Problem $06-20($algo$)$

There are two groups, each with a utility function given by $U(M)=\sqrt[\phantom{2}]{M},$ where $M=121$ is the

initial wealth level for every individual. Each member of group $1$ faces a loss of $46$ with probability

$0\mathrm{.}6.$ Each member of group $2$ faces the same loss with probability $0\mathrm{.}1.$

a$.$ What is the most a member of each group would be willing to pay to insure against this loss?

Instructions: Round your answers to $2$ decimal places.

Maximum a member of group $1$ is willing to pay is: $

Maximum member of group $2$ is willing to pay is: $

b$.$ If it is impossible for outsiders to discover which individuals belong to which group, how large a

share of the potential client pool can the members of group $1$ be before it becomes impossible for

a private company with a zero$-$profit constraint to provide insurance for the members of group $2?$

$($For simplicity, you may assume that insurance companies charge only enough in premiums to

cover their expected benefit payments and that people will always buy insurance when its price is

equal to or below their reservation price.$)$

Instructions: Enter your answer rounded to two decimal places.

Instructions: Enter your answer as a whole number.