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# L05 - PowerPoint PPT Presentation

L05. Choice. Problem:. We know preferences (utility function) and We want to know optimal choice. Choice. \$. \$. \$. \$. \$. \$. \$. \$. \$. \$. Choice: geometric solution. x 2. x 1. Abstract approach. In the example we were given we found demands - two numbers

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### L05

Choice

Problem:
• We know preferences (utility function)

and

• We want to know optimal choice
Choice

\$

\$

\$

\$

\$

\$

\$

\$

\$

\$

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
Abstract Cobb Douglass Function
• Cobb Douglass utility functions

and

are equivalent in terms of preferences

Cobb-Douglas: Summary

Utility function: or

Solution:

Shares of income

A) Let and

B) Let and

Interiority

Cobb – Douglass (always interior solution)

Perfect Complements (SOH)

Interior or corner solution?

Is solution always interior?
• Not necessarily
• Even with well behaved preferences

we might have a corner solution

• Example: Perfect Substitutes
Choice

\$

\$

\$

\$

\$

\$

\$

\$

\$

\$

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