Chapter 4 Utility Functions

1
Chapter 4Utility Functions
2
Utility

• Ordinal Utility The only property of a utility
  assignment is how it orders the bundles of
  goods. The size of the utility difference
  between two bundles does not matter.
• Cardinal Utility It attaches a significance to
  the magnitude of utility. The size of the
  utility difference between two bundles has some
  sort of significance.

3
04.01
4
Panel A A monotonic transformationPanel B
non-monotonic transformation since it sometime
decreases.
5
04.02
6
The utility function can be represented by a
general functionuf(x1, x2)
7
04.03
8
Quasi-linear Utility Function

• Ux1v(x2)x1ln(x2)

9
04.04
10
The Cobb-Douglas Utility Function

• U(x1)c (x2)d
• where represents the superscript Note goods
  are imperfect substitutes

11
04.05
12
Other Utility Functions

• Leontief Function uminax1, bx2 (perfect
  complements)
• Linear Function uax1bx2 (perfect
  substitutes)
• Lexicographic Preference A is preferred to B if
  (I) x1(A) gt x1(B) or (ii) x1(A)x1(B) but
  x2(A)gtx2(B).

13
Leontief Function
x2
Examples (1) Left and right shoes (2) coffee and
sugar
x1
14
Linear Function
x2
Example yellow and red pencils (assuming that
colors are not your concern)
x1
15
Lexicographic Function
x2
A is inferior to B Example x1 (health)
x2 (money) for a terminally ill patient
.
B
.
A
x1
16
Marginal Utility

• Definition Effect on utility with a little more
  of good 1
• Formally, MU1dU/dx1u(x1dx1, x2)- u(x1,
  x2)/dx1

17
MRS

• The rate at which a consumer is just willing to
  substitute a small amount of good 2 for good 1.
• Formally, MRSMU1/MU2dU/dx1/dU/dx2, i.e.,
  marginal utility ratio.
• This is nothing but the slope of the indifference
  curve
• Given strict convexity assumption, MRS diminishes
  as we move down along a indifference curve

18
This concludes the Norton Media LibrarySlide Set
for Chapter 4 IntermediateMicroeconomics 6th
Edition byHal R. Varian
W. W. Norton CompanyIndependent and
Employee-Owned