8. Assume there is perfect information in the market. Calculate an insurance premium for both the very skilful and less careful drivers that would enable mutually beneficial trade with the insurance company. Assume the administrative costs are still £10 per policy for both types of customer. 9. Assume now that there is asymmetric information in the market. When a customer purchases a policy, the insurance company does not know if they are skilful or less able drivers. What is the break-even/actuarially fair insurance premium if the insurance company assumes that 50 per cent of its customers are the skilful drivers and 50 per cent are the less able drivers? Assuming the administration costs are still £10 per customers, what premium might the insurance company charge on this basis? 10. U
Part H I J
every part contain 100 words minimum
Q1:
Assume you have £300,000 worth of assets (W). This includes savings, property and your car. You use the car to drive to school/university every day and there is a 1 in 20 (or 5 per cent) chance per year that you will be involved in an accident that results in the car being a write-off. Assume its market value is £40,000 and remains the same i.e. it does not depreciate. You can take out a full insurance policy for the year that pays out the full £40,000 market value of the car if you have the accident. Assume the insurance company has many customers with exactly the same assets as you and who all face the same risk of being involved in a similar accident.
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- What is the expected value of taking the gamble i.e. not buying the insurance policy?
- Assume your utility function is W0.25. What is your expected utility from taking the gamble?
- Calculate the certainty equivalent and risk premium of the gamble.
- What is the maximum amount you would be willing to pay for the insurance policy out of your £300,000 worth of assets?
- What is the break-even/actuarially fair insurance premium in this case?
- Draw a diagram to illustrate your answers to the previous questions.
- Assume the administration costs for the insurance company are £10 per customer. Explain how mutually beneficial trade is possible over a range of prices. Calculate the individual
consumer and producer surplus at one particular price.
Assume now that there are two types of driver. One half of them are very skilful drivers and each of these has only a 2 per cent chance per year of being involved in a car accident while the other half are less able/careful drivers who each have a 8 per cent chance per year of being involved in an accident.
8. Assume there is perfect information in the market. Calculate an insurance premium for both the very skilful and less careful drivers that would enable mutually beneficial trade with the insurance company. Assume the administrative costs are still £10 per policy for both types of customer.
9. Assume now that there is asymmetric information in the market. When a customer purchases a policy, the insurance company does not know if they are skilful or less able drivers. What is the break-even/actuarially fair insurance premium if the insurance company assumes that 50 per cent of its customers are the skilful drivers and 50 per cent are the less able drivers? Assuming the administration costs are still £10 per customers, what premium might the insurance company charge on this basis?
10. Using your answers to parts h. and i, predict what you think will happen in the market at the premium you suggested in the previous answer. Explain how this illustrates the process of adverse selection. Calculate any lost surplus per customer.
Q2:
To what extent do Finkelstein and Porteba (2004) find evidence of adverse selection in the UK annuity market?
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