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

Quiz! A) Let and B) Let and

Interiority Cobb – Douglass (always interior solution)

Cobb- Douglass preferences x2 x1

Is solution always interior? Not necessarily Even with well behaved preferences we might have a corner solution Example: quasilinear preferences

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

Quasilinear preferences x2 x1

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

Perfect Substitutes x2 x1

Magic (Substitutes) Formula

Magic (Complements) formula

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