L05 Choice

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

Choice $ $ $ $ $ $ $ $ $ $

Choice: geometric solution x2 x1

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

Abstract Cobb Douglass Function

Magic (Cobb-Douglass) formula Parameters:

Cobb-Douglas: Summary Utility function: or Solution: Shares of income

A) Let and B) Let and

Interiority Cobb – Douglass (always interior solution)

Cobb- Douglass preferences x2 x1

SOH (Perfect Complements)

SOH (Perfect Complements)

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

Perfect substitutes $ $ $ $ $ $ $ $ $ $

Perfect Substitutes x2 x1

Magic (Substitutes) Formula

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

Choice: Calculation

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