Skeleton Notes #8

Question 1

What do we assume about people with respect to income?

Answer 1

People generally have diminishing marginal utility

Question 2

An additional 10,000 has a _______ on utility/happiness/wellbeing when you start with 10,000

Answer 2

large effect

Question 3

An additional 10,000 has a ___________ on utility/happiness/wellbeing when you start with 70,000

Answer 3

relatively smaller effect

Question 4

Kahnemax and Deaton provide empirical evidence of the fact that people have generally diminishing marginal utility by measuring the effect of __________________

Answer 4

additional income on happiness, depression, stress, and career/life satisfaction

Question 5

What is the utility function based on income?

Answer 5

U(I)=sqrt(I)

Question 6

Draw a graph where you find the points where income is 25,000, 50,000, 75,000 with 100% certainty

Answer 6

skeleton 8.2

Question 7

Draw a graph where there is only a 50% chance that one will ever get 75,000, Perhapts due to an illness they have a 50% chance of only receiving 25,000. Show the expected income and expected utility for this person

Answer 7

E(I)=0.525+0.575=50
E(U)=0.55+0.58.66=6.83
Skeleton 8.2

Question 8

What does the graph on the right (skeleton 8.2) show about the relationship between level of certainty and utility?

Answer 8

Uncertainty lowers utility
The risk of a loss has a greater effect on U then the chance of a gain

Question 9

How much utility is lost when on goes from a guaranteed 50k to 25k

Answer 9

7.07-5=2

Question 10

How much utility is gained when one goes from a guaranteed 50k to 75k

Answer 10

8.66-7.07=1.6

Question 11

Due to diminishing marginal utility people prefer a _____ 50k over an ______ 50k

Answer 11

sure; uncertain

Question 12

a.) Jimmy is not guaranteed 75k, he has a probability ______ of being sick
b.) If he is sick he will lose the quantity q= _______
c.) Jimmy prefers a sure 50k over an uncertain 50k
What is the premium (r)?
If he gets sick he gets a payout of q=___________

Answer 12

p=0.5
q=75k-25k=50k
pg=0.550=25k
q=75k-25k=50k

Question 13

If jimmy is healthy his income Ih=
If Jimmy is sick, his income Is=
Thus his expected income with insurance E(I)p=

Answer 13

75000(inc)-25000(r)=50000
25000(inc)-25000(r)+50000(q)=50000
Ih=Is –> 50000

Question 14

Draw a graph of the role of insurance on utility and income

Answer 14

Skeleton 8.4

Question 15

How much utility/happiness does Jimmy gain due to the insurance contract?

Answer 15

Ui-Uui
7.07 - 6.83 = 0.24

Question 16

Draw a graph that depicts full and fair insurance

Answer 16

Skeleton 8.5

Question 17

How do you solve for q

Answer 17

Ih-Is –> full payout

Question 18

How to you solve for premium

Answer 18

r=p*q

Question 19

Draw graph depicting unfair insurance

Answer 19

Skeleton 8.5
r>p*g –> pay higher premium

Question 20

Draw a graph that depicts partial insurance

Answer 20

Skeleton 8.5
q<Ih-Is –> partial payout

Question 21

Lena has a 90% chance of being healthy for the entire year. If that happens, they make 360,000. In the chance that they get sick, their income is only 100000 (other family members work). Calculate her income and utility levels with no certainty for the healthy and unhealthy states. Also show her income and utility levels adjusting for uncertainty (uninsured). p=0.1

Answer 21

Iu=360000
Is= 100000
Uh=sqrt(360000)=600
Us=sqrt(100000)=316
E(I)=0.1(100000)+0.9(360000)=334k
E(U)=0.1(316)+0.9

Question 22

Lena has a 90% chance of being healthy for the entire year. If that happens, they make 360,000. In the chance that they get sick, their income is only 100000 (other family members work). Calculate the premium and payoff for a full and fair insurance contract for Lena p=0.1
q=
r=
Iins=
U(Iins)
UGain

Answer 22

q=Ih-Is=360000-100000=260000

r=pg= 0.1260000=26000

Iins=0.1(100000)+0.9(360000)=334000

U(Iins)=sqrt(334000)=577
Uui=0.1(316)+0.9(600)=572

UGain= U(Iins)-U(ui)= 577-572=5