Question

If there is no uncertainty in society,

it is possible for the probability of being sick to equal 20%

people will be willing to pay high premiums

the expected income when sick will always equal $100

the expected income when healthy will always equal $1 million

the probabilities of being healthy or sick is either 100% or zero %

Which of the following is true? With the assumption of risk-aversion and FAIR insurance, for a given probability of being sick and expected income,

utility with no insurance > utility from partial insurance > utility from full insurance

utility with no insurance > utility from partial insurance = utility form full insurance

utility with no insurance = utility from partial insurance = utility form full insurance

utility with no insurance < utility from partial insurance > utility form full insurance

utility with no insurance < utility from partial insurance < utility from full insurance

In 2018, Bannon's Income when sick = I_S , income when healthy = I_H , probability of being sick (p). The Expected Income = E(I₁₈)

In 2019, everything is the same except income when healthy is greater than in 2018. It is equal to: I_H + a

What will be the difference between E(I₁₉) and E(I₁₈) ?

a

IH + a

a x (p)

a x (1 - p)

a x IS

Answer 1

1)

In absence of uncertainty, every outcome is certain. So,

Correct option is

people will be willing to pay high premiums

2)

A risk averse cases, an agent will have a large utility for sure income will be higher. So, we can say that

In case of no insurance will be lowest

In case of full insurance, utility will be highest.

In case of partial insurance, utility will be in between.

Correct option is

utility with no insurance < utility from partial insurance < utility from full insurance

3)

Expected income in 2018

E(18)=p*IS+(1-p)*IH

Expected income in 2019

E(19)=p*IS+(1-p)*(IH+a)

E(19)-E(18)=p*IS+(1-p)*(IH+a)-[p*IS+(1-p)*IH]

E(19)-E(18)=a(1-p)

Correct option is

a x (1 - p)