PREFERENCES

Rationality in Economics Behavioral Postulate: A decisionmaker always chooses its most preferred alternative from its set of available alternatives. So to model choice we must model decisionmakers’ preferences.

Notation NOTE: We will work on the consumption choice problems with two goods: good 1 and good 2 x=(x 1,x 2 ) where x i =amount of good i in bundle x. y=(y 1,y 2 ) where y i =amount of good i in bundle y.

Notations for Preference Relations denotes strict preference so x y means that bundle x is preferred strictly to bundle y.  denotes indifference; x  y means x and y are equally preferred. denotes weak preference; x y means x is preferred at least as much as is y. ~  ~   

Assumptions about Preference Relations Completeness: For any two bundles x and y it is always possible to make the statement that either x y or y x. ~  ~ 

Assumptions about Preference Relations Transitivity: If x is at least as preferred as y, and y is at least as preferred as z, then x is at least as preferred as z; i.e. x y and y z x z. ~  ~  ~ 

Graphical Representation of Preferences-Indifference Curves Take a reference bundle x’. The set of all bundles equally preferred to x’ is the indifference curve containing x’; the set of all bundles y  x’. NOTE: Indifference curves do not always need to be a curve. It can be a linear line, L-shaped, etc..

Indifference Curves x2x2x2x2 x1x1x1x1 x” x”’ x’  x”  x”’ x’

Indifference Curves x 2 (Like) x 1 (Like) zxy z x y  x y z

Indifference Curves x 2 (Like) x 1 (Like) x All bundles in I 1 are strictly preferred to all in I 2. y z All bundles in I 2 are strictly preferred to all in I 3. I1I1 I2I2 I3I3

Indifference Curves Cannot Intersect x 2 (Like) x 1 (Like) x y z I1I1I1I1 I2I2 From I 1, x  y. From I 2, x  z. Therefore y  z. But from I 1 and I 2 we see y z, a contradiction. 

Slopes of Indifference Curves When more of a commodity is always preferred, the commodity is a the good that the consumer likes. If both commodities are the goods that the consumer like, then indifference curves are negatively sloped.

Slopes of Indifference Curves Better Worse x 2 (Like) x 1 (Like) x 1 (Like) Goods that the consumer like a negatively sloped indifference curve.

Slopes of Indifference Curves If less of a commodity is always preferred, then the commodity is a bad (i.e. that is good that the consumer dislikes)

Slopes of Indifference Curves Better Worse Good 2 (Likes) and Bad 1 (Dislikes) a positively sloped indifference curve. x 2 (Like) x 1 (Bad) x 1 (Bad)

Extreme Cases of Indifference Curves; Perfect Substitutes Two goods are perfect substitutes if the consumer is willing to substitute one good for the other at a constant rate. Example: Two goods: Red pencil and blue pencil Preference: Consumer likes pencils, but does not care about the color.

Extreme Cases of Indifference Curves; Perfect Substitutes Red Blue I2I2 I1I1 Bundles in I 2 all have a total of 15 units and are strictly preferred to all bundles in I 1, which have a total of only 8 units in them.

Extreme Cases of Indifference Curves; Perfect Complements If a consumer always consumes good 1 and 2 in fixed proportion, then the goods are perfect complements and only the number of pairs of units of the two commodities determines the preference rank-order of bundles. Example: Two goods: Left shoe and right shoe Preference: Consumer likes shoes, but always wear left and right together.

Extreme Cases of Indifference Curves; Perfect Complements Right Left I1I1 45 o Each of (5,5), (5,9) and (9,5) contains 5 pairs so each is equally preferred.

Extreme Cases of Indifference Curves; Perfect Complements Right Left I2I2 I1I1 45 o Since each of (5,5), (5,9) and (9,5) contains 5 pairs, each is less preferred than the bundle (9,9) which contains 9 pairs.

Marginal Rate of Substitution A consumer’s willingness to substitute one good for another while maintaining the same level of happiness (i.e. staying on the same indifference curve) is called the Marginal rate-of-substitution (MRS). MRS of good 1 for good 2 (notation: MRS 12 ) shows how much good 2 that the consumer is willing to give up to have an addition good 1 while staying on the same indifference curve. How can a MRS be calculated?

Marginal Rate of Substitution x2x2x2x2 x1x1x1x1 x’ MRS of good 1 for good 2 at x’ is the negative slope of the indifference curve at x’.

MRS & Ind. Curve Properties x2x2x2x2 x1x1x1x1 MRS = 5 MRS = 0.5 MRS is diminishing (IC becomes flatter) as x 1 increases.

MRS & Ind. Curve Properties x1x1x1x1 x2x2x2x2 MRS = 0.5 MRS = 5 MRS is increasing (IC becomes steeper) as x 1 increases.