Cost-benefit analysis

Explain what cost-benefit analysis is and what public authorities use it for before approving a project. Give an example of a project in your local city or town to which it could be applied.

A city council is considering building a bike lane. Classify these items as costs or benefits of the project: the construction of the bike lane, reduced congestion, annual maintenance, health improvements for cyclists, and lost parking spaces.

Explain the difference between a company's income statement (the revenue it receives minus the expenses it pays) and the cost-benefit analysis of a public project, which also values effects that nobody directly charges or pays for. Give an example of each type of effect.

A project has estimated benefits of $\$90,000$ and costs of $\$60,000$.

1. a) Calculate the net benefit and decide whether the project is advisable according to the cost-benefit criterion.
2. b) What warning would you give before relying entirely on this calculation? Mention at least one.

A town switches all its street lighting to LED: the investment costs $\$50,000$ and saves $\$10,000$ a year on the electricity bill. Calculate the payback period of the investment and explain what that figure means.

A city can only afford one of these projects: a swimming pool (cost of $\$500,000$, estimated benefits of $\$650,000$) or a sports center (cost of $\$400,000$, benefits of $\$560,000$).

1. a) Calculate the net benefit and the benefit-cost ratio of each one.
2. b) Which would you choose and on what criterion? Explain why net benefit and the ratio can recommend different projects.

The school is considering installing solar panels: they cost $\$24,000$ and save $\$4,000$ a year on the electric bill.

1. a) Calculate the payback period of the investment.
2. b) Name two non-monetary benefits that should also be counted in the analysis and explain how you would include them.

The figure shows the initial cost of a sports center's solar installation and the cumulative savings year by year, in thousands of dollars.

1. a) Read from the graph in which year cumulative savings equal the cost.
2. b) Explain what this point means and what happens from then on.

A bike lane costs $\$300,000$, has annual maintenance of $\$10,000$ and benefits (time, health, less congestion) are estimated at $\$60,000$ a year.

1. a) Calculate the net benefit over ten years (without discounting).
2. b) What key assumptions would you review before approving it (actual number of users, valuation of time)? Explain how the decision would change if there were half as many users as expected.

A public library does not charge admission and yet it "produces" a great deal of value. Explain why the cost-benefit analysis of a library must count benefits that are not charged for (reading, study, internet access) and what would happen if we only looked at its revenue.

A property developer requests the rezoning of a coastal wetland to build a hotel complex that would generate a net business profit of $18$ million dollars over $20$ years. The state environmental agency quantifies the ecological services that the wetland currently provides for free:

1. Hydrological regulation: the wetland mitigates flash floods. If it disappears, it will be compulsory to build storm drains with an investment cost of $8$ million dollars and an annual maintenance cost of $\$150,000$.

2. Natural purification: it filters $1.5$ million $\text{m}^3$ of wastewater per year; treating that same water in a conventional wastewater treatment plant would cost $\$0.40$ per $\text{m}^3$.

3. Storm buffering: reports estimate that without the wetland there will be flood damage to the downtown area with an average expected value of $\$500,000$ each year.

1. a) Calculate the total annual shadow price (imputed economic value) of the ecosystem services provided by the wetland and obtain its accumulated value over a $20$-year horizon (without applying discounting).
2. b) With the obtained data, evaluate whether the hotel rezoning is efficient from the point of view of social welfare.
3. c) The developer claims: "Those ecological costs are theoretical; nobody pays bills for the water the wetland cleans, whereas the hotels will generate real GDP." Technically refute this argument drawing on the concepts of market failure and opportunity cost.

To assess a road improvement, the government agency estimates the time drivers will save and assigns it a monetary value per hour.

1. a) Do you think it is reasonable to monetize time? Justify your answer.
2. b) What other effect that is difficult to monetize should be included in the analysis (noise, safety, environment)? Explain how you would address it.

A city council has a maximum budget of $\$800,000$ and must choose between two mutually exclusive projects:

• Project A (Underground parking garage with 100 spaces): construction cost of $\$600,000$ and expected direct revenue from fees of $\$900,000$ (in present value). A municipal report warns that the increase in road traffic toward downtown will cause $\$150,000$ in external congestion and pollution costs, plus $\$50,000$ in maintenance.

• Project B (Library and study center): construction cost of $\$800,000$ and direct revenue from membership cards and workshops of $\$200,000$. An external study values the social benefits (access to educational resources, study support, and reduction of school failure) at $\$800,000$.

1. a) Calculate the benefit-cost ratio ($B/C$) and the net benefit of both projects from the perspective of social cost-benefit analysis (integrating all costs and benefits, not just direct monetary ones).
2. b) The city council member in charge of finance states: "The parking garage is the only reasonable option: it generates a surplus, leaves $\$200,000$ of the budget unspent to pay off debt, and its financial ratio is $1.5$, whereas the library runs a deficit." Technically refute their position by differentiating between financial (private) profitability and social profitability.
3. c) If the city council decided to build the parking garage, design a pricing policy or usage restriction proposal that helps correct the detected negative externality without eliminating revenue.

A feasibility report for building a toll highway with an initial cost of $300$ million dollars and a $20$-year horizon presents the following annual estimates:

• Toll revenue collected from drivers: $25$ million dollars.

• Monetarily valued time savings for users: $10$ million dollars.

• Road maintenance and management: $5$ million dollars.

The report concludes that the annual net social benefit is $30$ million dollars ($25 + 10 - 5$), accumulating $600$ million over $20$ years, thus recommending the project without hesitation.

1. a) Identify and justify the methodological error committed by the report when counting the $25$ million in tolls as a social benefit. Why is the toll in social cost-benefit analysis a mere transfer and not a net gain in welfare for society?
2. b) After opening the road, it is found that the toll price deters $50\ \%$ of potential drivers, who choose to drive along a free state road that passes through three towns. Qualitatively model which unforeseen external costs now appear in the overall social cost-benefit analysis.
3. c) Considering that the marginal cost of one additional vehicle using an uncongested highway is practically zero ($CMg \approx 0$), explain what toll price would maximize economic efficiency and what financial dilemma this would pose for the government.

The city council in plenary session debates whether to transform a centrally located public plot of land valued at $12$ million dollars into a park with mature trees or sell it to a commercial developer who will create $80$ direct jobs. A neighborhood spokesperson states: "A park, lung health, or quietness are priceless; trying to measure them in dollars degrades politics and distorts reality." The City Council Member for Urban Planning replies: "If economists do not try to put a monetary value on those intangible benefits, the tacit value assigned to them in the final decision will be exactly zero dollars."

1. a) Interpret the council member's warning: why can refusing in principle to monetize intangible goods paradoxically lead to decisions that go against environmental and social protection?
2. b) Design a methodological proposal to estimate the value of the park in dollars by applying two different economic valuation methods for non-market goods (such as hedonic pricing in nearby housing, travel costs, or avoided health costs). Explain what each one would measure in this case.
3. c) Suppose that the estimated value of the park's benefits amounts to $14$ million dollars, but $85\ \%$ of that gain is concentrated in the property appreciation of adjoining high-income homes. Reason why a favorable social cost-benefit analysis alone does not guarantee that the decision is equitable or fair.

The U.S. Department of Transportation's highway safety office is assessing resurfacing and signage improvements on a high-accident road section at a total cost of $6$ million dollars. Road engineering models forecast that the intervention will prevent a statistically proven $3$ deaths over the next five years. To evaluate whether the project is a priority through a cost-benefit analysis, the technical team applies the official "Value of a Statistical Life" (VSL) of $1.8$ million dollars per person (obtained from willingness-to-pay surveys for marginal risk reductions).

1. a) Calculate the net social benefit of the project and determine what the formal technical recommendation derived from the cost-benefit analysis would be.
2. b) Upon learning that the work is being rejected based on the technical calculation, a citizens' group protests: "Human life is priceless; setting a monetary figure to decide whether to save people on the road is immoral." Justify why in the real management of public spending it is inevitable to implicitly or explicitly assign a monetary limit to road safety measures, and what would happen to the health and education budgets if we acted under the premise that a life has infinite economic value.
3. c) Based on this case, refute the idea that "cost-benefit analysis is a neutral and objective mathematical technique." Identify two ethical-political value judgments that completely determine the final outcome of this type of study.

Many grandiose projects end up costing twice the budget and receiving half the announced users (the "white elephant syndrome").

1. a) What biases and interests explain why they get approved (promoters' optimism, the political gain of a big project)?
2. b) Propose two improvements to the analysis process that reduce the problem (comparing with similar projects already built, review by independent experts) and explain how they work.