Final answer:
The function γ(X) represents the amount paid by the insurance company, which is $0 if X ≤ $100, X - $100 if $100 < X ≤ $5100, and $5000 if X > $5100, reflecting the policy's deductible and cap.
Step-by-step explanation:
The student has asked to understand how to express γ (the amount the insurance company has to pay on a claim) as a function of X (the dollar amount of a claim), given a policy with a $100 deductible and a $5000 cap. This situation involves applying concepts regarding insurance policies such as deductibles, copayments, and coinsurance.
Let X represent the total dollar amount of an insurance claim. To express the amount γ that the insurance company will pay as a function of X, we consider the deductible and the cap:
If X ≤ $100, then γ = $0 because the policyholder pays the entire claim out-of-pocket due to the deductible.If $100 < X ≤ $5100, then γ = X - $100, because the insurance company starts to pay after the deductible is accounted for, up to the cap.If X > $5100, then γ = $5000, because the insurance company will not pay more than the cap.
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- Therefore, the function that represents the amount γ paid by the insurance company in terms of the claim amount X can be described as:
γ(X) =
$0 if X ≤ $100
X - $100 if $100 < X ≤ $5100 $5000 if X > $5100
This example illustrates how deductibles and caps can mitigate moral hazard by requiring the insured to share in the cost of a loss, thus promoting responsible behavior.