Income and Substitution & Uncertainty Focused Study Guide
Income and Substitution Effect Focused Study Guide
Key Idea
Core Concept: A price change leads to two simultaneous effects:
Change in the slope (substitution effect)
Change in purchasing power (income effect)
Essential Definitions
Substitution Effect (SE)
Definition:
Caused by a change in relative prices, also interpreted as a slope change.
Analysis holds utility constant.
Implication: Consumers will substitute towards the cheaper good.
Translation:
“Price ratio changed” = Substitution Effect (SE)
“Slope changed” = Substitution Effect (SE)
Income Effect (IE)
Definition:
Caused by a change in purchasing power.
Analysis holds relative prices constant.
Implication: Consumers feel richer or poorer as purchasing power changes.
Translation:
“Can afford more” = Income Effect (IE)
“Budget set expanded” = Income Effect (IE)
Total Effect (TE)
Definition:
The total effect on quantity demanded resulting from a price change can be expressed as:
TE = SE + IE
Specific Corrections
Errors to Avoid:
Substitution Effect (SE) is defined solely by relative price changes.
Income Effect (IE) is solely defined by purchasing power changes.
Do not include preferences or quality changes as factors.
Understanding Changes:
Correct answer regarding price changes: Slope changes + Purchasing power changes
Slope of the budget line: Reflects relative price, calculated as rac{P_x}{P_y}.
Implication: Slope change = Substitution Effect
Graphical Representation
Graph Logic:
When the price of good X decreases:
Budget line rotates outward.
Pivot point: other good’s intercept.
Movement Sequence:
A → B = Substitution Effect
B → C = Income Effect
A → C = Total Effect
Direction Rules
Price of Good X Decreases:
Substitution Effect:
Always results in more of good X (because consumers move towards the cheaper good).
Income Effect:
Depends on type of good:
Normal good → more of good X
Inferior good → less of good X
Exam Strategies
**Typical Questions:
“What does a slope change represent?”
“What happens when relative prices change?”
“Which component isolates purchasing power?”
Key Recognitions for Questions:
If you see terms like:
“Relative price”, “slope”, “tradeoff” → Result in Substitution Effect
“Purchasing power”, “feels richer/poorer”, “afford more” → Result in Income Effect
Memorization Rule
Key Relationships to Remember:
Slope = Substitution Effect
Wealth = Income Effect
Total Effect = Both
Improved Understanding:
Previous confusion on wording addressed by linking language directly to concepts.
Recognizing terms guides towards the correct effect confidently.
Important Correction on Cause of Income Effect
Clarification:
Purchasing power changes cause the Income Effect, not the reverse.
Understanding Sequence:
Price changes → Purchasing power changes → Income Effect is the resultant response.
Effects of Price Changes
When Price of Good X Falls:
Substitution Effect:
More of good X (because relative price has changed)
Income Effect:
Dependent on good:
Normal goods → more of good X
Inferior goods → less of good X
Total Effect (TE):
Equivalent to the sum of SE + IE.
Correct Wording for Exams:
Avoid saying “we move toward more of X”.
Use phrasing such as “because X is relatively cheaper.”
Price Increase Effects
When Price of Good X Rises:
Substitution Effect:
Results in less of good X (always down).
Income Effect:
For Normal goods → down (decreased consumption)
For Inferior goods → up (increased consumption)
Uncertainty Focused Study Guide
Common Mistakes
Test Issues:
Missing Expected Value (EV) calculations.
Missing Expected Utility (EU) calculations.
Missing risk classification.
Failure in comparison logic.
Indicating a lack of a systematic approach.
Key Concepts
Expected Value (EV)
Definition:
Represents what one could expect on average from outcomes monetarily.
Formula:
EV = p_1x_1 + p_2x_2 + …
This provides the average dollar outcome based on probabilities and outcomes.
Expected Utility (EU)
Definition:
Illustrates satisfaction derived from those outcomes instead of just monetary value.
Calculation Steps:
Apply utility first to outcomes.
Multiply by respective probabilities.
Formula:
EU = p_1 imes U(x_1) + p_2 imes U(x_2)
Quick Example: Lottery Calculations
Example Lottery Scenario:
50% chance of winning 10, 50% chance of winning 30:
Expected Value (EV) Calculation:
EV = 0.5(10) + 0.5(30) = 20
This provides the average monetary outcome.
Expected Utility (EU) Calculation (Assuming Utility U(x) = √x):
EU = 0.5 ext{(} ext{√}10 ext{)} + 0.5 ext{(} ext{√}30 ext{)}
One-Line Rules to Remember
Key Formulas:
EV = ext{Probability} imes ext{Money}
EU = ext{Probability} imes ext{Utility}
Risk Types Classification
Types of Risk:
Risk-Averse:
Prefers certainty, seeks guaranteed outcomes, characterized as concave utility function.
Mathematical Relationship: U(EV) > EU
Risk-Neutral:
Linear preferences, indifferent to risk, only concerned with the expected value, where U(EV) = EU
Risk-Loving:
Prefers risky options, demonstrated by a convex utility function, characterized as: EU > U(EV)
Utility Functions for Types:
Risk-Averse: U(x) = ext{√}x (concave)
Risk-Neutral: U(x) = x (linear)
Risk-Loving: U(x) = x^{2} (convex)
Algorithm for Lotteries
Step-by-Step Process:
Identify probabilities and outcomes (e.g., 0.5 chance of 10, 0.5 chance of 30).
For Expected Value (EV):
EV = p_1x_1 + p_2x_2
For Expected Utility (EU):
EU = p_1U(x_1) + p_2U(x_2)
When comparing:
Calculate the EU of the lottery
Calculate the U of a certain amount
Compare them for decision making.
Final Contrast Example
Example Lottery:
50% chance of 0, 50% chance of 100, with a utility function of U(x) = √x:
Apply utility:
U(0) = 0
U(100) = 10
Compute Expected Utility (EU):
EU = 0.5(0) + 0.5(10) = 5
Compare to certainty:
Calculate Expected Value (EV):
EV = 50
Calculate Utility of Certain Amount:
U(50) ≈ 7.07
Conclusion: Since 7.07 > 5, this indicates risk-averse behavior in decision making.