Equation utility function help

In summary, the conversation discusses a utility function and how it relates to an individual's income and potential risk of a catastrophic accident. The individual's expected utility is determined to be 11.262, and they are asked to determine the maximum amount they would be willing to pay for insurance. By solving the equation ln(2W) = .98ln(80,000) + .02ln(20,000), the individual finds that they are indifferent between the risky situation and certain wealth of $38,906.20, and therefore should be willing to pay $1,093.80 for insurance. There is also mention of using the utility of expected consumption, which would result in a willingness to pay of $600.
  • #1
surferbarney0729
32
0
I understand the idea of the questio, but am perplexed as what to put in the equation to get it to equal $38906.20

Here is the question and answer
Your utility function is U = ln(2C) where C is the amount of consumption you have in
any given period. Your income is $40,000 per year and there is a 2% chance that you
will be involved in a catastrophic accident that will cost you $30,000 next year

I have solved the first parts, and EU is 11.262, but the last section is confusing me

What is the most that you would be willing to pay for insurance, given your utility
function?

To answer this question, first go back to the original utility to determine how much
money would yield the same utility as the expected utility of taking the risk. The wealth
that would yield utility of 11.262 solves ln(2W) = .98ln(80,000) + .02ln(20,000), so W =
exp(.98ln(80,000) + .02ln(20,000))/2 ≈ $38,906.20. You are indifferent between the risky
situation and certain wealth of $38,906.20 because they yield the same utility. Therefore,
you should be willing to pay $40,000 – 38,906.20 = $1,093.80 for insurance.

Any help on what my equation needs to look like to get 38,906.20?
 
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  • #2
It looks to me like you solved it. Can you clarify what your question is?

By the way, you are looking at expected utility. I could argue that the more correct method is utility of expected consumption. In that case I would be willing to pay $600.
 

1. What is an equation utility function?

An equation utility function is a mathematical formula that represents the relationship between a set of inputs and the resulting output. It is used to quantify the value or usefulness of a particular decision or action.

2. How is an equation utility function used in decision making?

In decision making, an equation utility function helps to determine the best course of action by assigning a numerical value to each potential outcome. This allows for a quantitative comparison of different options and helps to inform decision makers on the most beneficial choice.

3. Can an equation utility function be applied to any situation?

Yes, an equation utility function can be used in a variety of situations, such as business decisions, economic analysis, and even personal decision making. It is a versatile tool that can be tailored to specific scenarios and variables.

4. What are the key components of an equation utility function?

The key components of an equation utility function are the inputs, which represent the different options or choices, and the output, which is the resulting value or utility. Other factors that may be included in the equation could be probability, risk, and personal preferences.

5. How can I create my own equation utility function?

To create your own equation utility function, you will need to identify the inputs, determine the desired output or utility, and then determine the mathematical relationship between the two. It is important to consider all relevant factors and test the function with different scenarios to ensure its accuracy and usefulness.

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