Chapter 4

Utility Functions

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.

04.01

Panel A: A monotonic transformation Panel B: non-monotonic transformation since it sometime decreases.

04.02

The utility function can be represented by a general function: u=f(x1, x2)

04.03

Quasi-linear Utility Function:

U=x1+v(x2)=x1+ln(x2)

04.04

The Cobb-Douglas Utility Function

U=(x1)^c (x2)^d

where ^ represents the superscript Note: goods are imperfect substitutes

04.05

Other Utility Functions:

• Leontief Function: u=min[a*x1, b*x2] (perfect complements) • Linear Function: u=a*x1+b*x2 (perfect substitutes) • Lexicographic Preference: A is preferred to B if (I) x1(A) > x1(B) or (ii) x1(A)=x1(B) but x2(A)>x2(B).

Leontief Function x2 Examples: (1) Left and right shoes (2) coffee and sugar x1

Linear Function x2 Example: yellow and red pencils (assuming that colors are not your concern) x1

Lexicographic Function x2 A is inferior to B Example: x1 (health) x2 (money) for a terminally ill patient .

.

B A x1

Marginal Utility

• Definition: Effect on utility with a little more of good 1 • Formally, MU1=dU/dx1=[u(x1+dx1, x2)- u(x1, x2)]/dx1

MRS

• The rate at which a consumer is just willing to substitute a small amount of good 2 for good 1.

• Formally, MRS=MU1/MU2=[dU/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

W. W. Norton & Company

Independent and Employee-Owned

This concludes the Norton Media Library Slide Set for Chapter 4

Intermediate Microeconomics

6 th Edition by Hal R. Varian