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CBA

Cost-Benefit
Analysis

Master the economic framework for rational decision-making by comparing marginal costs and marginal benefits.

AP Microeconomics

What is Cost-Benefit Analysis?

Cost-benefit analysis is a systematic process for comparing the total expected costs against the total expected benefits of one or more actions. Economists use it to determine whether a decision is worth pursuing and to choose among alternatives.

Key Terms to Know

Marginal Benefit
The additional benefit gained from consuming or producing one more unit: \( MB \)
Marginal Cost
The additional cost incurred from consuming or producing one more unit: \( MC \)
Opportunity Cost
The value of the next best alternative foregone when making a choice

Why CBA Matters in Economics

Every economic decision, from an individual buying coffee to a government building a highway, involves trade-offs. Cost-benefit analysis provides a framework for rational choice that lies at the heart of microeconomic theory.

Individuals
Should I work an extra hour or enjoy leisure time?
Firms
Should we hire another worker or invest in automation?
Government
Should we fund public transit or expand highways?

The Optimal Decision Rule

Quantity $/Unit Q* MB MC MB = MC Net Benefit

Calculating Net Benefit

The net benefit of an action is the difference between total benefits and total costs. A positive net benefit means the action is economically efficient.

Pursue if:
\( \text{Net Benefit} > 0 \), i.e. \( TB > TC \)
Avoid if:
\( \text{Net Benefit} < 0 \), i.e. \( TC > TB \)

Marginal vs. Total Analysis

Marginal Analysis Total Analysis
Focus One additional unit All units combined
Question "Should I do one more?" "Should I do this at all?"
Formula \( MB \) vs. \( MC \) \( TB \) vs. \( TC \)
Decision Optimal quantity: \( MB = MC \) Go/no-go: \( TB > TC \)?
AP Exam Use Most common on AP Micro Used for project evaluation

How to Apply Cost-Benefit Analysis

1
Identify all costs. Include explicit costs (monetary) and implicit costs (opportunity costs, time, effort).
2
Identify all benefits. Include direct benefits and any positive externalities or spillover effects.
3
Quantify in comparable units. Convert all costs and benefits to dollar values where possible.
4
Compare at the margin. Check if \( MB \ge MC \) for each additional unit or action.
5
Decide: Continue the activity up to the point where \( MB \) \( = \) \( MC \), then stop.

Example 1: Study Hours

A student considers how many hours to study for an AP exam. Each additional hour has a marginal benefit (higher score) and a marginal cost (lost leisure).

Hours of Study Value ($) 1 2 3 4 5 6 10 20 30 40 50 MB MC

Example 2: Hiring Workers

A bakery considers hiring additional workers. The marginal revenue product (\( MRP \)) represents the marginal benefit, while the wage represents the marginal cost.

Worker \( MRP \) (MB) Wage (MC) Hire?
1st $120 $60 ✓ Yes
2nd $90 $60 ✓ Yes
3rd $60 $60 = Indifferent
4th $40 $60 ✕ No

Example 3: Public Project Evaluation

A city evaluates whether to build a new park. All costs and benefits are estimated over 10 years.

Costs
Construction: \( \$2M \)
Annual maintenance: \( \$50{,}000 \times 10 = \$500K \)
Total: \( \$2.5M \)
Benefits
Property value increase: \( \$1.8M \)
Health savings: \( \$600K \)
Tourism revenue: \( \$400K \)
Total: \( \$2.8M \)

Beware of Sunk Costs

A sunk cost is a cost that has already been incurred and cannot be recovered, regardless of future actions. Rational decision-makers should ignore sunk costs entirely.

Sunk Costs Already paid Cannot recover ✕ Future Decision Compare only \( MB \) vs. \( MC \) going forward

Externalities and CBA

A complete cost-benefit analysis must account for externalities: costs or benefits that fall on third parties not directly involved in the transaction.

Negative Externality
A factory pollutes a river, harming downstream communities. Social cost > private cost.
Positive Externality
Vaccinations protect the unvaccinated too. Social benefit > private benefit.

Common Mistakes

✕ Counting Sunk Costs
Including money already spent in your decision. Only future costs and benefits matter.
✕ Ignoring Opportunity Cost
Forgetting that choosing one option means giving up the next best alternative.
✕ Confusing Total and Marginal
Using \( TB > TC \) when the question asks about the optimal quantity, which requires \( MB = MC \).

Summary of Key Concepts

Concept Definition Decision Rule
Net Benefit \( TB - TC \) Pursue if \( > 0 \)
Optimal Quantity Where \( MB = MC \) Stop at this point
Opportunity Cost Value of next best option Always include in \( TC \)
Sunk Cost Past, irrecoverable cost Always ignore
Externality Third-party spillover Include in social CBA

Question 1 of 5

A firm should hire an additional worker when:

Question 2 of 5

You spent $200 on a non-refundable vacation package. Upon arrival, you feel ill and staying in bed has a benefit of $150, while attending activities has a benefit of $100. What should a rational person do?

Question 3 of 5

At the optimal level of output, which of the following is true?

Question 4 of 5

A student can earn $15/hour at a part-time job. She chooses to study for 3 hours instead. The opportunity cost of studying is:

Question 5 of 5

A factory produces widgets. The 5th widget has a marginal benefit of $12 and a marginal cost of $18. The 4th widget had \( MB = \$20 \) and \( MC = \$14 \). What is the profit-maximizing output?