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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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Presentation Transcript
slide1

L05

Choice

problem
Problem:
  • We know preferences (utility function)

and

  • We want to know optimal choice
choice
Choice

$

$

$

$

$

$

$

$

$

$

abstract approach
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
Abstract Cobb Douglass Function
  • Cobb Douglass utility functions

and

are equivalent in terms of preferences

cobb douglas summary
Cobb-Douglas: Summary

Utility function: or

Solution:

Shares of income

slide10
A) Let and

B) Let and

interiority
Interiority

Cobb – Douglass (always interior solution)

perfect complements soh
Perfect Complements (SOH)

Interior or corner solution?

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

we might have a corner solution

  • Example: Perfect Substitutes
choice20
Choice

$

$

$

$

$

$

$

$

$

$

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