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ECO200Y1a - Consumer Theory.doc
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Utility Theory
ONE GOOD UTILITY THEORY
• “Cardinal” measure of utility – precise, accurate, numerical measurement.
• Assume one good X:
• Total Utility =
(
)
XTU.
• Marginal Utility =
( )
(
)
X
X
X
∆
∆
=TU
MU.
• Diminishing marginal utility – “Can get too much of a good thing”..
Example: Deriving Demand
• MU drives D – diminishing marginal utility leads to a
negatively sloped D.
• Constant marginal utility of money – constant value
everywhere.
CONSUMER SURPLUS
• The difference of the value of the commodity and how much the consumer spend on it.
• Consumer surplus comes about because every unit is the same price, but consumers value each unit
differently.
Example
Given qp 212
−
=
, at 2
=
p,
( )( )
252125
2
1=−=CS.
• Note the $5 difference is due to the extra area from the triangles.
TWO GOOD UTILITY FUNCTION
•
(
)
(
)
(
)
YXYXTUTU,TU
+
=
– X and Y are not related goods.
• Equilibrium:
Y
Y
X
X
P
MU
P
MU=
6 5 4
6 5 4
2
4
4
6
8
10
2
D1
MU
Q
Q
MU
P
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ECO200Y1a - Consumer Theory.doc
Page 2 of 21
•
Y
Y
X
X
P
MU
P
MU=.
• If PX↓, then QX↑.
Indifference Theory
INDIFFERENCE CURVES
Definition
All points with the same level of satisfaction.
Assumptions
• Consumers are able to rank – given A and B, they are able to pick the preferred one.
• Transitivity/rational/consistent – if A > B > C, then A > C.
• More is preferred to less – 0
>
MU.
Derivation
• B is preferred to A (more of both goods) and A is
preferred to C (more of both goods), so B and C are
not on IC – IC negatively sloped.
• ↓↑<
∆
∆FC
F
C,0.
• Typically non-linear:
C
F
FC
MU
MU
F
C
MUFMUC
F
TU
F
C
TU
C
TUTU
−=
∆
∆
=⋅∆+⋅∆
=
∆
∆
∆+
∆
∆
∆
=
∆
∆
+
∆
∆
0
0
0F todue C todue
.
A
B
C
F
C
IC
∆
C
∆
F
X
X
P
MU
X
Y
Y
P
MU
Y
xxxx
xxxx
xxxx
xxxx
xxxx
xxxx
xxxx
xxxx
A
B
MUX/PX
MUY/PY
X
X
P
MU
Y
Y
P
MU
X
→
←
Y
PX
Q
D
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Page 3 of 21
• MRS: Willingness to trade on IC (holding TU constant) –
C
F
CFMU
MU
MRS=
/.
• IC convex because of marginal utility – diminishing marginal rate of substation.
• IC’s can’t cross – there is one and only one IC through any point.
Special Cases
F and C are perfect substitutes.
• MRS constant.
• IC is linear – slope of IC = MRS.
F is a “neutral” good (adds no satisfaction).
• IC is horizontal.
C is a “neutral” good (adds no satisfaction).
• IC is vertical.
F and C must be consumed in fixed proportions.
• Increases in only one good adds no satisfaction.
C is a “bad” (0
<
C
MU).
• Additional units of C will decrease satisfaction.
• 12 ICIC
>
.
F
C
IC2
IC1
F
C
IC2
IC1
F
C
IC2
IC1
F
C
IC2
IC1
F
C
IC2
IC1
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