# ECO206Y1 Lecture Notes - Indifference Curve, Utility, Lincoln Near-Earth Asteroid Research

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Topic 2 – Utility & Indifference Curve

(Lecture 2 Sept 21st)

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)

All these are examples of “positive monotonic transformation” of the Utility function;

The preference order is the same;

Indifference Set/curve

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

x2

x1

2. 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

-- Indifference curve pass to the right indicate higher utility

(assume “more is better”)

-- Slope of the indifference curve: