Economics
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The government is considering a public infrastructure project to build a new highway that connects two major cities. The project has an estimated cost of $500 million and is expected to generate economic benefits of $100 million per year for the next 10 years. The social discount rate is 5%, and there are externalities, including environmental damage valued at $10 million per year and traffic congestion savings valued at $5 million per year.
- Perform a cost-benefit analysis of the project by calculating the present value (PV) of the benefits and costs.
- Calculate the net present value (NPV) of the project and determine if it should be undertaken.
- Perform a sensitivity analysis by changing the discount rate to 3% and 7% and evaluating how it impacts the NPV.
- Include the environmental damage and traffic congestion savings in the analysis and determine how they affect the decision.
- Discuss the potential limitations of using cost-benefit analysis in this case.
Image Requirement: Provide a bar chart or line graph comparing the present value of benefits and costs over the 10 years for different discount rates (5%, 3%, 7%).
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Cost-Benefit Analysis of a New Highway Project
Project Details:
- Initial Cost: $500 million
- Annual Economic Benefits: $100 million for 10 years
- Social Discount Rate: 5%
- Environmental Damage: $10 million per year
- Traffic Congestion Savings: $5 million per year
Present Value Calculations
Formula for Present Value (PV):
PV = Future Value / (1 + Discount Rate)^n
where:
- PV = Present Value
- FV = Future Value
- n = Number of periods
Calculating PV of Benefits:
- Annual benefits = $100 million - $10 million (environmental damage) + $5 million (traffic congestion savings) = $95 million
- PV of annual benefits for 10 years:
- Year 1: $95 million / (1 + 0.05)^1 = $90.48 million
- Year 2: $95 million / (1 + 0.05)^2 = $86.18 million
- ...
- Year 10: $95 million / (1 + 0.05)^10 = $58.68 million
- Total PV of benefits = Sum of PV for each year
Calculating PV of Costs:
- PV of initial cost = $500 million
Net Present Value (NPV) Calculation
NPV = Total PV of Benefits - Total PV of Costs
Sensitivity Analysis
- Discount Rate of 3%: Recalculate PV of benefits and costs using a 3% discount rate.
- Discount Rate of 7%: Recalculate PV of benefits and costs using a 7% discount rate.
Limitations of Cost-Benefit Analysis
- Uncertainty: Future benefits and costs can be difficult to predict accurately.
- Value Judgment: Determining the monetary value of non-market benefits (e.g., environmental impacts) can be subjective.
- Distributional Effects: Cost-benefit analysis may not capture the distributional effects of a project, such as who benefits and who bears the costs.
