Asymmetric Information: Moral Hazard and Adverse Selection

Asymmetric information refers to situations where one participant knows more than another. Akerlof, Spence, and Stiglitz (Nobel Prize 2001) systematized these situations, showing that they generate fundamental market failures. These models explain insurance market crises, banking panics, labor market collapses, and have been developed in banks, insurance companies, and regulators.

The "Lemon" Market (Akerlof, 1970)

Used car model: N cars, share q of “lemons” (v_L = 1) and (1−q) of “peaches” (v_H = 2). Sellers know the quality, buyers do not. Sellers’ reservation prices: 1.5 (peach), 1 (lemon).

Adverse selection mechanism: Buyer offers E[v] = 2 − q·1 = 2 − q (average value). If q > 0.5: E[v] < 1.5 → peach sellers leave (better to keep). Now the market = only lemons: E[v] = 1. Buyer offers 1. The market functions, but only for lemons.

Complete collapse: with q > 0.5 the peach market disappears — “bad” goods drive out good ones (Gresham). DWL: all surplus from trading peaches (at least 0 to 0.5 per unit) is lost.

Solutions: Guarantees (costly signal of quality). Reputation in repeated interactions. Third-party certification (Carfax, AutoCheck, auditor ratings). Mandatory disclosure (lemon laws in the USA — car return within 30 days). Warranty dealers.

Adverse Selection in Insurance

Rothschild-Stiglitz model (1976): Two types: high-risk (p_H = 0.5) and low-risk (p_L = 0.2). The insurer cannot distinguish types. Loss L = 100. Full insurance for the group: price = E[p] = λ·0.5 + (1−λ)·0.2 (depends on the share λ of high-risk).

Result: There is no stable pooling equilibrium. Proof: at the pooling price, a competitor can offer a contract with slightly higher price and less coverage, attractive only to low-risk — pool breaks.

Separating equilibrium (if it exists): High-risk — full insurance coverage at rate p_H·L = 50. Low-risk — partial coverage C_L < L at rate p_L·C_L — payment for “separating” from high-risk. Separation condition: high-risk must not prefer the contract for low-risk: EU_H(full, 50) ≥ EU_H(C_L, p_L·C_L).

Moral Hazard

Mechanism: Insurance lowers the marginal cost of caution → caution decreases → probability of loss increases. Unobservable action (hidden action) after signing the contract.

Insurance–incentive trade-off: With full insurance: agent chooses zero caution (the only way to be accountable is to bear part of the loss). Optimal contract: partial coverage (franchise or co-insurance). Key result: there is no “first-best” solution under unobservable action.

Rand HIS effect (1974–1982): Randomized experiment — the first in healthcare history. With 0% co-payment medical consumption is 30% higher than with 25% co-payment — without significant health difference. Measured moral hazard in health insurance. Justifies co-payments as a tool.

Numerical Example

The manager chooses effort e ∈ {H, L}: with e_H, profit 1000 with prob. p_H = 0.8, 0 with prob. 0.2. With e_L: prob. 0.4, 0.6. Costs: c_H = 200, c_L = 50.

If e is observable: first-best — choose e_H if additional expected profit (0.8−0.4)·1000 = 400 > c_H − c_L = 150 → e_H. Contract: fixed salary w_H + c_H = w_H + 200, principal takes 1000·0.8 − (w_H+200). With IR: w_H = 0 → principal gets 800 − 200 = 600.

If e is unobservable: IC: EU_H(e_H) ≥ EU_H(e_L). For a linear contract (bonus share β): β·1000·(0.8−0.4) − (200−50) ≥ 0 → β ≥ 0.375. IR: 0.8·β·1000 − 200 ≥ 0 → β ≥ 0.25. Optimal β = 0.375: principal gets (1−β)·E[π] = 0.625·800 = 500 < 600 (loss from asymmetry).

Task: Manager with p_H = 0.8, p_L = 0.4, profit 1000/0, c_H = 200, c_L = 50. (a) Observable e: find the optimal contract. (b) Unobservable e: find the optimal bonus β*, salary w*, expected profit of the principal. (c) Calculate the “loss from asymmetry” (difference in profits in (a) and (b)). (d) How do the answers change if p_H = 0.9?