Question 1

Suppose a project provides the following benefits and costs: In period 0, benefits are $$50 and costs are 0$$; in periods 1 and 2, benefits are $$0 and costs are 50 $$each; in period 3, benefits are $$100 and costs are 25. $$Using a 5% discount rate, what is the net present value (NPV) of the project? Should you undertake the project from a benefit-cost perspective?

Accepted Answer

The NPV is $13.13; you should undertake the project.

Question 2

Rice is grown in California on land that would otherwise provide environmental benefits as wetland habitat. The demand for rice is perfectly elastic at $$40, and the (inverse) supply curve is P = 20 + Q$. Each unit of rice eliminates 10 in $$environmental benefits. What is the socially optimal quantity of rice to produce?

Accepted Answer

$$Q^* = 10$$

Question 3

Given the same scenario as above, what per-unit tax on rice production would yield the optimal (efficient) quantity of rice produced?

Accepted Answer

$$10$$

Question 4

Consider a utility of wealth function $$U(W) = W$$^{0.5}$$. An agent faces a lottery that pays 9 $$with$$ $$\frac{9}{16}$$ probability and 25 $$with$$ $$\frac{7}{16}$$ probability. What is the expected wealth from this lottery?

Accepted Answer

$$E[W] = 16.25$$

Question 5

Using the same lottery as above, what is the expected utility $$E[U(W)]$$?

Accepted Answer

$$E[U(W)] = 3.98$$

Question 6

What is the certainty equivalent (CE) of the lottery described above, given $$U(W) = W$$^{0.5}$$ and E$$[U(W)] = 3.98$$?

Accepted Answer

$$CE = 15.84$$

Question 7

Based on the utility function $$U(W) = W$$^{0.5}$$ and your calculations above, is the agent risk averse, risk neutral, or risk loving?

Accepted Answer

Risk averse, because the certainty equivalent is less than the expected value.

Question 8

Suppose 90% of a population is healthy (cost of illness $$100), and 10% is unhealthy (cost 1$$,000). The probability of illness is 5% for everyone. If an insurance company offers actuarially fair insurance to all, what is the premium charged?

Accepted Answer

$$\145$

Question 9

Given the premium calculated above, would healthy, risk-neutral individuals want to buy this insurance?

Accepted Answer

No, because the premium is higher than their expected cost.

Question 10

If only unhealthy individuals buy insurance at the actuarially fair premium calculated above, what problem does this illustrate?

Accepted Answer

Adverse selection

Question 11

A Principal hires a risk-neutral Agent who can provide effort from 0 to 10. Revenues are $$100 per effort, and costs are 40 $$per effort. What is the efficient level of effort?

Accepted Answer

10, because marginal revenue equals marginal cost at effort level 10

Question 12

Suppose the Principal offers the Agent a contract with a fixed payment of $$200 and a 1/3 share of revenue. If the Agent's reservation utility is 100$$, what is the Agent's optimal effort level?

Accepted Answer

5

Question 13

In the Principal-Agent scenario above, does the Principal gain or lose from entering into the contract described?

Accepted Answer

The Principal loses, because the Agent's effort is less than efficient.

Question 14

In a 'Pay for Performance' system for teachers, what Principal-Agent problem is this policy attempting to address?

Accepted Answer

Moral hazard, because teachers may not exert effort if pay is not linked to performance.

Question 15

If teachers are risk averse and pay for performance is implemented with the same average pay as before, what is a likely outcome?

Accepted Answer

Teachers will require higher average pay to compensate for increased risk.

Question 16

Assume it takes the same effort to teach a large or small class. Under a pay for performance policy, would teachers prefer larger or smaller classes?

Accepted Answer

Smaller classes, because there is less variation in average test scores.

Question 17

Which of the following best describes the adverse selection problem addressed by the Affordable Care Act?

Accepted Answer

Insurers cannot distinguish between healthy and unhealthy individuals, leading to higher premiums and fewer healthy people buying insurance.

Question 18

What is a key moral hazard problem in the mortgage crisis, as discussed in the study materials?

Accepted Answer

Lenders have little incentive to ensure borrowers can repay loans because they sell the loans to investors.

Microeconomics Final Exam Study Guidance

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