Rothschild-Stiglitz model (numerical and graphical illustration)

According to the Rothschild-Stiglitz model that we studied during yesterday’s class, insurers will limit contract choices such that there is no adverse selection.  In the numerical example that we implemented during class, there are equal numbers of high risk and low risk insureds; all have initial wealth of $125 and square root utility.  There are two states of the world – loss and no loss, and the probabilities of loss are 75% for high risk types and 25% for low risk types.  By offering high risk types full coverage at their actually fair price of $75 and offering low risk types partial (10%) coverage at their actuarially fair price of $2.50, both types of risks buy insurance and there is no adverse selection.

This illustrated in the figure below and in the spreadsheet located at http://fin4335.garven.com/fall2018/rothschild-stiglitz-model.xls.  Clearly neither the B or C contracts would ever be offered because these contracts incentive high risks to adversely select agains the insurer.

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