Consider a framework of choice under uncertainty where insurance is offered to mitigate the potential loss of income an individual would face in the bad state of the world, and where there are high-risk individuals (who are more likely to suffer a loss) and low-risk individuals (who are less likely to suffer a loss).

Explain and identify diagrammatically how in the presence of adverse selection a pooling equilibrium could be constructed by an insurance provider that offers insurance to both low-risk and high-risk individuals. Further, explain why such a pooling equilibrium could not be offered in a competitive insurance market where individual insurance providers competed against each other.