For 55-year-old women the likelihood of getting breast cancer is determined by t

Question

For 55-year-old women the likelihood of getting breast cancer is determined by the combination of family history and lifestyle choices, especially smoking. The probability of getting cancer between the ages of 55 and 65, given these factors is:

The expected cost for treating breast cancer is $12,000. Assume that in addition to the expected value of the policy, all 55-year-old women (no matter their risk) value the security of having insurance for breast cancer an additional $600 over the 10-year period between 55-65. Also assume that 1/6 of all women fall into each category. Suppose that the insurance market is competitive.

(a) Suppose that the insurance companies, by law, can not use a woman family medical history and smoking status in pricing the insurance policies. What will be the equilibrium price of the the insurance? What type, or types, of women purchase insurance?

(b) Suppose now that the insurance companies can observe a woman’s smoking status, but not family medical history, and is allowed to use the woman’s smoking status in its pricing of insurance policies. What will be the equilibrium price for smokers? What will be the equilibrium price for non-smokers? What type, or types, of women purchase insurance in this case?

Smoker Non-Smoker Family Excellent 5% 2% Medical Good 10% 5% History Bad 20% 10%

Explanation / Answer

Solution

Part (a)

Let the total number of women to be covered by the insurance be 6n.

Given, ‘assume that 1/6 of all women fall into each category’, number of women to be covered by insurance in each category is n.

Using the probability figures given, expected number of women to have breast cancer is: (n x 0.05) + (n x 0.10) + (n x 0.20) + (n x 0.02) + (n x 0.05) + (n x 0.10)

= 0.52n ………………………………………………………………………………….(1)

Expected cost ($) to be covered in case of cancer incidence

= (12000 + 600) = 12600 ……………………………………………………………..(2)

Expected cost of insurance to the company = (1) x (2) = 0.52n x 12600 = 6552n

To break even, the company must get at least this much amount from 6n patients which in turn implies,

the minimum price of the insurance must be 6552n/6n = $1092 Answer

Part (b)

Going by the same analysis as above,

For smokers

Expected number of women to have breast cancer is:

(n x 0.05) + (n x 0.10) + (n x 0.20) = 0.35n ………………………………………….(3)

Expected cost ($) to be covered in case of cancer incidence

= (12000 + 600) = 12600 ……………………………………………………………..(4)

Expected cost of insurance to the company = (3) x (4) = 0.35n x 12600 = 4410n

To break even, the company must get at least this much amount from 3n patients which in turn implies,

the minimum price of the insurance must be 4410n/3n = $1470 Answer 1

For non-smokers

Expected number of women to have breast cancer is:

(n x 0.02) + (n x 0.05) + (n x 0.10) = 0.17n ………………………………………….(3)

Expected cost ($) to be covered in case of cancer incidence

= (12000 + 600) = 12600 ……………………………………………………………..(4)

Expected cost of insurance to the company = (3) x (4) = 0.17n x 12600 = 2142n

To break even, the company must get at least this much amount from 3n patients which in turn implies,

the minimum price of the insurance must be 2142n/3n = $714 Answer 2

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.