Topic 1 — Asymmetric Information

Part of: Microeconomics Adverse Selection, Moral Hazard, Signaling Micro 3 — Tiomkin School of Economics, Reichman University Key concepts: Adverse Selection, Moral Hazard, Signaling, Market Failure, Rational Expectations Equilibrium

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1. What is Asymmetric Information?

In standard competitive market models, all agents either have full information or share the same partial information (uncertainty). Asymmetric information arises when different agents hold different private information — this changes strategic behaviour and can lead to market failures.

Key Takeaway

Private information creates incentive problems that competitive markets cannot easily solve. The informed party always has an advantage, and this gap can cause the market to fail.

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2. Adverse Selection

Definition: Adverse selection occurs when privately informed agents select actions based on their information that adversely affect the uninformed side of the market. The competitive equilibrium may not be Pareto efficient as a result.

2.1 The Mechanism: The Adverse Selection Death Spiral

The logic that drives adverse selection follows a self-reinforcing sequence:

1. Buyer cannot distinguish quality, so they offer an average-quality price
2. High-quality sellers receive a price below their reservation value and exit the market
3. Average quality in the remaining pool falls
4. Price falls further in response — triggering more exits
5. This continues until only the lowest quality remains (market collapse / lemons market)

Possible Outcomes:

2.2 Example 1: The Lemons Market (Akerlof)

George Akerlof (Nobel Prize 2001) showed that in a used-car market where sellers know quality but buyers only see the distribution, only the worst cars (lemons) may trade in equilibrium.

Setup:

Step-by-Step Solution:

Test 1 ✗ — Assume all cars (good + bad) are on sale

E[buyer value] = 0.75 × $3,000 + 0.25 × $2,000 = $2,750 Will a good-car seller accept $2,750? $2,750 < $2,800 → NO! Good cars exit.

Test 2 ✓ — Assume only bad cars are on sale

Buyer value = $2,000 | Seller value = $1,800 Will a bad-car seller accept $2,000? $2,000 ≥ $1,800 → YES! Equilibrium found.

Key Takeaway

Equilibrium: Only bad cars (lemons) are sold at a price of $2,000. This is a Market Failure — all cars could be sold under perfect information (each has a positive gain from trade), but only lemons survive under asymmetric information.

2.3 Multiple Equilibria & The 80% Threshold

In the two-type lemons model, we can ask: when is it possible for a good equilibrium (all cars sold) to exist?

Crucially, even when $p \geq 0.8$, the bad equilibrium (lemons only) still co-exists:

Key Takeaway

$p \geq 0.8$ is necessary but not sufficient for the good equilibrium. The bad equilibrium always co-exists. Which one materialises depends entirely on market beliefs.

type: lemons-threshold

Reading the threshold diagram

The blue line is the buyer's expected value as the share of good cars $p$ rises. Good-car sellers only stay if that line clears their reservation price of $2,800 (red dashes) — which happens exactly at $p = 0.8$. To the left of the threshold (red zone) the expected value is too low, good cars exit, and only lemons trade. To the right (green zone) the good equilibrium can exist — but the lemons equilibrium still co-exists, because beliefs are self-fulfilling.

2.4 Rational Expectations Equilibrium (REE) — The Method

For any market with multiple quality types, the standard method to find the REE is:

1. Step 1: Start by testing whether ALL types could be in the market
2. Step 2: Calculate E[buyer value] using the full distribution
3. Step 3: Check if E[buyer value] ≥ each seller's reservation value. If the highest type fails, remove them
4. Step 4: Recalculate E[buyer value] with the remaining types and repeat
5. Step 5: The equilibrium is the largest self-consistent set — the one where E[buyer value] satisfies all remaining sellers

2.5 Example 2: Adverse Selection in the Insurance Market

When insurers cannot distinguish between high-risk and low-risk individuals, the same adverse selection logic applies.

Setup: Two groups with utility $U(M) = \sqrt{M}$:

With full information: Insurer charges Group A a premium of 75 and Group B a premium of 225. Both groups purchase insurance (risk-averse agents prefer fair insurance).

type: risk-aversion

Why risk-averse agents buy insurance

Utility $U(M)=\sqrt{M}$ is concave, so the same swing in income hurts more on the downside than it helps on the upside. The red dashed chord is the expected utility of the risky income (E[U] = 17.5); the curve directly above the same mean income is the utility of guaranteed income (√325 ≈ 18.0). Because the curve sits above the chord, a person is strictly better off paying a fair premium to lock in the certain amount. That gap is exactly what makes insurance valuable — and what adverse selection then erodes.

Case 1 — Insurer cannot distinguish groups: If the insurer offers one price, only Group B (high-risk) will consistently purchase, leading to losses and Market Failure.

Case 2 — Insurer offers a menu of contracts: Full insurance at a premium of 225, or partial insurance (coverage of 24) at a premium of 6. This acts as a screening device — Group A self-selects into partial insurance, Group B into full insurance.

Key Takeaway

The competitive equilibrium with asymmetric information is inefficient — Group A (the healthier individuals) ends up only partially insured even though full insurance would be achievable with perfect information. This is one of the most significant market failures in healthcare.

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3. Moral Hazard

Definition: Moral hazard is a situation in which one party takes on more risk because they do not bear the full consequences of that risk. It occurs after a contract or insurance is in place (post-contractual), unlike Adverse Selection which arises before (pre-contractual).

3.1 Key Examples

Key Takeaway

Moral hazard does not just affect insurance — any situation where risk is transferred creates an incentive to behave less carefully. This is a core challenge in contract design, regulation, and public policy.

3.2 Health Insurance Example

Moral hazard causes overconsumption of healthcare when the insured does not face the full cost of treatment.

• Without insurance: patients consume healthcare only up to its true value
• With insurance: patients consume more than is socially optimal because the marginal private cost is near zero
• The gap between the quantity demanded with and without insurance represents a deadweight welfare loss

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4. Signaling

Definition: Signaling corresponds to a situation where the informed party takes a costly action to credibly communicate their private quality to the uninformed party. For a signal to be effective, it must be cheaper for high-quality agents to send than for low-quality agents.

type: signaling

The single-crossing condition, drawn

The signal (education, warranty length) is cheap for the high type (flat blue line) and expensive for the low type (steep red line). The green dashed line is the payoff from being believed to be high quality. In the shaded band, the high type's cost is below that payoff so they signal, while the low type's cost is above it so they don't — producing a separating equilibrium. If the two cost lines had the same slope, no amount of signalling could separate the types.

4.1 Example 1: Warranty as a Signal

Setup: Good cars (buyer value $3,000, seller value $2,800) vs. bad cars (buyer value $2,000, seller value $1,800). Sellers can offer a warranty.

Separating equilibrium outcome:

• Cars without warranty are identified as bad → sold at $2,000
• Cars with warranty are identified as good → sold at $3,000 + $250 = $3,250
• Good sellers earn $3,250 − $300 = $2,950 > $2,800 (their reservation price). They offer warranties.
• Bad sellers would earn $3,250 − $1,300 = $1,950 < $2,000 (no warranty price). They don't offer warranties.

Key Takeaway

The warranty works as a signal because the expected cost of honouring it is much lower for good-car sellers. High quality makes the signal cheap; low quality makes it prohibitively expensive.

4.2 Example 2: Education as a Signal (Spence, 1973)

Michael Spence showed that education can function as a signal even if it does not increase productivity. The key insight: getting a degree is easier (less costly) for high-productivity workers than for low-productivity workers.

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5. Summary & Quick Reference

Key Formulas