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Question 1 21 pts Consider the Rothschild-Stiglitz Model. In this example, we will examine the case of asymmetric insurance and heterogenous risk types. The utility function (for each consumer) has the following form: U (I) = 10.4 The frail types have a probability of becoming sick: Pfrail = 0.25 , and the robust types have a probability of becoming sick: Probust = 0.05 . All individuals start with income of $1000. If an individual becomes sick, they lose $200. The insurance company decides to offer 2 contracts: No Coverage Total Coverage Minimal Coverage Payout if sick (q) 0 $200 $23 premium (r) 0 $33 $1 So, the individuals can decided to stay at their endowment, or purchase an insurance contract. Calculate your expected utility values to at least 3 decimal spots. a. [8 points] What would the frail individuals do? (Calculate the expected utility from each option; choose the one with highest expected utility.) b. [8 points] What would the robust individuals do? (Calculate the expected utility from each option; choose the one with highest expected utility.) c. [5 points] If the market has 100 potential customers, of whom 75 are frail and 25 are robust, what is the insurance company's expected profit (assume the company is risk neutral)