A simple economics problem

Photo Credit: Flickr user “Wonderlane” – some rights reserved

Many years to Corbin Foucart for posting “The Simple Math Behind Insurance” for the inspiration. I love simple explanation for economic issues. Some economic things are very complicated. But not all of them. Many years to Corbin for letting simple things be simple. Also, the situation with the die is completely borrowed from him. Thanks for that, too.

Suppose I came to you with a single six-sided die and offered to play a game. Here is how the game goes: If I roll a 6, I will give you $6. If I roll any other number, you have to give me $2. Would you play the game?

I would advise you not to. If we played long enough, I would certainly come out on top. Allow me to explain. For every roll, there is a 1 in 6 chance of getting any of the numbers. Suppose I rolled 36 times. There would likely be about 6 of each number, right? So, with me taking $2 for each of my rolls of numbers 1, 2, 3, 4 and 5, (that is 30 rolls), I would be raking in 60 of your dollars. I still rolled 6 sixes, so I would be giving $36 back. I am still ahead $24. Thus, the game will ultimately end up in my favor.

Now, let’s look at how this model might relate to economics. Consider insurance. We will stick to auto insurance. You know how auto insurance works, right? A person pays monthly to a company that promises to provide the funds to fix (or replace) the car in the event of an accident. You might ask yourself, “How can a company whose business is to pay for other people’s accidents make any money?”

Great question. Answer? The same way that I made money off of you in the game the started this blog post. Even though I was paying out more than I was taking in, I was five times as likely to take money in as I was to pay out. Let’s relate this to insurance.

Suppose you have a small insurance company that insures 100 people.

Each person pays you $25 per month.

The odds, in any given month, of a car getting in a wreck is 1 in 100.

If a car gets in a wreck, you pay out $2000.

This problem is a modified version of the problem posed by Mr. Gordon.

So, each month 100 people pay you $25. So, you have received $2500. Each month, one person gets in a wreck, which costs you $2000.  So, you are ahead $500. You have just become a profitable insurance company. Obviously, there are going to be months where more than one person gets in a wreck, but there will also be months were no one does. That should balance out.

Now, let’s add a variable. Suppose that you know that a certain group of people (we will call them “teenagers”) are more likely to get in a wreck. Let’s also suppose that you just added 25 of those people to your insurance business. How do you change the way you charge your customers?

Suppose the 25 teenagers have a 4 in 100 chance of getting in a wreck.

How do you change your business model? Leave some ideas in the comments. The more specific, the better. (That is, “I’d charge the teenagers more” isn’t as good as it could be. How much more? Why?)

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