This

**preview**shows half of the first page. to view the full**3 pages of the document.**

Utility Function: CU = u(x1, x2, x3, … , xn)

Math representation of preference ordering:

a.

X>Y U(x)>U(y)

b.

X～Y U(x)=U(y)

* numbers in the utility function are “ordinal” not “cardinal”*

From the utility function, we only know the order of the preference (whether X is before Y),

not the strength of the preference (whether the utility of X is 3 times greater than Y)

* These utility functions are only unique to a “positive monotonic transformation”.

e.g. V[U(x) = [U(X)]2; 3 + 2U(X); 5 + lnU(X)

-- “Positive monotonic transformation” is like “relabeling of the preferences”;

-- It does not change the order of preferences;

Indifference Set/curve

Set of commodity bundles that satisfies U(x1, x2) = Uo(some level of utility)

x1

x2

-- Indifference curve pass to the right indicate higher utility

(assume “more is better”)

-- Slope of the indifference curve:

1.

Total Differentiate “U(x1, x2) = Uo”

MU of x1 MU of x2

*MU of x1: the utility one gets from consuming one more unit of x1, holding x2 constant.

Implication:

Measure the rate at which the consumer would be willing to substitute one good for another

e.g.

Suppose U(x1, x2) = x10.5 * x20.5

MRS (x2for x1) = U1/U2 = x2/x1

Assume U=100.

X1

X2

MRS

100

100

1

225

44.44

0.1975

400

25

0.0625

Topic 2 - Utility and Indifference Curves

September 21, 2011

10:29 AM

###### You're Reading a Preview

Unlock to view full version