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M13.L02 — Preferences and Indifference Curves

Module: Module 13 — Budget Constraints, Preferences, and Utility Lesson: L02 of 05 Duration: ~30 minutes Level: Intermediate Provenance: Principles of Microeconomics (Curtis and Irvine) | University of Utah Intermediate Microeconomics

Learning Objective

Construct indifference curves from preference relations and calculate marginal rates of substitution.

Preference Relations

For any two bundles A and B:

  • A ≿ B: "A is weakly preferred to B"
  • A ≻ B: "A is strictly preferred to B"
  • A ∼ B: "Indifferent between A and B"

An indifference curve shows all bundles yielding equal satisfaction.

Properties: 1. Downward sloping (more is better) 2. Cannot cross (transitivity) 3. Higher curves = more preferred 4. Diminishing MRS (convex to origin)

Marginal Rate of Substitution (MRS): MRS = -dx₂/dx₁ along IC

Worked Example

Australian Housing Preferences

Consider preferences between housing size (x₁) and commute time (x₂):

  1. Given U = x₁^(0.6)x₂^(0.4)
  2. MRS = -MU₁/MU₂ = -(0.6x₂)/(0.4x₁)
  3. At bundle (100m², 30min): MRS = -(0.630)/(0.4100) = -0.45 → Willing to sacrifice 0.45min commute per extra m²

Common Misconception

"Indifference curves show actual consumption choices"

Correction: They represent potential tradeoffs - actual choices depend on budget constraints.

Key Takeaways

  • Indifference curves map equally preferred bundles
  • MRS measures willingness to substitute between goods
  • Well-behaved preferences are complete, transitive, monotonic, and convex
  • Diminishing MRS reflects decreasing willingness to substitute

Practice

  1. Sketch indifference curves for perfect substitutes
  2. Calculate MRS for U=x₁ + 2x₂ at (4,3)
  3. Explain why crossing indifference curves violate transitivity

Further Resources

Provenance: Principles of Microeconomics (Curtis and Irvine) | University of Utah Intermediate Microeconomics