Insurance Math

Insurance Math

Problem One:  Consider two health plans with deductibles, coinsurance rate, and maximum allowable out-of-pocket limit as presented in the table below.

Characteristics of two health plans
	Health Plan One	Health Plan Two
Deductible	$5,000	$1,000
Coinsurance Rate	0.2	0.5
Maximum Allowable  Out-of-Pocket Limit	$10,000	$15,000

Questions:

At what level of total health expenditures does the insurance company start paying 100 percent of approved claims?

Write a piecewise linear function where out-of-pocket health care expenses is the Y variable and total health expenses is the X variable for the two health plans.   

Write a piecewise linear function where insurance company payment is the dependent variable and total health expenses is the X variable?

Demonstrate that the sum of the piecewise linear out-of-pocket expense function and the piecewise insurance payout function equals total health expenses in each part of the domain of the functions.

Answer to Problem One:

http://www.dailymathproblem.com/2018/07/basic-algebra-of-two-insurance-plans.html

Problem Two:   A person is considering two insurance plans.   The first plan has a $5,000 deductible and a $5,000 maximum allowable out-of-pocket expense limit.   The second plan has a  $3,000 deductible, a 20% coinsurance rate, and a $9,000 out-of-pocket expense limit.  

Write a function describing insurance payments received by the insured as a function of total health expenses incurred under the two health plans.   

When are actual out-of-pocket expenses under the first insurance plan greater than out-of-pocket expenses under the second insurance plan?

Answer to Problem Two:

http://www.dailymathproblem.com/2013/12/high-deductibles-versus-high-out-of.html

Problem Three:   The table below lists characteristics (deductible, coinsurance rate, and out-of-pocket expense limits) for three different health plans

Three Health Insurance Plans
	Plan Number One	Plan Number Two	Plan Number Three
Deductible	$2,500	$4,000	$8,000
Coinsurance Rate	20%	30%	0%
Out of-pocket Expense  Limit	$5,000	$10,000	$8,000

The table below describes total health expenditures (the amount paid by the insured and the amount paid by the insurance company) for a sample of 35,000 people.

Health Expenditures	Number of People
$0	8,000
$500	7,000
$3,000	6,000
$6,000	5,500
$12,000	5,500
$25,000	2,800
$150,000	200
Total	35,000

Questions:

What is the mean and the total health expenditure paid by the insurance firm for the three health insurance plans and this group of individuals?

A company offers all three insurance policies to its employees.  Discuss why average health expenditures will differ across these three plans?

Answer to Problem Three:

http://www.dailymathproblem.com/2014/04/incentives-for-three-health-plans.html