•
When we say that individual X has utility function
u( )
all we are saying is that this individual's
u(.) –all we are saying is that this individual s
preferences can be represented
by function u(.)
•
Saying that bundle A gives 10 units of utility
does not have any significance, except if we also
know that bundle B is worth 12 (8) units of utility.
Then it implies that bundle A is worse (better)
than B.
Utility
•
Ordinal Utility Function
Places market baskets in the order of most
preferred to least preferred, but it does not
indicate how much one market basket is
preferred to another
•
If we take utility function u(.) and transform it
using an increasing function f() into function
v(x,y,z)=f(u(x,y,z)) then v(.)and
u(.) are
equivalent, i.e. reflect the same preferences.
Utility Function
•
If I am always
indifferent between 1 can of Coke
and 1 coke Pepsi, then my preferences for Coke
and Pepsi can be represented by a utility
function u(C,P)=C+P where C and P are the
numbers of cans of Coke and Pepsi that I
consume.
But these preferences are also represented by
utility function u(C,P)=5C+5P,
but not by a utility function u(C,P)=2C+6P.
Ordinal Utility
•
Although we numerically rank baskets and
indifference curves, numbers are ONLY
for
ranking
•
A utility of 4 is not necessarily twice as good as
a utility of 2
•
If buying 1 pair of tennis sneakers makes you
happier than buying 2 shirts, then we say that
the sneakers give you more utility than 2 shirts
Indifference Curves and Utility Function
•
An Indifference curve at level u is a collection of
all such points (x
1
,..,x
n
) that satisfy u(x
1
,..,x
n
)=u.
This gives an easy way to draw indifference
curves.
• Take any points (x
x ) and (y
y ) s t
•
Take any points (x
1
,..,x
n
)
and (y
1
,..,y
n
) s.t.
individual i likes the first of them better than the
second.
•
Then: (x
1
,..,x
n
) is on a higher indifference
curve than (y
1
,..,y
n
) and
u(x
1
,..,x
n
) > u(y
1
,..,y
n
)

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