Lecture 10

Cost–Benefit Analysis

Byeong-Hak Choe

SUNY Geneseo

October 29, 2025

Cost–Benefit Analysis

What Is Cost–Benefit Analysis (CBA)?

CBA evaluates whether the present value of benefits exceeds the present value of costs for a project or policy.

All costs and benefits are expressed in today’s dollars using a discount rate ($r$)
Enables meaningful comparison of outcomes occurring at different times
Helps allocate scarce resources efficiently across competing alternatives

CBA in Government Decision-Making

Governments use CBA to decide:

Which projects should be funded under budget constraints
How to balance economic, health, and environmental goals
Whether policy benefits justify the present value of implementation costs

Example: Regulating Ozone Pollution

The U.S. Environmental Protection Agency (EPA) must decide:
Should the national standard for ground-level ozone be tightened?

Ozone affects:
- Human health (asthma, emphysema)
- Crop and vegetation damage
Stricter standards → higher abatement costs now, health benefits later

Example: Regulating Ozone Pollution

Hypothetical Scenario (Present Value Terms)

Option	PV of Costs (Billion $)	PV of Benefits (Billion $)
Maintain 75 ppb	—	—
Tighten to 70 ppb	16	24

\[ \begin{aligned} PV_{NB} &= PV_B - PV_C\\ &= 24 - 16\\ &= 8 \text{ billion} \end{aligned} \]

\[ PV_{B/C} = \frac{PV_B}{PV_C} = \frac{24}{16} = 1.5 \]

✅ Positive PV net benefits and $PV_{B/C} > 1$ → Economically justified.

Example: Regulating Ozone Pollution

The Real EPA Decision

EPA lowered ozone standard from 75 → 70 ppb
Industry: “Too costly — burdensome for economy”
Environmentalists: “Too weak — thousands of preventable deaths remain”

Example: Regulating Ozone Pollution

EPA’s Present Value Estimates

Standard (ppb)	PV of Costs (Billion $)	PV of Benefits (Billion $)	PV of Net Benefits (Billion $)
70	~5	10–22	+5–17
65	~15	18–35	+3–20
60	~40	25–50	–15–10

Note

Interpretation:
The 70 ppb standard produced positive PV net benefits.
Lower standards (65 or 60 ppb) have higher potential PV benefits, but with more uncertainty.

Steps in Conducting a PV-Based CBA

List all costs and benefits over time
Quantify each stream in monetary terms
Discount each future value to its present value using rate $r$
Sum PVs of costs and benefits:

\[ PV_B = \sum_t \frac{B_t}{(1 + r)^t}, \qquad PV_C = \sum_t \frac{C_t}{(1 + r)^t} \]

Compute PV Net Benefits and PV Benefit–Cost Ratio
Compare across policy alternatives, including a baseline (no action)

🧮 Decision Criteria (Using Present Value)

1️⃣ PV of Net Benefits

\[ PV_{NB} = PV_B - PV_C \]

$PV_{NB}$ (Present Value of Net Benefits) measures total welfare change in today’s dollars.
- Adds up all future benefits ($B_t$) and costs ($C_t$), converted into present value using the discount rate ($r$).
If $PV_{NB} > 0$, benefits exceed costs → policy improves total welfare and is worth undertaking.

2️⃣ PV Benefit–Cost Ratio

\[ PV_{B/C} = \frac{PV_B}{PV_C} \]

Compares the relative size of discounted benefits and costs.
If $PV_{B/C} > 1$, benefits outweigh costs in present-value terms.
Useful for comparing multiple projects when budgets are limited.

Opportunity Cost and Dynamic Efficiency

Even if $PV_{NB} > 0$:

Another policy might yield a higher $PV_{NB}$
Always consider the opportunity cost of choosing one project over another
Economics seeks to maximize $PV_{NB}$ — the condition for dynamic efficiency
- Dynamic efficiency is achieved when the allocation of resources over time maximizes the present value of net benefits to society.

Dynamic efficiency helps decide how much to use today and how much to save or invest for the future (e.g., in renewable energy, conservation, or infrastructure), since resources spent now can’t be used later.

⚖️ Distributional and Ethical Issues

CBA aggregates all PV benefits and costs across society
→ ignores who gains and who bears the costs
Example:
- PV benefits → wealthier households (longer lifespan, better access)
- PV costs → lower-income communities (energy price hikes)
Even with positive $PV_{NB}$, may still be inequitable
- Efficiency alone is not sufficient — a policy can maximize total welfare ($PV_{NB} > 0$), while still being unfair or socially unacceptable.

⚖️ Why Do Equity Concerns Matter?

Efficiency focuses only on the size of the total pie, not on how the pie is divided.
Without considering equity, benefits may concentrate among the wealthy, while costs fall on vulnerable or marginalized groups.
- Because market power, wealth, and access to information often allow higher-income groups to capture more of the benefits and avoid much of the burden.
Ignoring fairness can lead to social resistance, political backlash,
and reduced legitimacy of otherwise efficient policies.
Equity ensures inclusiveness — that economic progress also supports
justice, opportunity, and shared well-being.

Note

✅ Efficiency tells us how to grow the pie; equity tells us how to share it fairly.

💡 How Can We Address Equity Concerns?

Economists can address equity concerns by:

Applying distributional weights — give higher social value to welfare gains for lower-income groups
Reporting disaggregated impacts — show who gains and who loses (by income, region, or demographic)
Designing compensatory measures — use transfers or tax rebates to offset burdens on disadvantaged groups
Embedding ethical judgment — recognize that efficiency alone does not ensure fairness or justice