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University of Toronto
Department of Economics
ECO 204
2011 - 2012
Sayed Ajaz Hussain
Lecture 3

© Sayed Ajaz Hussain, Department of Economics, University of Toronto, STG

1

Lectures 1 and 2 ..
Method for solving unconstrained optimization:
max �� ��
��

The Envelope Theorem
Lagrangian method for solving equality constrained optimization: max �� �� ��. ��. �� �� = ��
��

Kuhn-Tucker method for solving inequality constrained optimization: max �� �� ��. ��. �� �� ≤ ��
��

See ECO 204 chapter 1 or come talk to us in office hours
Feedback? economics204@gmail.com

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

2

Today: Consumer Theory
Preference relations and “Rational” preferences
Commodities and Consumption set
Felicity
Utility functions

Positive monotonic transformation
Indifference Curves
Marginal Rate of Substitution
Feedback? economics204@gmail.com

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

3

Some Applications of Consumer Theory in ECO 204
Consumer Choice
Consumer Preferences and Income → Consumer Demand Function Consumer Demand Function → Consumer Preferences → Welfare analysis Finance
Portfolio allocation between a risk free asset and risky assets Inter-temporal savings
Marketing
Forming market segments
Advertising
Introducing and/or changing product attributes
Public Policy
Ban or curb harmful consumption of “harmful” goods?
How to promote higher birth rates?
Feedback? economics204@gmail.com

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

4

Economics: a Social Science
A few words about economic models: assumptions and methodology

Plausible
Assumptions

Feedback? economics204@gmail.com

Model and Generate
Testable Predictions

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

Test Model

5

Modeling a Consumer’s Decision Problem
Chooses from set of mutually exclusive alternatives:
Major in Commerce, .., Become Eco−man’s sidekick

Focus on choice of consumption levels of commodities:
�� goods and services available for purchase in market

Physical restrictions on consumption of commodities
represented by “consumption set” ��

Assume:
�� =

Feedback? economics204@gmail.com

��1 , ��2 , . . , ���� ≥ 0

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

Most of the time �� = 2

6

Examples of �� = 2 Consumption Sets
��2

Hours/day

24

��

��
��1

0

��2

0
��2
��

3
2

Else

��

1
0
Feedback? economics204@gmail.com

��1

0

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

��1

HW

7

Consumer’s Preferences Over Bundles in ��
“Better than” relation: ≻
Example: She likes Bottega Veneta bags more than LV bags
“Indifference” relation: ~
Example: He is indifferent between John Lobb and Edward Green shoes

Assume consumer has rational preferences:
Complete preferences: for any two bundles ��, �� in �� ∶ Either �� ≻ �� , or �� ≻ �� , or �� ~ �� Transitive preferences: for any bundles ��, ��, �� in �� it must be that If �� ≻ �� and �� ≻ �� then �� ≻ �� Feedback? economics204@gmail.com

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

8

HW

Representing Preference Rankings by “Felicity”
Suppose consumer’s preferences over 0,1,2,3 glasses of beers are: 1~2≻0~3
2 Felicity Plots for this Consumer: ��-axis is # of beers, ��-axis is “Felicity”

Interpretation of ��-axis values?
Felicity:
Feedback? economics204@gmail.com

© Sayed Ajaz Hussain, Department of Economics
University of Toronto, STG

9

Representing Preference Rankings by Felicity
Suppose a consumer’s preferences over (5,3) vs. (5,5)
bundles of # pretzels packets and # of beers are 5, 5 ≻ (5, 3) 2 Felicity Plots for this Consumer
��-axis is # of Pretzel packets, ��-axis is # of beers, ��-axis is...
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