Pooling Contract

Question 1

What type of Risk is there in Selection Problem?

Answer 1

Exogenous Prob. of Theft
Low Risk = p
High Risk = p'
p' > p
- Only Insured knows Own Type

Question 2

What is the Market Equilibrium of Selection Problem?

Answer 2

Lower Welfare than in Full Info for LOW Risk

Question 3

What is Market Equilibrium under Full Info?

Answer 3

Each Type chooses Full Insurance at Fair Odds rate appropriate to their Risk Type

Question 4

What does H.R Fair Odds Line (HH’) show?

Answer 4

More Expensive Premium per £ of Compensation necessary for Company to Break Even on contracts w/ High Risk

Question 5

What is the difference in Full Insurance point of each Type?

Answer 5

Low Risk on FF’ have Higher level of Wealth

- Indicates Lower cost of Purchase of Insurance Cover

Question 6

Why do Types have different sloped I.Cs at any point in State-Space?

Answer 6

Due to different Prob. of Theft for each Type

Question 7

Why is Low Risk I.C steeper than High Risk?

Answer 7

Low Risk are willing to give up more Wealth in Theft State for more in Non-Theft State
- Due to Less Likely to be in Theft State - p < p’

Question 8

What is dWt / dWnt for the Insurer?

Answer 8

• [(1 - p) / p] < 0

Question 9

What is dWt / dWnt for the Insured?

Answer 9

• [(1 - p) / p] x [U’(Wnt) / U’(Wt)]

Question 10

What is Market Fair Odds?

Answer 10

Odds an Insurer can offer to the Average Consumer while Breaking Even on Average
- As long as Contract is Accepted by Random Sample of both Types

Question 11

What is the Market Average Fair Premium MM’?

Answer 11

pm = (n1p1 + n2p2) / (n1 + n2)

Question 12

How does MM’ affect Low Risk and High Risk individuals?

Answer 12

Unfavourable Odds for Low Risk

Favourable Odds for High Risk

Question 13

What level of Insurance would each type want to choose along MM’?

Answer 13

Low Risk - Partial Insurance

High Risk - Full Insurance - but would like to choose more than F.I

Question 14

Where would a Pooling Contract generate Supernormal Profits?

Answer 14

Any Pooling Contract BELOW MM’ - if it attracts both Types

Question 15

What can’t a Pooling Contract below MM’ be an Equilibrium?

Answer 15

A Contract closer to MM’ will attract Both Types

- Competitive Market –> Market Average Fair Odds

Question 16

Which Contract along MM’ would eventually be offered?

Answer 16

Contract at L w/ Partial Coverage

• Optimal Contract to Low Risk
• L.R Utility Maximised at L - I.C EU Tangent to MM’

Question 17

Why is L the Optimal Pooling Contract along MM’?

Answer 17

I.C EU Tangent to MM’ at L
Any Contract to Right of L: Can be Improved by offering L - Preferred by both Types
Any Contract to Left of L: Can be Improved by offering L - Only L.R accept at L –> Supernormal Profits (Below FF’)
- Only H.R attracted to Left of L - above HH’ (Loss-making)

Question 18

Can L be a Pooling Equilibrium?

Answer 18

Can improve L by offering Contract in Q - Right of L in between I.Cs EU and EU’ and below FF’
Deviation to Q = Cream-skimming
Q attracts L.R - but not H.R

Question 19

Can Q be a Pooling Equilibrium?

Answer 19

Since Q is Below FF’ –> Supernormal Profits
L becomes Loss-making after Cream is Skimmed
- Only attracts H.R at Odds Favourable to them –> Contract Withdrawn
Profit or Losses can’t continue in NE - Competition always cause Insurers to offer new Contracts different from Cream-Skimming Contract
NO POOLING EQ.

Question 20

What is Wilson Equilibrium?

Answer 20

Insurance Comp. only introduces new Contract if it believes it will remain Profitable once those it makes unprofitable have left

Question 21

Is Q a Wilson Eq.?

Answer 21

Q makes L Unprofitable –> L is Withdrawn
=> Q becomes Unprofitable
- So Q would NOT be Introduced - would eventually become Unprofitable
Q is NOT Wilson Eq.