Q1. What is the net present value (NPV) of a project with the following stream of benefits and costs over 4 periods (periods 0 to 3), using a 5% discount rate? Should you undertake the project from a benefit-cost perspective?

Background

Topic: Net Present Value (NPV) and Discounting

This question tests your understanding of how to evaluate a project's worth by discounting future benefits and costs to their present value, and making a decision based on the NPV.

Key Terms and Formulas

• Net Present Value (NPV): The sum of present values of all benefits minus the sum of present values of all costs over the project's lifetime.

• Discount Rate: The rate used to convert future values into present values (here, 5%).

• Present Value Formula:

• Where:

  • = Future Value (benefit or cost in a given period)

  • = Discount rate (as a decimal, so 5% = 0.05)

  • = Number of periods into the future

Step-by-Step Guidance

1. List out the benefits () and costs () for each period (0 to 3) as given in the table.

2. For each period, calculate the present value of benefits and costs using the formula: .

3. Sum the present values of all benefits across the periods to get total present value of benefits.

4. Sum the present values of all costs across the periods to get total present value of costs.

5. Set up the NPV calculation: .

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Q2A. Considering the externality associated with rice production, what is the optimal quantity of rice to produce?

Background

Topic: Externalities and Social Optimum

This question tests your understanding of how negative externalities (here, environmental loss from wetland conversion) affect the socially optimal level of production, and how to incorporate external costs into supply decisions.

Key Terms and Formulas

• Externality: A cost or benefit not reflected in the market price, affecting third parties.

• Marginal Private Cost (MPC): The cost to producers (from the supply curve).

• Marginal External Cost (MEC): The cost imposed on others (here, $10 per unit).

• Marginal Social Cost (MSC):

• Optimal (efficient) quantity: Where Marginal Social Cost equals the market price (demand).

Step-by-Step Guidance

1. Write the private supply (inverse) curve: .

2. Identify the marginal external cost per unit: .

3. Write the marginal social cost curve: .

4. Set the marginal social cost equal to the market price (since demand is perfectly elastic at 30 + Q = 40 $.

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Q2B. What tax on rice production would yield the optimal (efficient) quantity of rice produced?

Background

Topic: Pigovian Taxes

This question tests your understanding of how a tax can correct for a negative externality by aligning private and social costs.

Key Terms and Formulas

• Pigovian Tax: A tax equal to the marginal external cost, imposed to internalize the externality.

• Marginal External Cost (MEC): $10 per unit.

Step-by-Step Guidance

1. Recall that the efficient tax equals the marginal external cost at the optimal quantity.

2. State the value of the marginal external cost per unit (from the problem statement).

3. Explain that imposing this tax shifts the supply curve upward by the amount of the tax, aligning private and social costs.

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Q3A. What is the expected payoff or expected wealth of a lottery that pays \frac{9}{16}\frac{7}{16}$?

Background

Topic: Expected Value in Decision Making Under Uncertainty

This question tests your ability to calculate the expected value (mean outcome) of a lottery with given probabilities and payoffs.

Key Terms and Formulas

• Expected Value (EV): The sum of each possible outcome multiplied by its probability.

• Formula:

• Where are probabilities, are payoffs.

Step-by-Step Guidance

1. Identify the possible outcomes: $9 and $25.

2. Identify the probabilities: for \frac{7}{16}$ for $25.

3. Set up the expected value formula: .

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Q3B. What is the utility of expected wealth for this lottery, ?

Background

Topic: Utility Functions and Expected Utility Theory

This question tests your understanding of how to apply a utility function to the expected value of wealth.

Key Terms and Formulas

• Utility Function: (specific form given in the problem).

• Expected Wealth: (from part A).

• Utility of Expected Wealth:

Step-by-Step Guidance

1. Use the expected wealth calculated in part A.

2. Plug this value into the utility function: .

3. Write out the expression for using the given utility function and the expected wealth value.

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Q3C. What is the expected utility of this lottery, ?

Background

Topic: Expected Utility Theory

This question tests your ability to compute the expected utility by applying the utility function to each outcome and weighting by probability.

Key Terms and Formulas

• Expected Utility:

• Where are probabilities, are payoffs.

Step-by-Step Guidance

1. Apply the utility function to each possible outcome: and .

2. Multiply each utility by its respective probability: and .

3. Add these two terms to set up the expected utility: .

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Q3D. What is the certainty equivalent associated with this lottery?

Background

Topic: Certainty Equivalent and Risk Preferences

This question tests your understanding of the certainty equivalent, which is the guaranteed amount of wealth that gives the same utility as the expected utility of the lottery.

Key Terms and Formulas

• Certainty Equivalent (CE): The amount such that .

• Utility Function: as given.

Step-by-Step Guidance

1. Set up the equation: (using your result from part C).

2. Write the utility function with as the argument.

3. Set this equal to the expected utility expression and prepare to solve for .

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Q3E. Is the agent with this utility function risk loving, risk neutral, or risk averse? Why?

Background

Topic: Risk Preferences and Utility Functions

This question tests your ability to interpret risk attitudes based on the relationship between expected utility, utility of expected wealth, and the certainty equivalent.

Key Terms and Formulas

• Risk Averse:

• Risk Neutral:

• Risk Loving:

Step-by-Step Guidance

1. Compare your results from parts B and C: and .

2. Determine which is larger and use the definitions above to classify the agent's risk preference.

3. Explain your reasoning based on the comparison.

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Q4A. If all people in the population buy insurance, what would be the actuarially fair price or premium?

Background

Topic: Insurance, Expected Value, and Adverse Selection

This question tests your ability to calculate the fair insurance premium based on expected costs, considering different risk types in the population.

Key Terms and Formulas

• Actuarially Fair Premium: The expected cost to the insurer per person.

• Expected Cost: , weighted by probability of illness and population shares.

Step-by-Step Guidance

1. Calculate the probability-weighted expected cost for a healthy person: .

2. Calculate the probability-weighted expected cost for an unhealthy person: .

3. Weight these by the population shares: 90% healthy, 10% unhealthy.

4. Add the two weighted expected costs to get the overall expected cost per person (the fair premium).

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Q4B. Assume that healthy and unhealthy people are risk neutral. Would healthy people want this insurance at the price you computed in part (A)?

Background

Topic: Insurance Demand and Risk Preferences

This question tests your understanding of how risk preferences affect the decision to purchase insurance at a given premium.

Key Terms and Formulas

• Risk Neutral: Indifferent between certain and uncertain outcomes with the same expected value.

• Compare expected cost of illness to the premium for healthy individuals.

Step-by-Step Guidance

1. Calculate the expected cost of illness for a healthy person: .

2. Compare this expected cost to the premium from part A.

3. Explain whether a risk neutral healthy person would prefer to buy insurance or not, based on this comparison.

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Q4C. If the insurance company cannot determine who is unhealthy or healthy, will they offer the insurance at the premium you computed in part (A)?

Background

Topic: Adverse Selection in Insurance Markets

This question tests your understanding of how asymmetric information can affect insurance market outcomes.

Key Terms and Formulas

• Adverse Selection: When one side of the market has more information than the other, leading to market inefficiency.

• Actuarially Fair Premium: Calculated in part A.

Step-by-Step Guidance

1. Use your answer from part B to determine which groups would buy insurance at the fair premium.

2. Explain how the participation of only certain groups (e.g., unhealthy people) would affect the insurer's expected costs.

3. Discuss whether the insurer would be willing to offer insurance at the original premium, given the potential for adverse selection.

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Q5A. What is the efficient level of effort by the Agent? (If the Principal could ensure the agent works at an agreed upon level, what would it be?)

Background

Topic: Principal-Agent Problem and Efficiency

This question tests your ability to determine the efficient allocation of effort by comparing marginal benefits (revenue) and marginal costs (agent's effort cost).

Key Terms and Formulas

• Efficient Level: Where marginal revenue equals marginal cost.

• Marginal Revenue: Additional revenue from one more unit of effort ($100 per effort level).

• Marginal Cost: Additional cost to agent from one more unit of effort ($40 per effort level).

Step-by-Step Guidance

1. For each effort level, calculate total revenue and total cost.

2. Compute marginal revenue and marginal cost for each increase in effort.

3. Identify the highest effort level where marginal revenue is at least as great as marginal cost.

4. Explain why this is the efficient level of effort.

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Q5B. If the Principal offers the Agent $200 as a fixed payment and a 1/3 share of revenue, does the Agent wish to sign the contract? If so, what effort level will they choose?

Background

Topic: Incentives and Contract Design in Principal-Agent Problems

This question tests your understanding of how contract terms affect the agent's incentives and participation.

Key Terms and Formulas

• Agent's Payoff:

• Reservation Utility: Minimum payoff agent requires ($100).

Step-by-Step Guidance

1. For each effort level, calculate the agent's total compensation: .

2. Subtract the cost of effort () to get the agent's net payoff.

3. Compare the net payoff to the reservation utility ($100) to see if the agent would accept the contract.

4. Identify the effort level that maximizes the agent's net payoff, given the contract terms.

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Q5C. Does the Principal gain or lose from entering into this contract?

Background

Topic: Surplus Division in Principal-Agent Contracts

This question tests your ability to evaluate the principal's outcome under the contract, considering the agent's chosen effort and compensation.

Key Terms and Formulas

• Principal's Payoff:

• Revenue:

• Payment to Agent:

Step-by-Step Guidance

1. Use the agent's chosen effort level from part B to calculate total revenue.

2. Calculate the total payment to the agent under the contract.

3. Subtract the payment to the agent from total revenue to find the principal's net payoff.

4. Compare this payoff to the scenario without the contract or with different effort levels to assess gain or loss.

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Q6A. Discuss the nature of the Principal-Agent problem that “Pay for Performance” seeks to solve in education.

Background

Topic: Principal-Agent Problem in Labor Markets

This question tests your understanding of how incentive problems arise when principals (school districts) cannot perfectly monitor agents (teachers), and how pay-for-performance aims to align incentives.

Key Terms and Concepts

• Principal-Agent Problem: When the agent's actions are not fully observable by the principal, leading to potential misalignment of interests.

• Incentive Alignment: Structuring compensation to motivate desired behavior.

Step-by-Step Guidance

1. Define the principal (school district) and agent (teacher) in this context.

2. Explain why the principal cannot perfectly observe or measure the agent's effort or effectiveness.

3. Describe how pay-for-performance attempts to link compensation to measurable outcomes (student learning gains).

4. Discuss potential challenges or limitations of this approach.

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Q6B. If teachers are risk averse, what happens if you institute a pay-for-performance policy with the same average pay as before?

Background

Topic: Risk Aversion and Incentive Contracts

This question tests your understanding of how risk aversion affects agents' responses to variable compensation schemes.

Key Terms and Concepts

• Risk Aversion: Preference for certain outcomes over risky ones with the same expected value.

• Pay Variability: Increased risk in compensation due to performance-based pay.

Step-by-Step Guidance

1. Explain how pay-for-performance increases the variability (risk) of teachers' compensation.

2. Discuss how risk-averse teachers value certainty and may require a risk premium to accept variable pay.

3. Analyze the likely effects on teacher satisfaction, recruitment, or effort if average pay remains unchanged but risk increases.

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Q6C. Under pay-for-performance, would teachers prefer larger or smaller classes (assuming effort is the same for any class size)? Why?

Background

Topic: Incentives and Risk Pooling

This question tests your understanding of how risk is affected by the number of students when pay is tied to average student performance gains.

Key Terms and Concepts

• Law of Large Numbers: Larger sample sizes reduce variability in average outcomes.

• Risk Pooling: Averaging over more students reduces the impact of any one student's performance on pay.

Step-by-Step Guidance

1. Explain how the average performance gain is calculated across students.

2. Discuss how increasing class size reduces the variance of average performance gains (risk to teacher).

3. Conclude whether teachers would prefer larger or smaller classes under these assumptions, and why.

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Q7. What adverse selection problem(s) does Health Care Reform (Affordable Care Act) seek to solve? How?

Background

Topic: Adverse Selection in Health Insurance Markets

This question tests your understanding of how adverse selection leads to market failures in health insurance, and how policy interventions can address these problems.

Key Terms and Concepts

• Adverse Selection: High-risk individuals are more likely to buy insurance, raising costs and potentially driving out low-risk individuals.

• Policy Solutions: Mandates, subsidies, risk adjustment, etc.

Step-by-Step Guidance

1. Define adverse selection and explain how it affects health insurance markets.

2. Describe the specific problems the ACA aims to address (e.g., uninsured healthy people, high premiums).

3. Explain how the ACA's provisions (individual mandate, subsidies, community rating) are designed to mitigate adverse selection.

4. Reference relevant academic papers as requested.

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Q8. What Principal-Agent or Moral Hazard problem(s) are important in the mortgage crisis? What might be a good solution?

Background

Topic: Principal-Agent and Moral Hazard in Financial Markets

This question tests your understanding of how incentive problems contributed to the mortgage crisis, and how policy or market solutions might address them.

Key Terms and Concepts

• Principal-Agent Problem: When agents (e.g., mortgage brokers) do not act in the best interest of principals (e.g., lenders, investors).

• Moral Hazard: When one party takes more risks because another bears the cost.

• Potential Solutions: Better monitoring, incentive alignment, regulation.

Step-by-Step Guidance

1. Identify the principal-agent and/or moral hazard problems present in the mortgage market (e.g., originate-to-distribute model).

2. Explain how these problems contributed to the crisis (e.g., poor loan quality, excessive risk-taking).

3. Discuss possible solutions, referencing relevant academic papers as requested.

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