lecture 2 - microeconomic basics i
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Microeconomic Basics ITRANSCRIPT
Lecture 2 - Microeconomic Basics I Consumer Theory: The Utility Concept
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Risø DTU, Danmarks Tekniske Universitet
Wrap-up last lecture In the last lecture we have: • define GDP
• different concepts of GDP
• what does GDP measure
• environment and economic growth
• more sustainable growth.
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Risø DTU, Danmarks Tekniske Universitet
Subdisciplines of EE
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Risø DTU, Danmarks Tekniske Universitet
Learning objectives At the end of this lecture you will be able to: • graphically and formally explain the concept of a utility function
• graphically and formally explain the concept of an indifference curve and
of the marginal rate of substitution.
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Risø DTU, Danmarks Tekniske Universitet
Content 1. What is utility? 1.1. Origins of the utility concept: Utilitarianism 1.2. Cardinal vs. ordinal utility 1.3. The utility function 2. More than one good: the consumption bundle 2.1. Bundle of goods and choices 2.2. Graphical example for two goods – the indifference curve 2.3. The marginal rate of substitution 2.4. The math behind the concept
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Risø DTU, Danmarks Tekniske Universitet
1.1. The origins of the utility concept
• Theological philosophy
• What defines a truly 'good' action?
• 'Good' is what generates the highest amount of total utility
• Everyone's utility counts the same
• Utilitarianism: Jeremy Bentham and John Stuart Mill
• How to measure utility?
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Risø DTU, Danmarks Tekniske Universitet
1.2. Cardinal vs. ordinal utility
Cardinal utility: Absolute measure, measure as meaningful as kg or km. BUT, does 10 'utils' mean the same to Fred as it does to George? Ordinal utility: Relative measure, only compares goods or bundles of goods to each other. If Fred is willing to give up 50 galleons for a Firebold but only 30 for a Nimbus 2000, but George only wants to give up 45 galleons for the Firebold and 35 for the Nimbus 2000, then we know that Fred derives a higher ordinal utility from a Firebold than George.
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Risø DTU, Danmarks Tekniske Universitet
1.3. The utility function
U(x)
x
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Risø DTU, Danmarks Tekniske Universitet
1.3. The utility function
U(x)
x
?
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Risø DTU, Danmarks Tekniske Universitet
1.3. The utility function
U(x)
x
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Risø DTU, Danmarks Tekniske Universitet
1.3. The utility function
U(x)
x
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Risø DTU, Danmarks Tekniske Universitet
1.3. The utility function
U(x)
x
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Risø DTU, Danmarks Tekniske Universitet
1.3. The utility function
U(x)
x x'
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Risø DTU, Danmarks Tekniske Universitet
1.3. The utility function
u(x)
x x'
u(x')
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Risø DTU, Danmarks Tekniske Universitet
2.1. Bundle of goods and choices
+
+
or
= B
= A
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
Indifference curve
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
3
1
3 6
A
B
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
3
1
3 6
A
B
C
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
3
1
3 6
A
B
C
D
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
Indifference curve
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
Indifference curve
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
Indifference curve
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
Indifference curve
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
Indifference curve
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
Indifference curve
D
C
B A
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot Dogs
Ice Cones
U0
U1
U2
U3
U0 < U1 < U2 < U3
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot dogs
Ice cones
U( Hot dogs; Ice cones)
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot dogs
Ice cones
U( Hot dogs; Ice cones)
A B
C
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot dogs
Ice cones
U( Hot dogs; Ice cones)
Indifference curves
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot dogs
Ice cones
U( Hot dogs; Ice cones)
U0 U1 U2
U3
Indifference curves
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot dogs
Ice cones
U( Hot dogs; Ice cones)
U0 U1 U2
U3
Indifference curves
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Hot dogs
Ice cones
U( Hot dogs; Ice cones) U0
U1 U2 U3
Indifference curves
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Risø DTU, Danmarks Tekniske Universitet
2.2. Graphical example for two goods – the indifference curve
Peter Fuleky, University of Washington 34
Risø DTU, Danmarks Tekniske Universitet
2.3. The marginal rate of substitution
Hot Dogs
Ice Cones
Indifference curve
D
C
B A
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Risø DTU, Danmarks Tekniske Universitet
2.3. The marginal rate of substitution
Hot Dogs
Ice Cones
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Δ HD
Δ IC
Risø DTU, Danmarks Tekniske Universitet
2.3. The marginal rate of substitution
Parc
Other goods
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Δ Parc
Δ OG
Risø DTU, Danmarks Tekniske Universitet
2.4. The math behind the concept
One way: Preference orderings >> Marginal rate of substitution >> Indifference curves >> Utility function Second way: Utility function >> Indifference curves >> Marginal Rate of substituion >> Preference orderings
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Risø DTU, Danmarks Tekniske Universitet
2.4. The math behind the concept
For a given utility function 𝑢 𝑥1, 𝑥2 Marginal utility of 𝑥1 (partial derivative):
𝑀𝑀1 = lim∆𝑥1→0
𝑢( 𝑥1 + ∆𝑥1 , 𝑥2)∆𝑥1
= 𝜕𝑢 𝑥1, 𝑥2
𝜕𝑥1
Keeping 𝑥2 constant. Calculating the MRS (total derivative):
𝑑𝑢 = 𝜕𝑢 𝑥1, 𝑥2
𝜕𝑥1 d𝑥1 +
𝜕𝑢 𝑥1, 𝑥2𝜕𝑥2
d𝑥2 = 0
Solving for d𝑥2 d𝑥1
gives
d𝑥2
d𝑥1 = −
𝜕𝑢 𝑥1,𝑥2𝜕𝑥1 �
𝜕𝑢 𝑥1, 𝑥2𝜕𝑥2 �
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(3)
(2)
(1)
Risø DTU, Danmarks Tekniske Universitet
2.4. The math behind the concept Examples for utility functions for two goods 𝑥1, 𝑥2: 1. 𝑢 𝑥1, 𝑥2 = 𝑎𝑥1 + 𝑏𝑥2 -> perfect substitutes 2. 𝑢 𝑥1, 𝑥2 = min 𝑎𝑥1, 𝑏𝑥2 -> perfect complements 3. 𝑢 𝑥1, 𝑥2 = 𝑣 𝑥1 + 𝑥2 -> quasi-linear 4. 𝑢 𝑥1, 𝑥2 = a ln 𝑥1 + 𝑏 ln 𝑥2 -> Cobb-Douglas
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Risø DTU, Danmarks Tekniske Universitet
2.4. The math behind the concept
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Repeating with Cobb-Douglas Utility function:
𝑢 𝑥1, 𝑥2 = a ln 𝑥1 + 𝑏 ln 𝑥2 Marginal utility: 𝜕𝑢 𝑥1,𝑥2
𝜕𝑥1= 𝑎
𝑥1 and 𝜕𝑢 𝑥1,𝑥2
𝜕𝑥2= 𝑏
𝑥2
Marginal rate of substitution:
𝑀𝑀𝑀 = − 𝜕𝑢 𝑥1, 𝑥2
𝜕𝑥1 �
𝜕𝑢 𝑥1, 𝑥2𝜕𝑥2 �
= − 𝑎𝑥1
𝑏𝑥2
� = −𝑎𝑏
𝑥1𝑥2
(1)
(2)
(3)
Risø DTU, Danmarks Tekniske Universitet
Summary and outlook • Preferences • Utility function
• Infifference curve
• Marginal rate of substitution
• Functional forms
• Market demand function
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