For more information on these topics, see Allen, Doherty, Weigelt, and Mansfield Chapter 15: Principal-Agent Issues and Managerial Compensation.
Moral hazard occurs when one party (the agent) takes increased risks or behaves differently because another party (the principal) bears the costs of those risks. This economic concept is particularly relevant in insurance, financial markets, and principal-agent relationships. The key characteristic of moral hazard is that it arises after a transaction or agreement has been made, where one party’s behavior can change in ways that disadvantage the other party.
Core Elements of Moral Hazard:
- Information Asymmetry: One party has more information about their actions than the other party
- Misaligned Incentives: The interests of the principal and agent diverge
- Risk Transfer: One party bears the risk while another party controls the risk level
- Monitoring Difficulties: The principal cannot easily observe or control the agent’s behavior
Classwork 27
1) Insurance
Consider a homeowner deciding whether to install fire prevention measures. Suppose their house has a value of $200,000, prevention measures cost $2,000, the probability of having a fire without prevention is 5%, and the probability of having a fire with prevention is 1%.
Calculate the expected losses to the homeowner with and without the fire prevention. The fire prevention is expensive: is it worth it to the homeowner to install it?
Given that the homeowner installs fire prevention, the probability they lose their house is 1%. What is the actuarially fair price for an insurance policy?
If the homeowner buys the insurance policy, will they still want to install the $2,000 fire prevention? Explain why or why not.
Given your answer to part c, does the insurance company break even on average if they set their price to the actuarially fair value from part b?
2) When Shareholders Gamble with Borrowed Money
Let’s explore how debt financing can create perverse incentives in pharmaceutical development. We’ll follow a drug company making crucial investment decisions while balancing shareholder interests and debt obligations.
Our pharmaceutical company starts with an existing product line that carries some uncertainty. The company will earn either 100 or 200 with equal probability, giving it an expected value of 150. The company has borrowed 100, an amount it can safely repay even in the worst-case scenario.
Explain why the expected value of the equity of the firm to the shareholders is 50.
The company now faces a choice between developing two different hypertension drugs. Formula A is moderately effective and carries low risk. It would generate guaranteed earnings of 220, requiring an investment of 200 (to be borrowed). This gives a net gain of 20.
Formula B, on the other hand, is highly effective but riskier. It requires the same 200 investment but would generate either 20 or 310 with equal probability. Calculate the expected net value of the Formula B option. Which project earns the firm a higher expected return?
If the firm chooses Formula A, the firm has either 100 or 200 from existing operations plus an additional 220 from the project. This gives a total value of either 320 or 420 (and an expected value of ___). The bondholders are paid back the debt of 300, leaving an expected value of ___ for the shareholders.
If the firm chooses Formula B, the firm has either 100 or 200 of value from existing operations, plus either 20 or 310 from Formula B. This gives 4 equally possible scenarios for the firm: making 100 + 20 = 120, 100 + 310 = 410, ___, or ___. In how many of these scenarios does the firm go bankrupt (their debt of 300 exceeds their value)?
Continuing from part d: If the firm goes bankrupt, they don’t pay the bondholders the full amount they borrowed. So in any of the four scenarios where the firm goes bankrupt, the shareholders end up with 0. Otherwise, the shareholders end up with the firm value minus the debt of 300. Show that under Formula B, the shareholders have an expected net value of 80.
This creates a fascinating dilemma: Shareholders prefer Formula B ($80 expected value) over Formula A ($70 expected value), even though Formula B has worse overall expected returns, risks bankruptcy, and puts bondholders at risk. This preference emerges because debt creates an asymmetric payoff structure: shareholders capture all the upside while bondholders bear the downside risk.
This scenario illustrates why bondholders often restrict how much firms can borrow, effectively forcing them to use internal funding for risky projects. When firms rely heavily on debt, shareholders tend to favor unusually risky investments because they can walk away from losses while keeping all the gains.