1.8 Decision making with risk Flashcards
What is the difference between risk and uncertainty and what are we going to deal with?
risk: facing an uncertain but quantifiable future ( e.g. you don’t know if its going to rain tomo or be sunny but a meteorologist can assign probabilities to these events.
uncertainty: facing an uncertain and unquantifiable future
What do agents use which allows them to choose between risky alternatives?
Lotteries
What is a lottery and show the mathematical distrubtion of it?
A lottery is a random variable with a probability distribution:
• List of different outcomes that might happen (in different ‘states of nature’) ( x1, x2 … xn)
• Probability associated with each outcome (or state) ( Pie1 )
Use this to make a lottery, if you flip a coin and get heads you win £10, if you get tails you lose £1
Example 2: you have £100 and are considering paying £1 for a lottery ticket.
There is a one in a thousand chance of winning, in which case you win £1000.
Otherwise, you get nothing! ( showcase this in a lottery)
How do we rank lotteries, which allow us to determine whether someone takes on a gamble? ( KEY)
We find out the Expected Utility the lotteries or the initial wealth, which gives the highest Expected utility is the one you choose.
What is the mathematical formula for expected utlitiy and what is expected utility theory? If there is no utility function then what?
We cant use the expected utility formula, hence we don’t know, we will need to find out what type of risk appetite the person has.
There is no right or wrong answer…which you prefer depends on your
preferences and your initial level of wealth.
Although we could look at the spread of wealth of the 2 random variables and deduce from there.
Lets say initial wealth is £100, what is the state of nature for each lottery in the good state and bad state?
1) good state it is 121 bad state 19.
2) good state it is 169 bad state is 64
3) good state is 225 bad state is 16.
As the individual will pick the lottery that maximises his expected utility, we find the expected utility of each one. Remember we do the same thing for his initial wealth, this is if he takes none of the lotteries.
If the income rises, will the answer change e..g to £1000?
Yes it will, actually lottery 3 ranks the highest.
Why is expected utility subjective and when is it not?
The probabilities often based on individual beliefs about the future.
Sometimes probability is based on an objective process, where there isn’t much scope for psychology. e.g. flipping a coin the probability is half half.
What is a really important property of expected utility?
It is cardinal
What does it mean that Expected Utility is cardinal?
You cannot do a monotonic transformation of utility functions can keep the preference ordering across lotteries the same. e.g. if i square the utlitiy function, i change my risk appeite.
So what does the utility function tell us?
It tells us the shape of the function.
What does the 3 attitudes to risk and what are their shapes?
Risk averse- individual has a concave shape from origin its slope gets flatter as wealth increases.
Risk loving - individual has a convex shape from origin its slope gets steeper as wealth increases.
Risk neutral - has a linear utility function
What is the difference between Expected utility and Expected value?
The Expected value for an outcome = sum of values of each outcome, weighted by the probaility of each outcome ( like mean)
The Expected utility = probability of each outcome, weighted by utility of each outcome
What does the expected value mean in words compared to expected utlitiy?
TBA
For each case what is higher the Expected value or expected utility?
Risk adverse -the utility of expected value of a lottery is
higher than the expected utility of playing the lottery for a risk averse person.
Risk loving - the utility expected value of a lottery is
lower than the expected utility of playing the lottery for a risk loving person.
Risk natural = the utility expected value of lottery = expected utility of the lottery.
We will see later on.
Why is it for a risk adverse person the shape is concave utility function?
Diminishing marginal utility of income - the additional utility of money, gets lower and lower, as you get more money. Because a risk averse person obtains more utility from certain income than from risky income, it follows that a smaller amount of certain income generates the same utility as the risky income.
Why is it for a risk loving person has a convex utility function?
Increasing marginal utility of wealth - the additional utility of money, gets higher and higher as you get more money. Because a risk loving person obtains less utility from certain income than from risky income.
Why does a risk neutral person have a linear utility function?
Constant marginal utility of income. if he is indifferent between a certain given income and an uncertain income with the same expected value. so his marginal utility remains constant with an increase in income.
Show some examples of utility functions of a risk adverse person?
U(w) = log(w)
Show some an example of a risk loving and risk neutral utility function?