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MICROECONOMIC THEORY 1
Lecture 2: Ordinal Utility Approach To Demand Theory
Lecturer: Dr. Priscilla T Baffour; ptbaffour@ug.edu.gh
Priscilla T. Baffour (PhD)
Microeconomics 1 1 2017/18
Content
Assumptions
Curvature of indifference curves
Impossible indifference curves
Satiation
Monotonic Preferences
The budget Constraint
Consumer equilibrium
Priscilla T. Baffour (PhD) Microeconomics 1
2 2017/18
Assumptions
• The consumer is rational
• Ordinal utility-the consumer ranks his preferences based on satisfaction derived from each good.
• Total utility depends on quantity consumed
• Consistency and transitivity of choice
• Diminishing marginal rate of substitution
– IC is convex to the origin
– Slope of IC decreases
Priscilla T. Baffour (PhD) Microeconomics 1
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Indifference Curve
• IC is the locus of points-bundle of goods- that yield the same level of satisfaction.
• An indifference curve defines the substitution between goods X and Y that is acceptable in the mind of the consumer.
• Indifference map shows all ICs which rank the consumer’s preference.
Priscilla T. Baffour (PhD) Microeconomics 1
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Indifference Curve
• IC is convex to the origin. The convex shape indicates as you move towards the southeast along a typical IC, the consumer gives up less and less of Y for an extra unit of X. In other words what is sacrificed for an extra unit of X diminishes.
• The negative of the slope of IC is the marginal rate of substitution.
The rate of substitution declines along an IC (diminishing marginal rate of substitution)
Priscilla T. Baffour (PhD) Microeconomics 1
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Second order condition
Priscilla T. Baffour (PhD) Microeconomics 1
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• Essentially ensures that the utility curve is convex.
Impossible Indifference Curves
• Lisa is indifferent between e and a, and also between e and b…
– so by transitivity she should also be indifferent between a and b…
– but this is impossible, since b must be preferred to a given it has more of both goods.
B B
urr
ito
s,
p
er
se
me
ste
r
Z , Pizzas per semester
I 1
I 0
a
b
e
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 8
Impossible Indifference Curves (cont.)
• Lisa is indifferent between b and a since both points are on the same indifference curve…
– But this contradicts the “more is better” assumption. Can you tell why?
– Yes, b has more of both and hence it should be preferred over a.
B ,
Bu
r r ito
s p
er
se
me
ste
r
Z , Pizzas per semester
I
a
b
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 9
Priscilla T. Baffour (PhD) Microeconomics 1
Curvature of Indifference Curves
• Casual observation suggests that most people’s
indifference curves are convex.
• Special Cases:
– Perfect substitutes - goods that a consumer is
completely indifferent as to which to consume.
– Perfect complements - goods that a consumer is
interested in consuming only in fixed proportions.
2017/18 11
Figure 4.4(a): Perfect Substitutes
• Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like?
– Straight, parallel lines with an MRS (slope) of −1.
– Bill is willing to exchange one can of Coke for one can of Pepsi.
Co
k e
, C
ans p
er w
ee
k
1 2 3 4
P epsi, Cans per w eek
1
0
2
3
4
I 1 I 2 I 3 I 4
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 12
Figure 4.4(b): Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
1 2 3
Pi e , Slices per w eek
1
2
3
0
I 1
I 2
I 3
a
d
e c
b
If she has only one piece
of pie, she gets as much
pleasure from it and one
scoop of ice cream, a,
as from it and two
scoops, d,
or as from it and
three scoops, e.
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 13
Bads
• A commodity the consumer doesn’t like.
Noise
Sleep
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 14
Neutrals
• The consumer doesn’t care about it in one way or the other
Noise
Sleep
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 15
Satiation
• A situation where there is some overall best bundle (x1, x2) for the consumer, and the closer she is to that bundle, the better off she is in terms of her own preferences.
• In this scenario ICs have a negative slope when the consumer has “too little” or “too much” of both goods and a positive slope when he has “too much” of one of the goods.
– Having too much of one of the goods makes it a bad, reducing the consumption of the bad good moves her closer to the “bliss point”
– If she has too much of both goods, they both become bads, so reducing the consumption of both moves her closer to her “bliss point”
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 16
Monotonic Preference
• Premised on the idea that more is better, and that, we are examining conditions before the consumer reaches a satiation point.
• Monotonicity implies that indifference curves have a negative slope.
• Averages are preferred to extremes.
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 18
Monotonic Preference
• More of both goods is better for this consumer
X2 Better bundles
Worse bundles
X1
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 19
Budget Constraint
• Budget line (or budget constraint) - the bundles of
goods that can be bought if the entire budget is spent
on those goods at given prices.
• Opportunity set - all the bundles a consumer can buy,
including all the bundles inside the budget constraint
and on the budget constraint.
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 20
Budget Constraint (cont.)
• If Lisa spends all her budget, Y, on pizza and burgers,
then
pBB + pZZ = Y
– where pBB is the amount she spends on burgers and
pZZ is the amount she spends on pizzas.
• This equation is her budget constraint.
– It shows that her expenditures on burgers and pizza
use up her entire budget.
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 21
Budget Constraint (cont.)
• How many burgers can Lisa buy?
– To answer solve budget constraint for B (quantity of
burgers):
B
Z
ZB
ZB
P
ZPYB
ZPYBP
YZPBP
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 22
Budget Constraint (cont.)
• From previous slide we have:
– If pZ = $1, pB = $2, and Y = $50, then:
B
Z
P
ZPYB
$50 ($1 )25 0.5
$2
ZB Z
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 23
Figure 4.7: Budget Constraint
From previous slide we have that if:
– pZ = $1, pB = $2, and Y = $50, then the budget constraint, L1, is:
$50 ($1 )25 0.5
$2
ZB Z
B
,
Bu
rge
rs
pe
r se
me
ste
r
Opportunity set
50 = Y / p Z
L 1
25 = Y / p B
20
10
10 0 30
Z , Pizzas per semester
a
b
c
d
Amount of Burgers
consumed if all income
is allocated for Burritos.
Amount of Pizza
consumed if all income
is allocated for Pizza.
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 24
Figure 4.8(a) Changes in the Budget
Constraint: Price of Pizza Doubles B
, B
urg
ers
r
per
sem
este
r
Loss
50
L 1 ( p Z = $1)
L2 (pZ = $2)
25
25 0
Z , Pizzas per semester
B = Y PB
- PZ = $1
PB
Z
If the price of pizza doubles, (increases from $1 to $2) the slope of the budget line increases
This area represents
the bundles she can no
longer afford
$2 Slope = -$1/$2 = -0.5
Slope = -$2/$2 = -1
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 25
Figure 4.8(b): Changes in the Budget Constraint: Income Doubles
Gain
L 3 ( Y = $100)
L 1 ( Y = $50)
0
B = $50
PB
- PZ
PB
Z
If Lisa’s income increases by $50 the budget line shifts to the right (with the same slope!)
$100
This area represents the
new consumption
bundles she can now
afford!!!
100 50
Z , Pizzas per semester
B, B
urr
itos p
er
sem
este
r
50
25
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 26
Consumer equilibrium
• The consumer maximizes utility at a point where the slope of
the indifference curve (MRS) is equal to the slope of the
budget constraint.
• At the chosen point we have tangency of the indifference curve
and the budget constraint,
• px/py = MRS = MUx/MUy, i.e., MUx/px = MUy/py.
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 27
The budget constraint and the indifference curve have the same slope at the point e where they touch.
Therefore, at point e:
Slope of I2
Figure 4.9 Consumer Maximization, Interior
Solution (cont.) B
, B
ur r
ito
s p
er
se
me
ste
r
25
50 0
Z , Pizzas per semester
I2
e
MRTP
P
MU
MUMRS
B
Z
B
Z
Slope of BL
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 28
30
Corner solution: Boundary-optimal solution with only commodity x2 being consumed
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1
32
Corner solution with strictly concave preferences
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1
Recap on Taxes, Subsidies & Rationing
Forms of Taxes
1. Quantity (specific) tax
2. Ad valorem (value) tax
3. Lump sum tax
Forms of Subsidies
• Specific subsidy
• Ad valorem
• Lump sum
Rationing
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 33
Problem
A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer’s opportunity set change?
2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 34
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