ACCPT2- Uncertainty

Question 1

Which are the 2 states which exist?

Answer 1

The good state and the bad state, where consumption is CG and CB respectively.

Question 2

How do can an individual be in-between the 2 states of consumption?

Answer 2

An individual can buy k units of insurance which pays out k in the bad state and costs γ per unit

Question 3

Is the probability of the bad event known? If so, what is it?

Answer 3

The bad event happens with known probability π [hence the probability of the good event is (1-π)]

Question 4

What are the individuals endowments?

Answer 4

The individual has an endowment of consumption in the good and bad state of EG and EB respectively

Question 5

What do we say the uncertain situation represents?

Answer 5

A risky prospect

Question 6

What do we call it when γ = π, and what does this mean?

Answer 6

• When γ = π we called this actuarially fair

* The expected consumption is equal at all points on the budget line

Question 7

What 3 types of individual are there and what are the shapes of their indifference curve?

Answer 7

• Risk-loving - concave indifference curve
• Risk-neutral - straight-line indifference curve
• Risk-averse - convex indifference curve

Question 8

On which line will a risk averse person’s tangency fall, when there is actuarially fair insurance, and what does this mean?

Answer 8

On the 45 degree line, which is significant as it means that the person has full insurance- and bears no risk at all

Question 9

Would a low-risk individual have a steeper or flatter budget line and indifference curves?

Answer 9

A low risk individual would have a flatter budget line than a higher risk individual; therefore their indifference curves will also be flatter.

Question 10

What will high-risk individuals do if offered low-risk fair insurance? What will low-risk individuals do if offered high-risk insurance?

Answer 10

• High-risk individuals will over-insurance if offered low-risk prices
• Low-risk individuals will under-insure if offered high risk prices

Question 11

What happens if the consumer buys no insurance?

Answer 11

They remain at their original endowment point, EG and EB

Question 12

What is an individuals consumption in the good state?

Answer 12

CG = EG - γk

Question 13

What is an individuals consumption in the badd state?

Answer 13

CB = EB + K(1-γ)

Question 14

What is a?

Answer 14

a = EB + (1-γ) EG/γ

Question 15

What is the slope of the budget line?

Answer 15

-γ/1-γ

Question 16

What is different about the utility function under uncertainty?

Answer 16

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.

Question 17

What is another name for the expected utility function?

Answer 17

The von Neumann-Morgenstern utility function

Question 18

What is the expected utility function?

Answer 18

EU(CB,CG;π)=πU(CB)+(1-π)U(CG)

Question 19

Is the expected utility curve linear?

Answer 19

Yes

Question 20

What is the MRSBG?

Answer 20

γ/(1-γ)

Question 21

How do we check if an individual is risk averse just by looking at their utility function?

Answer 21

We check the second derivative of their utility function, if it is less than 0, they are risk averse

Question 22

How do we solve a problem?

Answer 22

Input what we know, then input the equations for Cb and Cg and solve to find k, Cg and Cb*

Question 23

Is a risk averse person’s utility function convex or concave?

Answer 23

A risk averse person’s utility function is concave- i.e utility as a function of consumption is increasing, but at a decreasing rate.

Question 24

If a risk-averse individual’s utility function is convex, what does this mean for the first and second derivative of this function?

Answer 24

• U’(C) > 0

* U’‘(C) < 0

Question 25

How do we calculate expected consumption?

Answer 25

EC = πCb + (1-π)Cg

Question 26

Why is the EU lower than U(EC)?

Answer 26

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

Question 27

How many values will we get for CEC and why?

Answer 27

We should get 2 values, as we are solving a quadratic

Question 28

So how do we work out CEC?

Answer 28

• First calculate EU

* Then set the utility function = to the value of EU

Question 29

The further the CEC is away from expected consumption, the more…

Answer 29

the penalty the individual fears from having a risky prospect, relative to a guaranteed consumption level.