3. Other Contract Design Problems

301. Information Rent

Parties entering in a contract have different information → asymmetric information (relevant facts)
This is adverse selection → hidden information

Buyer of used car, health insurer about health of insured

Moral hazard vs. adverse selection → not the same

Example: symmetric information = car buying

• if each party knows how high the other party values the good → likely the trade takes place
  mutually beneficial trade = efficient trade → since both know

Which price? if seller values at 50, buyer at 100

• depends on relative bargaining power
• but no matter what price 50 ⇐ x ⇐ 100 → still mutually beneficial
  Buyer with bargaining power → extracts all benefit

LEMMA

When both parties are symmetrically informed (same information), they will agree on mutually beneficial trade. The way gains are split depends on relative bargaining power.

Car selling → asymmetric information with buyer all bargaining power (seller knows the real value → has owned it).

• buyer doesn’t know whether he faces seller of high or low quality car
  → only two reasonable offers: 50 or 20
• if > 50 → not rational
• if < 20 → select always reject it
• 20 < x < 50 → sell if if it’s low quality, keep it if it’s high quality
  • Thus he can lower it
    Buyer offering 20 → inefficient trade

If he offers 50 → expected gain of 25, with offer of 20 → gain only 15
Note: this occurs even though buyer has all bargaining power

• this gain is called the information rent

302. Adverse Selection

Information asymmetry only had a distributional effect by shifting money from the buyer to the seller of low-quality cars. → avoids inefficient trade

However → usually that inefficient trade cannot be avoided with asymmetric information

Same example as before but car 1 valued at 70 by seller (instead of 50).
→ reasonable buyer can only offer 20 or 70
However → if he offers 70 → receives car only valued by him at 50

• his payoff is a loss of 20 in this case
  expected gain only 5
  → because seller has 15 gain → he will only ever offer 20

Thus the high quality car is never going to be traded ever! Thus inefficient trade!

This is adverse selection → sellers of high quality cars exit the market!

Tradeoff:

• increasing chance that beneficial trade occurs with seller of high quality good
• reducing information rent of low-quality good seller

With continuum of qualities → both effects at once

• too little trade of high-quality goods
• sellers get information rent

303. Unravelling

George Akerlof → 2001 nobel prize for paper “market for lemons”

with a continuum of goods, uniformly distributed → buyer offering 50 gets 25 expected value car

• he values it at 35 → -7.5 expected gain (50% of the sellers, those of high quality cars do not sell)
• always partitions the market
  Therefore, he offers less → 25, 20, 15, 10
  At 10 it stops, because ev = 5, he values at 15 → thus makes a gain

→ This is called unravelling (90% market failure)

Example Health Insurance (uninformed sellers)

• if you have pre-existing conditions or high-risk hobbies
  • value insurance highly
    if only one plan is offered → some do not buy. Avg pool risk grows (as only high risk people buy) → insurance raises prices

Solutions:

• Mandate Insurance
• physical examination → life insurances for example
  • levels information field
• menu of different contracts
  • this allows auto-sorting of buyers

Vicious cycle → adjusting price terms → change composition of the market → requires adjusting price terms → …