Topic 1: Risk adversion and Insurance Flashcards
What property of utility functions make them risk adverse? Why?
- Decreasing marginal utility
- This means excess units of goods are les valuable then the previus goods of the same amount. As a result a 50-50 gamble is not very attractive to the consumer, as the amount they loose is of more value to them then the amount they gain.
How is expected utility calculated?
How is the maximum premium a consumer would purchase calculated?
By considering the amount of income/wealth that when guarentied would leave them exactly as well off (constant utility) as some lottery
In insurance, what is the actuarily fair premium rate?
The rate at which the insurance company will make zero profit, given the only cost is payouts.
In insurance, what is the risk premium?
The amount consumers will pay over the actuarily fair rate for insurance
In insurance, what is the certainty equivilent?
The amount of guarentied income that gives the same utility as some lottery.
what does this do??
In insurance, What is the maximum willingness to pay?
The risk premium + the expected loss, the maximum amount consumer will pay every month for insurance.
Draw a graph showing the payouts of a two prize lottery, with one line showing all lotteries with the same two outcomes, but different expected payoffs, and one showing lotteries with differing expected payoffs but no risk. In addition, describe indifference curves that could be on this graph, for both risk adverse and risk loving consumers
- risk loving: concave lines hitting constant payoff line on it’s axis intercept
- risk adverse: convex lines, intersecting with constant payoff lottery line at the intersection of the no risk lottery line, and tangent to it.
What does the line on this graph signify?
The line signifies the expected outcomes of a series of lotteries with a given set of outcomes, and a variable propability of one or the other occuring. Any point on the line is the expected income of such a lottery and the utility it would bring. The two points that intersect with the utility function are no risk lotteries, where the expected income is one of the two payoffs in the lottery.
Draw a graph showing a consumer who in a risky situation, gets 125 utility from an expected income of $400, and 125 utility from a guarentied income of $300. What is the risk premium for the consumer? If the high outcome in the lottery is $520 then what is the maximum willingness to pay, act fair premium and certainty equivilent?
Risk premium = $100
Actuarily fair premium = $120
Maximum willingness to pay = $220
Certainty equivilent = $300
