Consumer Preferences

1
Consumer Preferences

• Wetzstein Chapter 2

2
Road Map

• Investigate how consumer preferences are employed
  by consumers in making individual choices
• Investigate/Understand properties of utility
  functions
• Begin building an understanding of the law of
  demand

3
Law of Demand
Price (/X)
Demand
Quantity (X)
4
Axioms of Rationale Choice

• Axiom 1 Completeness
• All bundles can be compared
• Axiom 2 Transitivity
• Bundles can be ordered
• Axiom 3 Nonsatiation
• Always prefer a little bit more
• Axiom 4 Diminishing MRS
• Convexity/Averages preferred to extremes
• Others
• Continuity and Reflexivity

5
Utility

• Individual preferences can be expressed in a
  function
• Utility
• Often, we hold lots of potential things fixed and
  focus on one or two goods for convenience

6
Axiom 1 Completeness

• Households can always order their preferences
• If x and y are two commodity bundles, then

Y
d
Completeness says that I1 and I2 can be compared
c
b
I2
a
I1
X
7
Axiom 2 Transitivity

• Household preferences cannot be cyclical
• If x y and y z, then x z
• Transitivity does not allow z x in this case.
• Without transitivity, could not order preferences.

Y
b gt a, d gt c, and a d ? b gt c BUT, b and c
are on U2, and therefore b c which is a
contradiction.
b
a
d
U1
U2
c
8
Axiom 3 Nonsatiation

• More of a commodity is preferred to less
• Utility functions are always increasing in
  additional consumption of good commodities.

Y
Given an initial commodity bundle, every bundle
with at least one more of one commodity will be
preferred.
c
a
b
d
9
Nonsatiation

• This means that all first-order partial
  derivatives of the utility function must be
  positive
• MU is the additional utility associated with
  consuming slightly more xn

10
Indifference Curves

• An indifference curve is a set of points that
  yields exactly the same utility
• Every point along an indifference curve
  represents a different combination of commodities
• BUT, each combination is equally preferred.

11
Indifference Curves
Y
a
d
U
X

• Indifference curves have a negative slope.
• If an individual gives up some X, she must be
  compensated with more Y to maintain the same
  level of utility.

12
Indifference curve maps (or Indifference space)
Y
Utility increases for increasing combinations of
X, Y U3 gt U2 gt U1
U3
U2
U1
X
13
Axiom 4 Diminishing MRS.

• Indifference curves have negative slope
• The slope represents the rate at which the
  individual is willing to give up X to get more of
  Y

Y
a
d
U1
X
14
MRS

• Marginal Rate of Substitution is the negative of
  the slope of the indifference curve
• MRSYX
• Diminishing MRS

15
MRSYX
Y
dY/dX is negative, i..e. slope MRS is dY/dX
dY
U1
X
dX
16
Starting at S1, where X is small, one would Have
to give up a large amount of Y to get More X,
holding utility constant. At S2, where X is
larger, one has to give up Less Y to get more X,
holding utility constant.
Y
U1
X
S2
S1
17
Convexity of Indifference Curves
Preferences are strictly convex if any two
Points on or above an indiference curve can Be
joined by a straight line that is
completely Above U1 Averages are preferred to
extremes. Well balanced, diversified bundles are
Preferred to bundles heavily weighted to
one Commodity.
Y
a
c
U1
b
X
18
Example on Board
19
Utility Functions often Used

• Cobb Douglas gt U(X,Y) XaYb
• a, b are positive constants, often ab1.
• Perfect Substitutes gt U(X,Y) aX bY
• Perfect Complements gt U min(aX,bY)
• CES gt U(X,Y) if d?0
• ln(X) ln(Y) if d0

20
Cobb-Douglas

• Fulfills the 4 axioms
• Is fairly easy to use and therefore is widely
  implemented.

Y
U3
U2
U1
X
21
Perfect Substitutes

• U aX bY
• MRSYX a/b
• Violates 4th axiom.

Y
U3
U2
U1
X
22
Perfect Complements

• U min(aX,bY)
• MRS undefined at point where lines meet
• Violates non satiation and DMRS.

Y
U3
U2
U1
X
23
Bad Commodities
If Y is the bad commodity, then to get you to
consume more of Y, You have to be compensated
With more of X. EX Pollution To get people
to Live in polluted areas, that have Few
environmental amenities, Have to compensate them
with Higher income (i.e., so they can Purchase
more of the other Commodities, X.)
Y
U1
U2
U3
X