lecture 2 - microeconomic basics i

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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