Decision Under Uncertainty Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A city decides whether to build a flood barrier (cost \10M). Flood probability in 50 years: 0.30; flood damage if no barrier: \50M; damage with barrier: \$5M. Calculate expected costs for building vs. not building.

Solution

  1. 1
    Cost of building barrier: certain \10M+expectedflooddamage=10M + expected flood damage = 10M + 0.30 \times 5M = 10 + 1.5 = \11.5M11.5M
  2. 2
    Cost of not building: expected flood damage = 0.30 \times 50M + 0.70 \times 0 = \15M$
  3. 3
    Build barrier: \11.5M expected cost; Don't build: \15M expected cost
  4. 4
    Decision: build the barrier (saves \$3.5M in expected costs)

Answer

Build barrier (EV cost \11.5M) vs. don't build (EV cost \15M). Build saves \$3.5M in expected costs.
Cost-benefit analysis under uncertainty uses expected value to compare investment decisions. Even a large upfront cost can be justified if it reduces expected future losses sufficiently. This framework is used for infrastructure, insurance, and policy decisions.

About Decision Under Uncertainty

Decision under uncertainty involves choosing between options whose outcomes are not known for certain, typically by comparing expected values or risk profiles.

Learn more about Decision Under Uncertainty →

More Decision Under Uncertainty Examples

Example 1 medium

An umbrella decision: if you bring an umbrella, you carry it all day (cost: mild inconvenience, [for

Example 2 hard

A startup has three investment options: A (safe: gain [formula]80K, 30% chance [formula]200K, 70% ch

Example 3 easy

You can either (A) study for certain +10 points on the final, or (B) not study: 50% chance +20 point

← All Decision Under Uncertainty Examples Decision Under Uncertainty Concept