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Intermediate microeconomics
Chapter 3
Lectures
Utility function
Demonstration of a utility function with its level curves
Preferences relation from utility function
Different utility functions may represent the same preferences
Cardinal and ordinal utility
Monotonic transformation
Utility function when goods are perfect substitutes
Utility function when goods are perfect complements
Quasi-linear preferences
Cobb-Douglas preferences
Utility functions representing Cobb-Douglas preferences
Marginal utility
MRS and marginal utility
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Utility function when goods are perfect substitutes
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Summary
Perfect substitutes with a one-to-one substitution:
u
(
x
1
,
x
2
)
=
x
1
+
x
2
u
(
x
1
,
x
2
)
=
x
1
+
x
2
Any monotonic transformation such as
4
x
1
+
4
x
2
4
x
1
+
4
x
2
or
(
x
1
+
x
2
)
2
(
x
1
+
x
2
)
2
will do as well.
Perfect substitutes with an arbitrary rate of substitution:
u
(
x
1
,
x
2
)
=
a
x
1
+
b
x
2
u
(
x
1
,
x
2
)
=
a
x
1
+
b
x
2
M
R
S
=
−
a
/
b
M
R
S
=
−
a
/
b