Modelling insurance market with adverse selection Assignment Help

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Modelling insurance market with adverse selection:

We will discuss the important features of Rothschild-Stiglitz theorem, which basically highlights the following result:

When information is private, giving rise to the problem of adverse selection, market outcomes cannot produce Pareto efficiency. Particularly, when there is imperfection  in the market such that one of the parties to a transaction is better informed  than the other, inefficiencies  would  crop up.  You  will  notice equilibrium of such a market that violates the first welfare theorem.

Let us  see  how  the model  works.  For  this purpose, we will follow the presentation  as  well  as  notations  of  Autor,  2004.  Suppose a risk-averse individual faces two states of the  world  in which her initial wealth is characterised by no-accident and accident. If there is no accident, wealth is  w  and with accident, wealth is  w -  d (where d >  0 stands indicates damage).  

1898_Modelling insurance market with adverse selection.png

where the vector  a =  (a1,  a2)  describes the insurance contract. You can think that  the  insurance premium  a,,  is paid  in both  the  accident and no-accident states. Hence,  a, is the net payout of the policy in event of accident. If  you  denote  the  probability of  an  accident  as  p, then  an  individual purchases insurance when  the  expected utility of being insured exceeds  the expected utility of being uninsured, i.e.

2257_Modelling insurance market with adverse selection1.png

On the other hand, the insurance company will sell a policy if expected profits are non-negative, i.e.,

359_Modelling insurance market with adverse selection2.png

Let us assume a competitive market, so that this equation holds with equality. Therefore, in equilibrium:

666_Modelling insurance market with adverse selection3.png

To derive the equilibrium conditions of the model, we follow the formulation Rothschild-Stiglitz who propose the following conditions:

1)  No insurance contract makes negative profits (break-even condition).

2)  No contract outside of the set offered exists that, if offered, would make a non-negative profit. For,  if there were a potential contract that could be offered  and would be more'  profitable than  the  contracts  offered  in equilibrium,  then the current contracts cannot be an equilibrium.

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