Intermediate Microeconomics Lecture Notes

Page 1: Course Overview

• Course Title: EC 202 Intermediate Microeconomics

• Instructor: Autumn 2024

• Reading: Chapters 2, 5, and 6 from Varian; Chapters 4, 5, and 6 from Perloff

Page 2: Employability Talk Announcement

• Speakers: Amy Anderson & Russell Bullock

• Topic: Government Economics Service Careers in the Civil Service & Application Skills

• Date: 16 October 2024

• Time: 5 PM

• Location: Room LTB08

• Attendance: First come, first served for first- and second-year undergraduate students.

Page 3: Recap of Previous Lecture

• Optimization Principle: Individuals choose the best consumption bundle they can afford.

• Key Concepts Introduced:

  1. Utility functions and preferences

  2. Revealed preference

• Keywords:

  • Utility function

  • Transitivity

  • Weak Axiom of Revealed Preference (WARP)

  • Indifference curve

  • Marginal Rate of Substitution (MRS)

• Objective of Today: Define what consumers can afford and study their optimal choices.

Page 4: Lecture Part 1 - Budget Sets

• Reading Reference: Varian, Chapter 2

Page 5: Understanding Budget Sets

• Basic Concept:

  • A budget set includes all goods a consumer can afford given their income (m pounds).

• Economic Principle: Resources are limited, necessitating decision-making about allocation.

Page 6: Budget Constraint Equation

• Constraint Expression: $a imes p<em>a + b imes p</em>b ext{ ≤ } m$

  • Where:

  • $a$ = quantity of apples bought

  • $p_a$ = price of apples

  • $b$ = quantity of bananas bought

  • $p_b$ = price of bananas

• Graphical Representation: Graphical methods are used to visualize the budget constraint.

Page 7: Example of Budget Set

• Example Scenario:

  • $m = 10$ pounds

  • $pa = 10$ (apple) and $pb = 5$ (banana)

• Budget Constraint:
  $10 = a imes 10 + b imes 5$

• Visual Representation: Area below the budget constraint represents the budget set.

Page 8: Graphing the Budget Constraint

• Visual Elements:

  • Slope of the budget constraint is given by:
    $ext{slope} = - rac{p<em>b}{p</em>a}$

• For the Example:

  • The constraint $10 = 10a + 5b$ is represented graphically.

Page 9: Opportunity Costs

• Definition:

  • Slope reflects how much of good $a$ must be sacrificed for one unit of good $b$.

• Example Interpretation:

  • Slope of -1/2 means one apple requires sacrificing 2 bananas.

• Economic Insight: Cost of goods can be measured in forgone alternatives, rather than direct monetary cost.

Page 10: Concept of Opportunity Cost Continued

• General Definition:

  • Reflects the most highly valued alternative sacrificed when making a choice.

• James Buchanan Quote:

  • "Choice implies rejected as well as selected alternatives…"

• Significance: Helps to evaluate resource allocation decisions.

Page 11: Changes in Budget Sets

• Types of Changes:

  1. Income fluctuations

  2. Changes in prices of goods

Page 12: Example of Increased Income

• Scenario: Initial income of $10 increases to $20

• Impact: Budget set expands allowing for greater consumption without affecting slope (price remains the same).

Page 13: Example of Price Decrease

• Scenario: Price of bananas decreases from $5 to $2.50

• Impact: Budget set expands and slope changes from -1/2 to -1/4 due to the price change.

Page 14: Limitations of Graphing

• Graphing Constraints:

  • Charts can only represent two (or at most three) goods.

  • One good is typically whatever is of primary interest, while the other could represent all other goods or constant money.

• Numeraire Price Concept:

  • One good can be treated as having a price of 1 for simplification.

Page 15: Individual Behavior vs. Collective Dynamics

• The previous focus was solely on individual consumer behavior in isolation.

• Future lessons will examine interactions between consumers in microeconomic contexts as an important consideration.

Page 16: Lecture Part 2 - Optimization

• Reading Reference: Varian, Chapter 5

Page 17: Consumer’s Optimal Choice

• Statement: Consumers maximize utility subject to budget constraints.

• **Mathematical Expression:
  $ext{Max } u(a, b) ext{ subject to } p<em>a a + p</em>b b ext{ ≤ } m$

Page 18: Consumer’s Optimal Choice Graph

• Visual Elements:
  Indifference curves and budget constraints graphically defined, showing optimal points where they intersect.

Page 19: Optimal Consumption Point

• At point E, the indifference curve is tangent to the budget line, indicating maximum utility.

• Equilibrium Condition:
  $ext{MRS} = rac{U<em>1}{U</em>2} = rac{p<em>1}{p</em>2}$

Page 20: Challenging Cases

• Perfect Substitutes Scenario:

  • In situations of perfect substitutes, the solution may be at a 'corner' and not defined by the traditional MRS concept.

Page 21: Application of Borrowing Constraints

• Concept:

  • Illustrates intertemporal choices regarding consumption and saving given external lending constraints.

• Example of Optimal Savings: Discussion on how marginal utility may influence saving decisions when restricted.

Page 22: Demand for Perfect Complements

• Theory Explained:

  • Demand functions indicate optimal consumption split based on prices and income for complementary goods.

• Mathematical Representation:
  $r imes p<em>r + l imes p</em>l = m$

Page 23: Cobb-Douglas Demands**

• Utility Function Reference:
  $u(x<em>1,x</em>2) = x<em>1^c x</em>2^d$

• Optimal Demands Derived:

  • $x<em>1^* = rac{c}{c+d} rac{m}{p</em>1}$

  • $x<em>2^* = rac{d}{c+d} rac{m}{p</em>2}$

• Suggested Reading: Further inquiry into constrained optimization
  techniques.

Page 24: Cob-Douglas Utility Functions

• Reason for Use:

1. Convexity - Averaging is preferred.

2. Monotonicity - More is better.

3. Produce stable demand proportions across income levels.

Page 25: Part 3 - Comparative Statics

• Purpose: Analyze impacts from price or income changes on optimal consumption bundles.

• Definition: Compare original optimal choices to new ones after economic changes.

Page 26: Demand Function Structure

• Implication of Variables:

  • Demand can shift according to income, and prices need to be controlled for ceteris paribus conditions.

Page 27: Changes in Own Price

• Analysis Procedure: Determine changes in quantity demanded based on price variation of a particular good while controlling for other prices and income.

Page 28: Effects of Price Reduction

• Example Scenario: Price decline leads to either increased demand for substitutes or reduced necessity for others, showcasing Giffen goods behavior.

Page 29: Individual Demand Modeling

• Transitioning Variables: Replace item examples with variables $x1$ and $x2$ to generalize consumer demand for other goods.

Page 30: Price Expansion Path

• Graphical Interpretation: Moving along the price pathway illustrates changing consumption bundles based on price variations.

Page 31: Demand Curve Examples: Perfect Substitutes

• Advice on Representation: Graph demand curves by fixing a price of $p2$ and plotting variability of $x1$.

Page 32: Demand Curve Examples: Perfect Complements

• Behavior Representation: Regardless of price changes, goods demanded in fixed proportion lead to horizontal lines in graphs.

Page 33: Income Adjustments

• As income fluctuates, consumption of at least one item is expected to shift, guided by non-satiation properties.

Page 34: Impacts of Income Change

• Every adjustment in the budget constraint (new budget line impacts) leads to variations in consumption reflecting extra spending potential.

Page 35: Income Expansion Path

• Graphical Storytelling: Highlights the optimal bundle shifts as incomes increase for both goods.

Page 36: Non-normal goods

• The income availability illustrates cases where goods are inferior beyond a threshold where consumption decreases.

Page 37: Engel Curves Definition

• Purpose: Relate income fluctuations to consumption patterns, depicting relationships graphically.

Page 38: Price Relationships

• Discuss relationship dynamics of substitute goods (increase demand with price rise in alternatives) versus complements (decrease demand when alternatives increase in price).

Page 39: Part 4 - Elasticities Overview

• Elasticities Defined: Income elasticity measures the responsiveness of demand as income shifts.

Page 40: Income Elasticity Summary

• Description and implications of income elasticities determine good classifications (normal vs inferior goods).

Page 41: Engel’s Law Discussion

• Importance of Income Elasticities: Contextualize expenditures over time and the necessity for insightful food policies addressing poverty.

Page 42: Price Elasticity Definition

• Key measure of demand sensitivity to price changes, significant for business and taxation strategies.

Page 43: Price Sensitivity Analysis

• Case study reflecting differences in price responsiveness across platforms showing strategic implications for businesses.

Page 44: Cross-Price Elasticities Explained

• Illustrative of how consumer demand reacts to whole the price changes of related goods, highlighting substitutability and complementary attributes.

Page 45: From Individual to Market Demand

• Observing aggregate demand curve construction from the sum of individual consumer preferences under unified pricing.

Page 46: Demand Curve Interpretations

• Graph representations when assessing the effects of price and income shifts on overall consumer behavior.

Page 47: Case Study on Food Stamps vs. Cash Grants

• Graph Exchange Exercises:

1. Graph budget constraints under different allowances.

2. Analyze preference implications of cash versus conditional food allowances demonstrating economic preference theories.