03/25: ECON 310 - Study Notes on Income and Substitution Effects, Uncertainty, and Lottery Theory

Announcements

• The lecture on income and substitution effects will conclude today.

• Homework on income and substitution effects is due on Monday before class.

• Introduction to uncertainty will commence after today’s discussion.

• Homework on uncertainty will be due Wednesday before class.

Income and Substitution Effects

Review of Demand Curve

• Demand Curve: Graphs the relationship between two economic variables:

  • Price

  • Quantity Demanded

• A downward-sloping demand curve indicates:

  • As price decreases, quantity demanded increases.

  • Conversely, as price increases, quantity demanded decreases.

Exercise: Normal Good and Demand Curve

• Consider the statement: "If a good is normal, its demand curve necessarily slopes down."

• Tool for analysis: Income and Substitution Effects

  • Total Effect = Substitution Effect + Income Effect

Example: Increase in Price of Good (Normal Good)

• Assumption: Good x is normal.

• Scenario: Price of good x increases.

  • Consequence:

  • Feel poorer (decrease in purchasing power).

  • Demand for good x decreases due to:

    • Income Effect:

    • Negative impact (buy less as you feel poorer).

    • Substitution Effect:

    • Price of x goes up, relative to y, causes shifts in purchasing behavior (buy less of x, more of y).

• Conclusion: Total effect on demand for x is negative (consistent with downward-sloping demand curve).

Clarification on Income and Substitution Effects

• Income Effect: Reflects how changes in price affect consumer purchasing power.

• Substitution Effect: Reflects changes in quantity demanded based on the relative price of goods.

• They are separate and do not depend on each other but contribute to the total effect.

• Indicator of Demand Curve Slope:

  • If total effect is negative (purchasing less), demand curve slopes down.

Exploring Between Normal and Inferior Goods

• Second inquiry: If starting with a downward-sloping demand curve, can we say that x is necessarily a normal good?

• Analysis Assumption: Starting from total effect > 0 (demanding more).

Case 1: Normal Good

• Price increases, which makes the income and substitution effects both potentially negative but cannot confirm the nature of the good.

• Therefore, uncertainty about whether x is normal or inferior remains.

• Conclusion: First statement true; second statement false.

Practical Applications

• Importance of distinguishing between behaviors in normal and inferior goods affects demand and consumer choices.

• Extension of analysis into labor markets, wage impacts, and consumer behavior relating to AI's productivity.

Introduction to Uncertainty

Definition of Lottery

• A lottery comprises different potential outcomes assigned probabilities:

  • Probabilities must satisfy:

  • Sum to 1.

  • Must be non-negative.

Example: Fruit Lottery

• Assigned probabilities for outcomes (apple, orange, banana):

  • Apple: 0.25

  • Orange: 0.35

  • Banana: 0.40

Expected Value Calculation

• The expected value of a lottery is calculated using:

  • Probability of outcome multiplied by its corresponding value.

• Example Lottery with Monetary Values:

  • Outcomes: $5, $10, $20 with probabilities 0.10, 0.15, 0.75.

• Calculation Example

  • Expected Value (EV) = $0.10 imes 5 + 0.15 imes 10 + 0.75 imes 20$

  • EV = $13.50$

Impact of Risk on Decision Making

• In decision theory, one must consider expected utility over expected value for better decision-making under uncertainty.

• Expected utility provides a richer grounding for the way individuals approach choices concerning risk.

Summary and Questions

• Homework reinforces concepts of income and substitution effects; due Monday.

• Expected utility will aid comprehension of uncertain scenarios in consumer choices, setting up for further analysis moving forward.