1.
2 Ordinal Utility Theory and Preferences
INTRODUCTION
❖ Ordinal Utility Theory explores how consumers rank their preferences for different goods and services
without assigning specific numerical values to satisfaction levels. Unlike cardinal utility, which measures
utility in absolute numbers, ordinal utility focuses on the order or rank of preferences, providing a more
realistic and practical approach to understanding consumer behavior.
KEY HIGHLIGHT
❖ Indifference Curve Properties:
• Slope: Always negative due to trade-offs between goods.
• Convexity: Reflects diminishing MRS, indicating imperfect substitutability.
• Higher Preference: Higher curves offer more utility.
❖ MRS Calculation:
𝑴𝑼𝑿
• Formula: 𝑴𝑹𝑺𝑿,𝒀 =
𝑴𝑼𝒀
• Diminishing MRS: As more of one good is consumed, less of the other is needed to maintain
satisfaction.
Ordinal Utility Approach
❖ Definition: Ordinal utility measures satisfaction in terms of preference rankings rather than exact
numbers, allowing consumers to express preferences as "more preferred," "less preferred," or "equally
preferred."
❖ Consumer Preferences:
• Preferences are expressed as:
▪ X > Y: X is preferred over Y.
▪ Y > X: Y is preferred over X.
▪ X ∼ Y: Indifference between X and Y.
• Rationality Assumption: Consumers aim to maximize
satisfaction given income and price constraints, making
rational choices based on preference rankings.
Indifference Curve, Set, and Map
❖ Indifference Curve (IC):
• Definition: An indifference curve represents all combinations of two goods that provide the
same level of satisfaction to the consumer. The consumer is indifferent among these
combinations.
• Graphical Representation: Indifference curves are typically convex and downward-sloping,
indicating diminishing marginal rates of substitution.
𝜟𝒀
𝑴𝑹𝑺𝑿,𝒀 =
𝜟𝑿
❖ Indifference Set (Schedule):
• Description: A table listing combinations of goods that yield the same utility. It helps illustrate
how consumers tradeoff between goods.
❖ Indifference Map:
• Definition: A collection of indifference curves representing different utility levels. Higher curves
indicate higher satisfaction levels.
1.2 Ordinal Utility Theory and Preferences
Properties of Indifference Curves
1. Negative Slope: Reflects trade-offs between goods. To increase one
good's quantity, the other must decrease to maintain satisfaction.
2. Non-Intersection: Indifference curves cannot intersect, as this would
imply inconsistent preference rankings.
3. Higher Curves Preferred: Curves farther from the origin represent
higher utility levels and are preferred.
4. Convexity: Indicates diminishing marginal rates of substitution;
consumers are willing to give up fewer units of one good for
additional units of another as they consume more.
Marginal Rate of Substitution (MRS)
• Definition: MRS is the rate at which a consumer can substitute one good for another while maintaining
the same satisfaction level.
𝑴𝑼𝑿
𝑴𝑹𝑺𝑿,𝒀 = −
𝑴𝑼𝒀
• Interpretation: A declining MRS indicates that as more of one good is consumed, consumers are less
willing to give up units of another good.
Special Types of Indifference Curves
• Perfect Substitutes:
• Description: Goods that can be substituted at a constant rate. Indifference curves are straight
lines with constant slopes.
• Utility Function: 𝑼(𝑿, 𝒀) = 𝒂𝑿 + 𝒃𝒀
• Perfect Complements:
• Description: Goods consumed together in fixed proportions. Indifference curves are L-shaped.
• Utility Function: 𝑼(𝑿, 𝒀) = Min(𝒂𝑿, 𝒃𝒀)
Summary
Ordinal Utility Theory offers a powerful lens to understand consumer preferences by focusing on
relative rankings rather than precise measurements. This approach uses tools like indifference
curves and the marginal rate of substitution to analyze consumer choices and behavior
effectively. Whether dealing with perfect substitutes or complements, this theory provides
valuable insights into how consumers allocate their resources to maximize satisfaction.
Ever wonder why some things just go perfectly together, like peanut butter and
jelly? That's the magic of perfect complements—two goods that are meant to be
consumed in perfect harmony, like a duet of deliciousness!
