Problem 1: Demand for Health Insurance
The objective of this problem is to understand the expected utility of purchasing health insurance. In short, why do we purchase health insurance from a "neoclassical economics" perspective?
a) Explain in 2-3 sentences why it is in most people's best interests to purchase insurance from an economic utility perspective.
b) Take the case of fire insurance for a home.
- Assume you own a home that is worth $1M (Congratulations!) and there is no depreciation
- Assume the Probability of a fire = 0.1% (= 0.001)
- Assume if there is a fire, the value of the house goes from $1M → $0
What is the Expected Value of the house?
c) Assume Utility = √(House Value)
(Note: Utility = Square Root of House Value)
Draw the utility curve with House Value on the X axis and Utility on the Y axis. [Note, you can do this mathematically, or just by connecting the five points below]
Be sure to include in the graph the location of 5 points:
1. House Value = 0
2. House Value = $500K
3. House Value = $800K
4. House Value = $1M
5. House Value = $1.2M
d) What is the expected Utility? Be precise and round the 2 decimal places.
Note: Utility is the Utility in scenario 1 where the house does not burn down, multiplied by probability of scenario 1, plus the utility in scenario 2 where the house does burn down multiplied by the probability of scenario 2.
e) What is the utility of the person if they purchased insurance for a cost of $1000?
f) Describe in words why the purchase of insurance provides a higher utility than utility without the purchase of insurance.
g) What is the maximum amount a person would pay for insurance? (Hint solve backwards)
Problem 2: Moral Hazard
a) Lisa is insured. The plan has a 10% coinsurance rate and no deductible. Lisa receives an appendectomy that costs $8,000. What is the cost of care to Lisa?
b) Please draw a demand curve (line) for Hip Replacements. Please based on the following points
|
Demand Curve
|
Point 1
|
Point 2
|
|
Price
|
$20,000
|
0
|
|
Quantity
|
0
|
1,000,000
|
c) What is the demanded quantity at a price of $8,000? [Note this can be solved graphically or mathematically]
d) What is the quantity at Lisa's payment that you solved for in part a?
(Note, this can be solved for algebraically or graphically)
e) Draw a supply curve (line) meeting the following parameters
|
Supply Curve
|
Point 1
|
Point 2
|
|
Price
|
$0
|
$20,000
|
|
Quantity
|
0
|
1,000,000
|
Label Q the point of equilibrium
f) Draw a red line (or dotted line) at the Price that Lisa pays. Label the quantity that would be purchased Q'.