Lecture 4 Consumer Choice

Consumer Choice

Overview of Lecture

• Chapter 4: Perloff's Microeconomics - Focuses on consumer choice and behavior

  • Key Topics:

    • Preferences

    • Utility

    • Budget Constraint

    • Constrained Consumer Choice

Statistics on Consumer Behavior

• Statistic: Among Americans under 35, 50% of women and 25% of men have tattoos (Source: Harper’s Index, Harper’s Magazine, August 2014).

Premises of Consumer Behavior

• Individual tastes or preferences determine the pleasure derived from goods/services.

• Consumers face constraints or limits on their choices.

• Consumers aim to maximize well-being derived from consumption while subject to those constraints.

• Microeconomics offers insights into individual consumer decision making, relying on a model of individual behavior based on the following premises:

  • Preferences: Understanding consumer preferences helps in predicting choices.

  • Constraints: Recognizing financial and resource limitations.

  • Maximization: The goal is to achieve the highest possible satisfaction within given limits.

Properties of Consumer Preferences

1. Completeness

• Consumers can rank two bundles of goods, resulting in one of the following:

  • Prefers the first bundle to the second

  • Prefers the second bundle to the first

  • Is indifferent between the two

2. Transitivity

• Preferences are consistent; if:

  • A is preferred to B, and

  • B is preferred to C,

  • Then A is preferred to C.

3. More is Better

• Holding other factors constant, the more of a commodity available, the better.

  • Good: A commodity that is preferred in larger quantities, e.g., fruits.

  • Bad: A commodity that is preferred in smaller quantities, e.g., pollution.

  • Example: Quote by Arnold Schwarzenegger highlights the nature of subjective satisfaction with wealth: “Having more money doesn’t make you happier. I have 50 million dollars but I’m just as happy as when I had 48 million.”

Preference Maps

Indifference Curves

• Indifference Curve: Represents all bundles of goods that are equally desirable to the consumer.

• Indifference Map: A set of indifference curves that visually represent consumer preferences.

• Using properties of consumer choice, preferences can be summarized graphically, creating a preference map.

Example of Indifference Curves with Bundles

Bundles of Pizzas and Burritos (Illustrated Example 1)

• Preferences illustrated indicating

  • Lisa prefers bundle e over area B.

• Graphical representation with axes:

  • Bundles of Burritos (Y-Axis) vs. Pizzas (X-Axis).

  • Preferences illustrated within a given area.

Bundles of Pizzas and Burritos (Illustrated Example 2)

• The second representation provides further information on Lisa’s consumption choices and preferences indicating her preference structure visually with specific quantities of goods.

Properties of Indifference Maps

1. Position Preference: Bundles further from the origin are more preferred.

2. Coverage: Each indifference curve passes through all possible bundles.

3. Non-Crossing: Indifference curves cannot intersect each other.

4. Downward Slope: A curve slopes downward, showing trade-offs between two goods.

Willingness to Substitute Between Goods

• Marginal Rate of Substitution (MRS): The maximum amount of one good a consumer will sacrifice to acquire one more unit of another good. It is expressed mathematically as:

$MRS = - \frac{\Delta B}{\Delta Z}$ where (Z) is on the horizontal axis.

Marginal Rate of Substitution Examples

• Convexity in Indifference Curves: Typical consumer indifference curves are convex to the origin, which indicates a diminishing marginal rate of substitution as one moves along them.

  • As consumption increases, the willingness to substitute diminishes.

Special Cases in Indifference Curves

• Perfect Substitutes: Completely indifferent regarding which to consume.

• Perfect Complements: Goods consumed in fixed proportions.

Application of Indifference Curves

• Food and Clothing: At low quantities, curves appear as right angles, indicating perfect complements, but as quantities increase, the curves flatten, indicative of closer to perfect substitutes, demonstrating change in consumer preference contextually.

Utility Theory

• Utility: A numerical value indicating consumer's preference levels for different bundles of goods.

  • Example: If Bundle x gives Bonnie 10 utils and Bundle y gives 8 utils, then Bonnie prefers x to y.

• Utility Function: Expresses utility in relation to goods:
  $U(Z, B)$

Types of Preferences in Consumer Theory

Ordinal vs Cardinal Preferences

• Ordinal Preferences: Preferences ranked without absolute values (e.g., letter grades).

• Cardinal Preferences: Include absolute measures (e.g., money) that permit comparison of how much more one rank is over another.

Relation of Utility to Indifference Curves

• Utility as an Ordinal Measure: Gives relative rankings without emphasizing absolute differences.

• Indifference Curves: Contain bundles yielding a specific utility level.

Marginal Utility

• Marginal Utility: Extra utility obtained from consuming the last unit of a good.

  • Formula representation:
    $MU_Z = \frac{\Delta U}{\Delta Z}$

Utility and Marginal Utility Example

• Using a utility function, if Lisa consumes more pizza while holding burritos constant, her utility may change, showing quantifiable relationships:

  • If utility rises from 230 to 250 after consuming an additional pizza, then
    $\Delta U = 250 - 230 = 20$

  • Hence, marginal utility from one more pizza is 20.

Relationship Between Utility and MRS

• MRS is negatively related to utility derivatives:
  $MRS = - \frac{MU<em>Z}{MU</em>B}$

Budget Constraint Overview

Budget Line

• Budget Line: Represents bundles that can be purchased with a full budget at given prices.

• Opportunity Set: All consumable bundles, including those within or on the budget line.

Budget Constraint Examples

• Budget equation:
  $p<em>B B + p</em>Z Z = Y$

• This shows how expenditure is distributed across two goods according to available income Y, with prices for each good represented by p.

Financial Implications of Budget Constraints

• Formulaic breakdown:
  $B = \frac{Y}{p_B}$ to determine maximum burritos purchasable with current income.

Budget Impact on Consumption: Price Changes

• Price Adjustment: If pizza price doubles, the budget constraint slope reflects this change:

  • Shift from:
    $- \frac{p<em>Z}{p</em>B}$ to a new ratio.

  • Graphically shows bundles lost due to price change.

Changes in Budget Constraint: Income Adjustment

• If income doubles, budget line shifts right but maintains the same slope, indicating that more consumption possibilities are now affordable.

Problem Solving in Consumer Choice

• Comparison of Income Doubling vs. Price Reduction: Budget lines and opportunity sets remain constant in aggregate preference or outcome.

Constrained Consumer Choice

• Given summary of preferences and budget constraints, consumer optimal bundle yields maximum pleasure.

• The optimality condition: At the point of tangency between budget constraint and highest indifference curve where marginal utilities per price equal each other.

Consumer Maximization Example

• Indifference curves tangentially touch budget constraint at point e indicating a balance between the two.

• Slope of indifference curve equals slope of budget line at optimal points, confirming maximum utility achieved at this point.