Pooling Contract Flashcards
What type of Risk is there in Selection Problem?
Exogenous Prob. of Theft Low Risk = p High Risk = p' p' > p - Only Insured knows Own Type
What is the Market Equilibrium of Selection Problem?
Lower Welfare than in Full Info for LOW Risk
What is Market Equilibrium under Full Info?
Each Type chooses Full Insurance at Fair Odds rate appropriate to their Risk Type
What does H.R Fair Odds Line (HH’) show?
More Expensive Premium per £ of Compensation necessary for Company to Break Even on contracts w/ High Risk
What is the difference in Full Insurance point of each Type?
Low Risk on FF’ have Higher level of Wealth
- Indicates Lower cost of Purchase of Insurance Cover
Why do Types have different sloped I.Cs at any point in State-Space?
Due to different Prob. of Theft for each Type
Why is Low Risk I.C steeper than High Risk?
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’
What is dWt / dWnt for the Insurer?
- [(1 - p) / p] < 0
What is dWt / dWnt for the Insured?
- [(1 - p) / p] x [U’(Wnt) / U’(Wt)]
What is Market Fair Odds?
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
What is the Market Average Fair Premium MM’?
pm = (n1p1 + n2p2) / (n1 + n2)
How does MM’ affect Low Risk and High Risk individuals?
Unfavourable Odds for Low Risk
Favourable Odds for High Risk
What level of Insurance would each type want to choose along MM’?
Low Risk - Partial Insurance
High Risk - Full Insurance - but would like to choose more than F.I
Where would a Pooling Contract generate Supernormal Profits?
Any Pooling Contract BELOW MM’ - if it attracts both Types
What can’t a Pooling Contract below MM’ be an Equilibrium?
A Contract closer to MM’ will attract Both Types
- Competitive Market –> Market Average Fair Odds
Which Contract along MM’ would eventually be offered?
Contract at L w/ Partial Coverage
- Optimal Contract to Low Risk
- L.R Utility Maximised at L - I.C EU Tangent to MM’
Why is L the Optimal Pooling Contract along MM’?
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)
Can L be a Pooling Equilibrium?
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
Can Q be a Pooling Equilibrium?
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.
What is Wilson Equilibrium?
Insurance Comp. only introduces new Contract if it believes it will remain Profitable once those it makes unprofitable have left
Is Q a Wilson Eq.?
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.
