Some simplifying
assumptions
Consumer’s objective: to maximize
his/her utility subject to income
constraint
2 goods (X, Y)
Prices Px, Py are fixed
Consumer’s income
(I) is given

Consumer Equilibrium
Marginal utility per price
additional
utility derived from spending the next
price on the good
MU per last dollar = MU
P

Consumer Equilibrium
Optimizing condition:
If
spend more on good X and less of Y
X
Y
X
Y
MU
MU
P
P
X
Y
X
Y
MU
MU
P
P

Numerical Illustration
Q
x
TU
X
MU
X
MUx
Px
Q
Y
TU
Y
MU
Y
MUy
Py
1
30
30
15
1
50
50
5
2
39
9
4.5
2
105
55
5.5
3
45
6
3
3
148
43
4.3
4
50
5
2.5
4
178
30
3
5
54
4
2
5
198
20
2
6
56
2
1
6
213
15
1.5

Simple Illustration
Suppose:
X
= fishball
Y
= fishcake
Assume: P
X
=
2
P
Y
= 10

Cont.
2 potential optimum positions
Combination A:
X = 3 and Y = 4
–
TU = TU
X
+ TU
Y
= 45 + 178 = 223
Combination B:
X = 5 and Y = 5
–
TU = TU
X
+ TU
Y
= 54 + 198 = 252

Cont.
Presence of 2 potential equilibrium
positions suggests that we need to
consider income. To do so let us examine
how much each consumer spends for
each combination.
Expenditure per combination
–
Total expenditure = P
X
X + P
Y
Y
–
Combination A:
3(2) + 4(10) = 46
–
Combination B: 5(2) + 5(10) = 60

Cont.
Scenarios:
–
If consumer’s income = 46, then the
optimum is given by combination A. .…
Combination B is not affordable
–
If the consumer’s income = 60, then the
optimum is given by Combination
B….Combination A is affordable but it
yields a lower level of utility

The Ordinal Approach
Economists following the lead of Hicks,
believe that utility is measurable in an
ordinal sense--the utility derived from
consuming a good, such as X, is a function
of the quantities of X and Y consumed by a
consumer.
U =
f
( X, Y )

Cont.
Ordinal Utility Theory (TUO)
–
Can be measured in qualitative,
not quantitative, but only lists
the main options (indifference
curves & budget line).

#### You've reached the end of your free preview.

Want to read all 34 pages?

- Spring '15
- Utility