1. Chapter 4 UTILITY

2. Utility is seen only as a way to describe preferences.
A utility function
a way of assigning a number to every possible consumption bundle such that more-preferred bundles get assigned larger numbers than less preferred bundles.
Ordinal utility: rank matters, size does not.
Cardinal utility: size matters, too.

3. Monotonic transformation
Transforming one set of numbers into another set of numbers in a way that preserves the order of the numbers.

4. Monotonic transformation
u(x1, x2) represents the preference:
iff
f(u) is a monotonic transformation:
A monotonic transformation of a utility function is a utility function that represents the same preference as the original utility function.

5. 4.1 Cardinal Utility Cardinal utility: Both order and size matter.
Tells how much more the consumer likes one bundle over another.
Size is inconsequential to consumer behavior.
Ordinal utility is enough.

6. 4.2 Constructing a Utility Function
Suppose more distant indifference curves represents higher utility.
Draw a diagonal line.
Find the distance from the origin to an indifference curve along the diagonal line.
Assign that distance to the indifference curve.

7. 4.3 Some Examples of Utility Functions
u(x1, x2) =x1x2
A typical indifference curve
{(x1, x2): k=x1x2}
Algebraic expression of the indifference curve
x2=k/x1

8. 4.3 Some Examples of Utility Functions
Perfect Substitutes
Preferences of perfect substitutes can be represented by a utility function of the form
u(x1, x2)=ax1+bx2
Here a and b measure the “value” of goods 1 and 2 to the consumer. The slope of a typical indifference curve is given by -a/b.

9. 4.3 Some Examples of Utility Functions
Perfect Complements
A utility function that describes a perfect complement preference is given by
u(x1, x2)=min{ax1,bx2}
where a and b are positive numbers that indicate the proportions in which the goods are consumed.

10. 4.3 Some Examples of Utility Functions
Quasilinear Preference
The utility function is linear in good 2, but nonlinear in good 1:
u(x1, x2)=v(x1)+x2

11. Cobb-Douglas Preference
c and d are positive numbers that describe the preferences of the consumer.

12. 4.4 Marginal Utility Marginal utility
consumer’s utility change as we give him or her a little more of good 1.
The change in utility by a marginal consumption of good 1:

13. 4.5 Marginal Utility and MRS
A utility function u(x1, x2) can be used to measure the marginal rate of substitution (MRS).
Consider a change in the consumption bundle, (△x1, △x2), that keeps utility constant
MU1△x1+MU2△x2=△U=0
Solving for the slope of the indifference curve we have
MRS=△x2/△x1=－MU1/MU2