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7. In an insurance market there are three indistinguishable types of potential clients: of low medium and high risk. Each of these groups is composed of 1000 persons. The probability of an accident (loss) in each of these groups amounts to 1%, 2%, and30-respectively. If a loss occurs, the resulting damage is 100004근ety. The maximum amount that a client from a given group will pay for insurance is 1500 zloty, 2900 zloty, and 3500 zloty respectively. What average (i.e. expected) maximum profit can an insurer-monopolist make offering full insurance (assume that the only cost is the paid out compensation)?

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Answer: Given information is as follows The probability low risk potential client out of 1000 persons is 1%. The probability low risk potential client out of 1000 persons is 2%. The probability low risk potential client out of 1000 persons is 3%. The total amount damage, if there is occurrence of loss, is 100,000 zloty, The maximum amount for low risk client pays for insurance is 1500 zloty, The maximum amount for medium risk client pays for insurance is 2900 zloty, The maximum amount for high risk client pays for insurance is 3500 zloty Total expected damage: The total expected damage is calculated as follows: Total Expected Damage = 1000 (0.01x 100,000 + 0.02x 100.000 + 0.03x 100,000) = 1000x (6000) 6,000,000 Thus, the required total expected damag e is 6,000,000Total revenue: The total revenue is calculated as follows Total Revenue = 1000(1500 +2900 +3500) = 1000x (7900) 7,900,000 Thus, the required total revenue is 7,900.000 Total Profit: The required profit for insurer-monopolist is calculated as Total Profit Total Revenue Total Expenditure =7.900.000-6.000.000 1,900,000 Thus, the required total profit is 1,900,000

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