1. Consider an environment in which: People are rational, risk averse, and aim to maximize expected utility. . All people have the same initial wealth, $100,000. All people face the possibility of a loss of the same size, $80,000. There are two types of people, Type H and Type L. Type H people have a higher prob suffering the loss than Type L people. Type H people have a 75% (three-fourths) char suffering the loss; Type L people have a 25% (one-fourth) chance of suffering the loss Otherwise, the two types are identical; they have the same risk preferences (same utilit the same initial wealth, and the same loss when it occurs. Half of the people are of Ty other half are of Type L. Insurance markets are perfectly competitive without any transaction costs, so that man risk-neutral, expected profit-maximizing insurance companies compete to sell insuran peoples' possible losses. Please CLEARLY draw a LARGE diagram to illustrate a POOLING contract situation. Ti should plot wealth if the loss does not occur on the x-axis and wealth if the loss does occur axis. Be sure to label your axes and any relevant lines and points. Be sure to include (and the roman numerals below, putting relevant dollar values on the axes): 1. the point representing no insurance; ii. the point representing full insurance that would be break-even if sold only to Type H peop 111. the point representing full insurance that would be break-even if sold only to Type L peopl 1V . the point representing full insurance that would be break-even if sold to all people; V. the curve or line showing the set of points that are exactly as good (not better than, not wor point (iv) for Type H people; vi. the curve or line showing the set of points that are exactly as good (not better than, not wor point (iv) for Type L people; Vii. the point representing a contract that Type L people would prefer to point (iv), Type H pec not prefer to point (iv), AND that would be profitable when sold only to Type L people