I have two questions on my homework that I got wrong and don't understand what the right answer should be:
- Scenario:Suppose you've just spent 800 dollars on a new laptop and have the option of getting insurance that covers repairs and replacements for any damage to it (think something like AppleCare).This costs an extra 200 dollars. Within the insurance period, you estimate that there’s a 15% chance that your laptop will need 100 dollars in repairs and a 5% chance you will need to pay the full cost of replacing it, 800 dollars. All of these costs would be avoided with the insurance.
Let’s say we’re using a simple expected utility model. Ignore any wealth aside from the purchase of the laptop.
Every dollar you spend (or otherwise lose) up to $500 feels like a loss of 1 utile.
Every dollar after $500 feels like a loss of 2 utiles.
Every dollar after $1000 feels like a loss of 4 utiles.
So the cost of the laptop itself is -1100 utiles (-500 * 1 - 300 * 2), and if you get the insurance that’s another -200 utiles (-100 * 2), since this cost falls in the range between $500 and $1000).
If you don’t get the insurance, what’s the expected utility of potential damage to it? You’re considering this damage as a loss of utility, without regard for the original cost of the laptop, so the cost of the laptop shouldn’t be part of your calculation.
I got -70 as the answer for the problem but it was wrong.
- Now, let’s introduce an idea from Prospect Theory, which is that low probabilities are often underestimated. To model this, we use a function that maps objective probabilities (that is, how likely something really is) to subjective probabilities, and the subjective probabilities are what people use to make decisions.
Now, do the same expected utility calculations as in the previous problem, but using these subjective probability values instead of the objective probability values. You can find the relevant subjective probabilities on the following figure.
subjective probability = 0.145 at objective prob = 0.05subjective prob = 0.23 at objective prob = 0.15
For this problem I got -182.5 but was also wrong...please help!