ACCPT2- Uncertainty Flashcards
Which are the 2 states which exist?
The good state and the bad state, where consumption is CG and CB respectively.
How do can an individual be in-between the 2 states of consumption?
An individual can buy k units of insurance which pays out k in the bad state and costs γ per unit
Is the probability of the bad event known? If so, what is it?
The bad event happens with known probability π [hence the probability of the good event is (1-π)]
What are the individuals endowments?
The individual has an endowment of consumption in the good and bad state of EG and EB respectively
What do we say the uncertain situation represents?
A risky prospect
What do we call it when γ = π, and what does this mean?
- When γ = π we called this actuarially fair
* The expected consumption is equal at all points on the budget line
What 3 types of individual are there and what are the shapes of their indifference curve?
- Risk-loving - concave indifference curve
- Risk-neutral - straight-line indifference curve
- Risk-averse - convex indifference curve
On which line will a risk averse person’s tangency fall, when there is actuarially fair insurance, and what does this mean?
On the 45 degree line, which is significant as it means that the person has full insurance- and bears no risk at all
Would a low-risk individual have a steeper or flatter budget line and indifference curves?
A low risk individual would have a flatter budget line than a higher risk individual; therefore their indifference curves will also be flatter.
What will high-risk individuals do if offered low-risk fair insurance? What will low-risk individuals do if offered high-risk insurance?
- High-risk individuals will over-insurance if offered low-risk prices
- Low-risk individuals will under-insure if offered high risk prices
What happens if the consumer buys no insurance?
They remain at their original endowment point, EG and EB
What is an individuals consumption in the good state?
CG = EG - γk
What is an individuals consumption in the badd state?
CB = EB + K(1-γ)
What is a?
a = EB + (1-γ) EG/γ
What is the slope of the budget line?
-γ/1-γ
What is different about the utility function under uncertainty?
It is only an expected utility function as the individual doesn’t know for certain whether they will be in the good or bad state.
What is another name for the expected utility function?
The von Neumann-Morgenstern utility function
What is the expected utility function?
EU(CB,CG;π)=πU(CB)+(1-π)U(CG)
Is the expected utility curve linear?
Yes
What is the MRSBG?
γ/(1-γ)
How do we check if an individual is risk averse just by looking at their utility function?
We check the second derivative of their utility function, if it is less than 0, they are risk averse
How do we solve a problem?
Input what we know, then input the equations for Cb and Cg and solve to find k, Cg and Cb*
Is a risk averse person’s utility function convex or concave?
A risk averse person’s utility function is concave- i.e utility as a function of consumption is increasing, but at a decreasing rate.
If a risk-averse individual’s utility function is convex, what does this mean for the first and second derivative of this function?
- U’(C) > 0
* U’‘(C) < 0
How do we calculate expected consumption?
EC = πCb + (1-π)Cg
Why is the EU lower than U(EC)?
As EC is not a guaranteed level of consumption, and the utility function shows us what happens when a guaranteed level of consumption is translated into utility
How many values will we get for CEC and why?
We should get 2 values, as we are solving a quadratic
So how do we work out CEC?
- First calculate EU
* Then set the utility function = to the value of EU
The further the CEC is away from expected consumption, the more…
the penalty the individual fears from having a risky prospect, relative to a guaranteed consumption level.
