L05

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L05

• Choice

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Problem

• We know preferences (utility function)
• and
• We want to know optimal choice

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Choice

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Choice geometric solution
x2
x1
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Abstract approach

• In the example we were given
• we found demands - two numbers
• Now we use abstract parameters
• we find demand functionsNow we
• 4 types of preferences

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Abstract Cobb Douglass Function

• Cobb Douglass utility functions
• and

are equivalent in terms of preferences
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Abstract Cobb Douglass Function

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Magic (Cobb-Douglass) formula
Parameters

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Cobb-Douglas Summary

• Utility function or
• Solution
• Shares of income

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• A) Let and
• B) Let and

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Interiority

• Cobb Douglass (always interior solution)

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Cobb- Douglass preferences
x2
x1
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SOH (Perfect Complements)
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SOH (Perfect Complements)
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Perfect Complements (SOH)

Interior or corner solution?
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Is solution always interior?

• Not necessarily
• Even with well behaved preferences
• we might have a corner solution
• Example Perfect Substitutes

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Perfect substitutes

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Perfect Substitutes

x2
x1
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Magic (Substitutes) Formula

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Choice

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Is solution interior?

• Hence demand and
• Geometric interpretation
• How to solve for corner solution?
• Find a buddle using standard conditions
• If some then in optimum

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Choice Calculation

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In Practice

• Cobb-Douglass, Perfect Complements?
• Quasilinear ?
• Perfect Substitutes?