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M16.L04 ā€” Uncertainty and Expected Utility

Module: Module 16 ā€” Applications of Consumer Theory Lesson: L04 of 05 Duration: ~30 minutes Level: Intermediate Provenance: Intermediate Microeconomics with Excel (Barreto) | MIT OCW 14.01

Learning Objective

Evaluate choices under uncertainty using the expected utility framework.

Expected Utility Theory

Von Neumann-Morgenstern utility function: EU = Ļ€ā‚U(cā‚) + Ļ€ā‚‚U(cā‚‚) Where: - Ļ€ = probabilities of states - U(c) = utility from consumption

Key properties: 1. Risk aversion: U''(c) < 0 (concave) 2. Risk neutrality: U''(c) = 0 (linear) 3. Risk loving: U''(c) > 0 (convex)

Worked Example

Australian context: Consider flood insurance for a $500k home: - 5% chance of total loss - 95% chance no loss - Premium: $30k

  1. Expected value: EV = 0.05*(-500k) + 0.95*(0) = -$25k

  2. Risk premium: For U(c)=āˆšc, EU(no insurance) = 0.050 + 0.95āˆš500k ā‰ˆ 672.67 Certainty equivalent ā‰ˆ $452k Risk premium = $500k - $452k - $25k = $23k

Australians pay ~$12b annually in general insurance premiums (APRA 2023).

Common Misconception

"People always choose the option with highest expected value"

Actually, risk-averse individuals may accept lower EV to reduce uncertainty (e.g., buying insurance).

Key Takeaways

  • Expected utility ā‰  expected monetary value
  • Risk preferences determine insurance demand
  • State-contingent commodities allow hedging
  • Australian insurance markets reflect risk aversion

Practice

  1. Calculate EU for U(c)=ln(c) with 50% chance of \(100/\)200
  2. Find the risk premium for U(c)=c^0.5 and a 10% chance of $1m loss
  3. Graph risk aversion levels for different utility functions

Further Resources

Provenance: Intermediate Microeconomics with Excel (Barreto) | MIT OCW 14.01