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M16.L05 — Risk Aversion and Insurance

Module: Module 16 — Applications of Consumer Theory Lesson: L05 of 05 Duration: ~30 minutes Level: Intermediate Provenance: University of Utah Intermediate Microeconomics | Khan Academy Microeconomics

Learning Objective

Measure risk aversion and analyze insurance market equilibrium.

Arrow-Pratt Measure

Absolute risk aversion: ARA(c) = -U''(c)/U'(c)

Examples: 1. Constant ARA: U(c) = -e^{-Îąc} 2. Decreasing ARA: U(c) = ln(c) 3. Zero ARA: U(c) = c (risk neutral)

Australian health insurance: - 55% have private hospital cover (APRA 2023) - Medicare provides universal baseline

Worked Example

Australian context: Consider a farmer with: - Initial wealth: $200k - 20% chance of $80k drought loss - Utility: U(c) = √c

  1. Risk premium calculation: EU = 0.2*√120k + 0.8*√200k ≈ 440.91 CE ≈ $194,400 Risk premium = $200k - $194.4k - $16k = $9.6k

  2. Actuarially fair premium = 0.2*$80k = $16k

  3. Maximum willingness to pay ≈ $25.6k

Common Misconception

"Insurance companies always profit from risk aversion"

Actually, adverse selection (e.g., sicker people buying more health insurance) can create market failures. Australia addresses this with: - Lifetime Health Cover loading - Private Health Insurance Rebate

Key Takeaways

  • Concave utility ⇒ risk aversion
  • Insurance demand increases with risk aversion
  • Actuarially fair insurance provides full coverage
  • Australian dual system balances public/private

Practice

  1. Calculate ARA for U(c) = c^0.8
  2. Find the optimal insurance coverage for a $50k loss with 10% probability
  3. Graph how risk aversion affects insurance demand

Further Resources

Provenance: University of Utah Intermediate Microeconomics | Khan Academy Microeconomics