) preferred to extremes x and y.

Convex preferences? x2x2x2x2 x1x1x1x1 x2x2x2x2 x1x1x1x1