Skeleton Notes #8 Flashcards
What do we assume about people with respect to income?
People generally have diminishing marginal utility
An additional 10,000 has a _______ on utility/happiness/wellbeing when you start with 10,000
large effect
An additional 10,000 has a ___________ on utility/happiness/wellbeing when you start with 70,000
relatively smaller effect
Kahnemax and Deaton provide empirical evidence of the fact that people have generally diminishing marginal utility by measuring the effect of __________________
additional income on happiness, depression, stress, and career/life satisfaction
What is the utility function based on income?
U(I)=sqrt(I)
Draw a graph where you find the points where income is 25,000, 50,000, 75,000 with 100% certainty
skeleton 8.2
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
E(I)=0.525+0.575=50
E(U)=0.55+0.58.66=6.83
Skeleton 8.2
What does the graph on the right (skeleton 8.2) show about the relationship between level of certainty and utility?
Uncertainty lowers utility
The risk of a loss has a greater effect on U then the chance of a gain
How much utility is lost when on goes from a guaranteed 50k to 25k
7.07-5=2
How much utility is gained when one goes from a guaranteed 50k to 75k
8.66-7.07=1.6
Due to diminishing marginal utility people prefer a _____ 50k over an ______ 50k
sure; uncertain
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=___________
p=0.5
q=75k-25k=50k
pg=0.550=25k
q=75k-25k=50k
If jimmy is healthy his income Ih=
If Jimmy is sick, his income Is=
Thus his expected income with insurance E(I)p=
75000(inc)-25000(r)=50000
25000(inc)-25000(r)+50000(q)=50000
Ih=Is –> 50000
Draw a graph of the role of insurance on utility and income
Skeleton 8.4
How much utility/happiness does Jimmy gain due to the insurance contract?
Ui-Uui
7.07 - 6.83 = 0.24
Draw a graph that depicts full and fair insurance
Skeleton 8.5
How do you solve for q
Ih-Is –> full payout
How to you solve for premium
r=p*q
Draw graph depicting unfair insurance
Skeleton 8.5
r>p*g –> pay higher premium
Draw a graph that depicts partial insurance
Skeleton 8.5
q<Ih-Is –> partial payout
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
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
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
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
