1. PREFERENCES

2. 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.

3. Notation
NOTE: We will work on the consumption choice problems with two goods: good 1 and good 2
x=(x1,x2) where xi=amount of good i in bundle x .
y=(y1,y2) where yi=amount of good i in bundle y.

4. 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. p p ~ f ~ f

5. 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. ~ f ~ f

6. 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. ~ f ~ f ~ f

7. 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..

8. Indifference Curves x2
x’ ~ x” ~ x”’ x’ x”
x”’ x1

9. Indifference Curves
x2 (Like)
z x y p p x z y
x1 (Like)

10. Indifference Curves I1 x2 (Like) All bundles in I1 are
strictly preferred to all in I2. x z I2
All bundles in I2 are strictly preferred to all in I3. y I3
x1 (Like)

11. Indifference Curves Cannot Intersect
From I1, x ~ y. From I2, x ~ z.
Therefore y ~ z. But from I1 and I2 we see y z, a contradiction.
x2 (Like) I2 I1 p x y z
x1 (Like)

12. 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.

13. Slopes of Indifference Curves
x2(Like)
Goods that the consumer like a negatively sloped indifference curve.
Better
Worse
x1 (Like)

14. 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)

15. Slopes of Indifference Curves
x2(Like)
Good 2 (Likes) and Bad 1 (Dislikes) a positively sloped indifference curve.
Better
Worse
x1 (Bad)

16. 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.

17. Extreme Cases of Indifference Curves; Perfect Substitutes
Red
Bundles in I2 all have a total of 15 units and are strictly
preferred to all bundles in I1, which have a total of only 8 units in them. 15 I2 8 I1
Blue 8 15

18. 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.

19. Extreme Cases of Indifference Curves; Perfect Complements
Right
45o
Each of (5,5), (5,9) and (9,5) contains 5 pairs so each is equally preferred. 9 5 I1
Left 5 9

20. Extreme Cases of Indifference Curves; Perfect Complements
Right
45o
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. 9 I2 5 I1
Left 5 9

21. 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: MRS12) 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?

22. Marginal Rate of Substitutionx2
MRS of good 1 for good 2 at x’
is the negative slope of the
indifference curve at x’. x’ x1

23. MRS & Ind. Curve Propertiesx2
MRS = 5
MRS is diminishing (IC becomes flatter) as x1 increases.
MRS = 0.5 x1

24. MRS & Ind. Curve Propertiesx2
MRS is increasing (IC becomes steeper) as x1 increases.
MRS = 0.5
MRS = 5 x1