2. Cost Benefit Analysis - FINAL EXAM

What is Cost-Benefit Analysis (CBA)?

Cost-Benefit Analysis is a way to decide if something is worth doing.

• You compare:

  • Benefits (good things)

  • Costs (bad things)

👉 Everything is measured in money (dollars)

The main rule of cost benefit Analysis

You decide based on net benefit:

• Net Benefit (NB) = Benefits − Costs

• If:

  • NB > 0 → Do it

  • NB < 0 → Don’t do it

👉 Another way:

• Choose the action where Benefits > Costs

Example of cost benefit analysis ?

Joan decides whether to smoke based on:

Benefits:

• Taste

• Relaxation

• Diet control

• Better work performance

• Costs:

  • Money (expense)

  • Health problems

  • Time spent

  • Inconvenience (smoking areas)

  • Social disapproval

  👉 She will smoke only if benefits > costs

  👉 If choosing how many cigarettes:

  • She picks the number that gives the highest net benefit

When is CBA used ?

Mostly used for public decisions

Example:

• Should NYC provide free HIV prevention programs?

👉 CBA helps:

• Compare projects

• Decide if something benefits society

Expected value ? - High importance

Used when outcomes are uncertain

👉 Formula:

• Expected value = probability × outcome value

Example of Expected value ? ER example

onathan may visit ER:

• 60% → 1 visit ($50)

• 20% → 2 visits ($100)

• 20% → 3 visits ($150)

Expected Cost:

• = 0.6(50) + 0.2(100) + 0.2(150)

• = $80

👉 This is a weighted average

You don’t know exactly how many times Jonathan will go to the ER.

But you want one number that represents the “average cost.”

What does probability have to be?

“Mutually exclusive” = no overlap

• Events cannot happen at the same time

✔ Example (from your lecture idea):

• 1 ER visit

• 2 ER visits

• 3 ER visits

👉 You can’t have 1 AND 2 visits at the same time, so they are mutually exclusive.

“Collectively exhaustive” = covers everything

You included ALL possible outcomes

Example:

• 1 visit

• 2 visits

• 3 visits

👉 These must represent every possible scenario

Another example that is important HIV?

Step 1: Expected Costs Without drug:

• 0.255 × 98,915 = $25,223

With drug:

• 0.083 × 98,915 = $8,210

---

Step 2: Expected Benefit

• = Cost avoided

• = 25,223 − 8,210

• = $17,013

---

Step 3: Cost of Drug

• = $1,045

---

Step 4: Net Benefit

• = 17,013 − 1,045

• = $15,968 per mother

• Treatment is worth it

• Benefits are much greater than costs

👉 If private → mother benefits
👉 If public (Medicaid) → society benefits

• The drug prevents expensive outcomes (HIV infection in the baby)

• After subtracting the cost of the drug, there is still $15,968 left over in value

• 15,968 dollars was saved by the mother taking the drugs

Public Policy Goal: Goal is to maximize Net Social Benefit (NSB)

NSB = Total Social Benefits − Total Social Costs

Value of Life

CBA sometimes tries to assign a dollar value to life

How much money a person would have earned if they didn’t die early

Method 1 : Human Capital Approach

It means:
How much money society loses if that person dies early.

Value of life = future earnings

• Person dies at 35

• Would work until 65 → 30 years

• Salary = $50K/year

👉 Value:

• 30 × 50K = $1.5 million

What does he amount of Human Capital approach represent and how does it compare to the problem solved

It represents:

• Lost income

• Lost productivity

• Lost contribution to society

✔ In simple terms:

“If this person didn’t die, they would have earned $1.5 million. So society ‘lost’ that amount.”

What is the problem with the human capital approach?

• Says unemployed people = $0 value

• ❌ Says rich people are “worth more”

• ❌ Ignores unfair wages (discrimination)

Method 2: Willingness -To-Pay

👉 Based on how much someone would pay to avoid death

“The willingness-to-pay method estimates the value of life based on how much individuals are willing to pay to reduce their risk of death.”

Willingness- to-pay

“The willingness-to-pay method estimates the value of life based on how much individuals are willing to pay to reduce their risk of death.”

Example:

• A person says:
  👉 “I would pay $1,000 to avoid dying”

• Their risk of dying = 1 in 1,000

Multiply:

• Money willing to pay × inverse of risk

So:

• $1,000 × 1000 = $1,000,000

• It means:

  “Based on this person’s decision, their life is valued at about $1 million”