6.3 Principal/Agent Problem – MBA Managerial Economics

When Does the Problem Arise?

The conflict emerges when:

Interests diverge – The agent’s personal goals conflict with the principal’s objectives.
Information asymmetry exists – The agent has more knowledge about their actions than the principal can observe.

Examples of Alignment vs. Conflict:

Aligned Interests: On a sinking ship, the captain and crew share the same goal—survival. The captain’s decisions naturally align with the crew’s best interests.
Conflicting Interests:
- Corporate Setting: Shareholders (principals) want to maximize profits, while managers (agents) may prioritize job security, personal perks, or career advancement.
- Military Context: A general (agent) may focus on winning battles, while soldiers (principals) prioritize survival.
- Politics: Elected officials (agents) might serve special interests rather than their constituents (principals).

Why Is Monitoring Difficult?

Principals often cannot fully observe or measure an agent’s effort or decisions. For example:

A business owner cannot easily track a manager’s true work ethic.
Shareholders may not know whether executives are taking excessive risks or avoiding necessary ones.

Common Conflicts in Business

Managers may act in ways that harm shareholder value, such as:

Shirking effort – Doing the minimum to keep their job.
Avoiding risk – Choosing safe, low-reward projects to protect job security.
Prioritizing reputation – Avoiding bold moves that could fail and damage their career.
Building personal brands – Focusing on short-term visibility over long-term growth.
Maximizing perks – Enjoying lavish benefits at the company’s expense.

A manager might reject a high-risk, high-reward project to avoid potential failure—even if shareholders, who hold diversified investments, would prefer the gamble. This illustrates how misaligned incentives can lead to suboptimal outcomes.

Example: The Basic Trade-off

Consider a simple case where:

Let $e$ refer to the manager’s level of effort
Revenue depends on the manager’s effort: $R(e) = 100e^{0.5}$
The manager has disutility of effort: $u(e) = 10e$
Manager has a fixed salary $S = 50$

The manager’s net benefit is their salary minus their disutility of effort: $B(e) = S - u(e) = 50 - 10e$.

Notice that $B$ is maximized when the manager chooses $e = 0$, because any effort reduces their net benefit. But this leads to $R(0) = 0$, which is not optimal for the shareholders.

To address this misalignment, company owners might use incentive-compatible compensation schemes that link the manager’s pay to observable outcomes.

1) Profit Sharing

Let’s modify the previous example by adding profit sharing and costs:

Revenue $R(e) = 100e^{0.5}$
Total costs $TC = 20$
Profit $\pi(e) = R(e) - TC = 100e^{0.5} - 20$
Manager gets 10% of profits
Manager’s total compensation: $S(e) = 0.10 \pi(e)$
Manager’s disutility of effort $u(e) = 10e$
Manager’s net benefit: $B(e) = 0.10 \pi(e) - 10e = 0.10 (100 e^{0.5} - 20) - 10e$

The manager chooses $e$ to maximize $B(e)$. Find the manager’s optimal level of effort $e$ by taking the derivative of their net benefit and setting it equal to 0.
Show that the manager will work harder if they earn a larger portion of firm profits.
Show that the manager will work less hard if their disutility of effort is higher.

2) Uncertainty

Another issue in managerial compensation is that if:

The firm’s profits are uncertain,
The manager is risk-averse,
And the stockholders have a diversified portfolio and are therefore risk-neutral,

Then the stockholders are the party that can bear the risk cheaply, not the manager. Let’s see this in an example:

Suppose the firm profits are $400 with probability 0.5 and $900 with probability 0.5.
The manager’s utility is $U = \sqrt{\text{Income}}$ (they are risk averse)
The firm must offer the manager a compensation package with an expected utility of 10, or the manager will work at another company
The shareholders are risk-neutral with a utility function of $U = \text{Income}$.

Suppose the manager gets a flat salary of $100. Calculate their expected utility, and calculate the utility of the shareholders, who now get $300 w.p. 0.5 and $800 w.p. 0.5.
Now suppose the manager gets a salary of some proportion of the firm profits $\alpha \pi$. Find the $\alpha$ that would give the manager an expected utility of 10, and find the shareholder’s utility for the amount left over.
The manager gets an expected utility of 10 for the compensation plan in part A and for the compensation plan in part B, so the manager is indifferent between both these plans. But the shareholders are not: which compensation plan would the shareholders prefer? Who bears risk more cheaply: the manager or the shareholders? How does this result conflict with the result from the previous question, where we found that the manager should be given a proportion of profits to induce them to expend effort?

3) Review Questions

What is the fundamental cause of the principal-agent problem?
Why would a manager’s compensation be tied to profits of the firm?
Why would at least part of a manager’s compensation not be tied to the profits of the firm?