1. Suppose that there are 100 young people looking to buy health insurance.
They consist of the following:
- 20 people that like to ride motorcycles, each willing to pay $2,500
- 20 people that like to ski, each willing to pay $2,200
- 20 people that like to skateboard, each willing to pay $1,800
- 15 people that like to ride bicycles, each willing to pay $1,200
- 15 people that like to hike, each willing to pay $1,000
- 10 people that like to take yoga classes, each willing to pay $800
Assume that the insurance company does not know the activities that individuals enjoy doing in their leisure time. They do know that, on average:
- Those that like to ride motorcycles will cost, on average, $2,200
- Those that like to ski will cost, on average, $2,000
- Those that like to skateboard will cost, on average, $1,500
- Those that like to ride bicycles will cost, on average, $1,000
- Those that like to hike will cost, on average, $600
- Those that like to take yoga classes will cost, on average, $700
a) What is the actuarially fair premium for this pool of 100 people?
b) Is this an example of adverse selection? Explain by indicating you know what adverse selection means.
c) For the Affordable Care Act to avoid an adverse selection death spiral, why is it important that young adults decide to buy health insurance?
2. Graphing adverse selection
In addition to the notes from class, use the assigned reading "Selection in Insurance Markets: Theory and Empirics in Pictures" by Liran Einav and Amy Finkelstein to answer the questions. This reading is available on Blackboard ("Reading Week 8: October 26), and outlines (using pictures) the issue of adverse selection.
a) First, graph each of the following curves ("lines") in Excel. Paste the picture into your Word document.
- The demand curve is: P = 520-5Q
- The marginal cost curve is: P = 320 - 4Q
- The average cost curve: P = 320 - 2Q
Hint: For me this worked best by graphing the three lines (demand, marginal cost, average cost) the same way that you graphed externality and supply/demand problems.
c) Find the equilibrium price and quantity.
- Hints: What makes health insurance markets unique is that the costs that demand(ers) generate is what creates the firm's supply curve. We will assume that firms make 0 profits. Therefore, firms make decisions based upon their average costs, or the expected payout on premiums.
- The equilibrium in a health insurance market is where the average cost is equal to demand.
- The answer is in the reading.
d) Find the efficient price and quantity.
- The answer is in the reading where this quantity (Qeff) is. The corresponding price is then read off of the demand curve for that quantity.
- Next, find the numerical value based upon your MC/AC/Demand equations.
3. Why Buy Insurance
- Assume you have the following Utility function: U = √Income. This utility function corresponds to risk aversion.
- Assume that you earn $100,000.
- You have a 75% chance of staying healthy and a 25% chance of getting sick
- If you get sick, it will cost you $25,000 in medical bills.
- You are offered health insurance at the actuarially fair price.
b) What is your expected income if you do not buy health insurance?
c) If you decide to purchase insurance, what would be the actuarially fair premium?
d) What is your expected income if you buy health insurance (assume that you fully insure)?
e) What is your expected utility if you do not buy health insurance?
f) What is your expected utility if you do buy health insurance?
g) You have a friend who is considering whether or not to buy health insurance. Assume this friend has NOT taking ECON 380 and therefore does not know terminology like "risk aversion" or "expected utility". Explain clearly to this friend in everyday language why they are better off by purchasing health insurance.