Evaluating a Uniform Premium Strategy
An insurance company provides theft insurance for a specific model of bicycle valued at $2,000. It offers this insurance to all cyclists in a city for a single, uniform annual premium. The company has identified two distinct customer segments:
- Group A: Cyclists who store their bikes indoors in a secure location. The probability of theft for this group is 2% per year.
- Group B: Cyclists who lock their bikes on public streets. The probability of theft for this group is 10% per year.
To simplify its offerings, the company calculates its premium based on the average risk of the two groups combined, assuming an equal number of customers in each. Therefore, the premium is set to exactly cover the expected claims from a policyholder with a 6% chance of theft.
Analyze the financial consequences for the insurance company of charging this single premium to both groups. In your analysis, explain the profitability for the company from each group and predict the likely long-term effect on the company's pool of customers.
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Introduction to Microeconomics Course
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An insurer provides a policy for a piece of art valued at $50,000. Historical data suggests a 0.5% probability of a total loss due to damage or theft during the one-year policy term. To exactly cover the average anticipated cost of a claim, the insurer must charge a premium of $____.
An insurance company offers two separate one-year policies for full coverage against total loss.
- Policy A is for a piece of equipment valued at $5,000 with a 4% probability of loss. The premium for Policy A is $240.
- Policy B is for an art piece valued at $20,000 with a 1% probability of loss. The premium for Policy B is $230.
Which policy has a larger 'loading charge' (the amount charged in the premium that exceeds the mathematically expected claim cost)?
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