Answers
Answers Exercises Welfare State Economics
- Course
- Institution
- Book
Answers to the working group exercises
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
Welfare State Economics - Active Labour Market Policies Extra scheme
-
Welfare State Economics (WSE) - Important terms/concepts
-
Samenvatting van het vak Economics of the Welfare State aan de VU Amsterdam
4 reviews
By: mouradmejdi95 • 4 year ago
By: sockiej • 5 year ago
By: Svanderzwan8 • 4 year ago
By: neelchakravarty • 5 year ago
Seller
Follow
leidenab123
Reviews received
Content preview
Week 2 Insurance Theory1. Suppose you think that poorly educated families are less able to smooth consumption
in the absence of unemployment insurance than are well-educated families. How would
you empirically test this supposition? What types of data do you want to use?
(1) Low-middle-high education and unemployment insurance. Through regression analysis
(2) Consumption smoothing; unemployment insurance; pensions, an income you take from
your current self and transfer it to your future-self (saving to smooth consumption)
(3) Select families high education and low education in sample, to minimize the variation of
education levels within family.
2. Your utility function U = ln(2C) where C is the amount of consumption you have in a
given period. Your income is 40,000 euro per year and there is a 2% chance that you
will be involved in a catastrophic accident that will cost you 30,000 euro next year.
a. What is your expected utility without insurance?
Expected utility: E(U) = Ū = p1U(y1) + p2U(y2)
P1 = 0.02 P2 = 0.98
Y1 = ln(2*10.000) Y2 = ln(2*40.000)
E(U) = Ū = 0.02 * ln(2C) + 0.98 * ln(2C)
E(U) = Ū = 0.02 * ln(2*10.000) + 0.98 * ln(2*40.000)
E(U) = Ū = 11,26
Its the weighted average of 2 possible points of utility depending on the likelihood of the 2
occasion.
b. Calculate an actually fair insurance premium. What would your expected utility be
were you to purchase the actuarially fair insurance premium?
Actuarial premium = p1 (Y2 – Y1)
0.02 * (40.000-10.000)
0.02 * (30.000)
= 600
Actuarial fair insurance premium (AFIP): It just covers the costs of a bad event, not making a
profit. Look at the probability of that bad event and the costs of that event.
You lost 30K at the probability 0.02% that you will lose income. He is willing to pay €600 as
a premium for a certain income. You have to deduct the 600 form the 40.000 since that’s the
premium, but in return you have the certainty of having an income equal to 40.000-600 =
39.400€ (total income – premium). <U = log (2* 39.400) = 11.27 > What you see its
beneficial for him to pay insurance.
1
,c. What is the most that you would be willing to pay for insurance, given your utility
function?
ln(2*40.000-p) = 11.26
2(40.000-p) = e11.26
40.000-p = (e11.26)/2)
P = 40.000 – ((e11.26/2)
P = 40.000 – 38.906 = 1.094
So utility without insurance should be equal to with insurance.
11.26205603 = log (2C)
C = (exp (11,26)/2) = 38,906 <You do the inverse of LN, so you get e11.26
40.000 – 38.906 = 1.094 < What you pay at maximum to get insured.
3. Chimnesia has two equal-sized groups of people: smokers and nonsmokers. Both
types of people have utility U = ln(C), where C is the amount of consumption people
have in any period. So long as they are healthy, individuals will consume their entire
income of 15,000 euro. If they need medical attention (and have no medical insurance),
they will have to spend 10,000 euro to get healthy again, leaving them with only 5,000 to
consume. Smokers have a 12% chance of requiring major medical attention, while
nonsmokers have a 2% chance.
Insurance companies in Chimnesia can sell two types of policies. The “low deductible”
(L-) policy covers all medical costs above 3,000 euro, while the “high-deductible” (H-
)policy only covers medical costs above 8,000 euro.
a. What is the actuarially fair premium for each type of policy and each group?
P1 = 12% Y1 = 15000
P2 = 2% Y2 = 5000
If either of them gets sick they both got to pay 10.000. The policy insures them both, so you
got to reduce the amount of 10.000 with the policy. There are 2 types or risks with 2 types of
insurances. This is from the perspective of the insurer. The costs are 10.000, but he covers
3000 or 8000. So the difference is 7000 or 2000.
L-policy (covers costs >3000€)
10.000 – 3000 = 7000€
Smokers: 12% * 7000 = 840€
Non-smokers: 2% * 7000 = 140€
H-policy (covers costs >8000€)
10.000 – 8000 = 2000€
Smokers: 12% * 2000 = 240€
Non-smokers: 2% * 2000 = 40€
2
, b. If insurance companies can tell who is a smoker and who is a nonsmoker and charge
the actuarially fair premiums for each policy and group, show that both groups will
purchase the L-policy.
In the first part of the formula the smoker or non-smoker uses the insurance so he has to pay
to premiums for either the H-policy or L-policy. In the second part of the formula you put the
risk that nothing happens and you just pay the premium. The formula which gives the highest
U (utility) will be picked. You need to check what gives the highest utility for them to pick a
policy.
U(y1) = ln(C-Mc-p)
U(y2) = ln(C-p)
P1 = 0.12
P2 = 0.88
Utility = p1 * ln(C-Mc-p) + p2 * ln(C-p)
Usmokers(L) = 0,12 * ln(15.000-3000-840) + 0,88 * ln(15.000-840) = 9.530
Usmokers(H) = 0,12 * ln(15.000-8000-240) + 0,88 * ln(15.000-240) = 9.506
Usmokers(N) = 0,12 * ln(15.000-10.000) + 0,88 * ln(15.000) = 9.483
In this option the smokers choose policy L because it gives the highest utility 9.530 > 9.506 >
9.483. Less insurance = less utility.
Unonsmokers(L) = 0,02* ln(15.000-3000-140) + 0,98 * ln(15.000-140) = 9.602
Unonsmokers(H) = 0,02 * ln(15.000-8000-40) + 0,98* ln(15.000-40) = 9.598
Unonsmokers(N) = 0.02 * ln(15.000-10.000) + 0.98 * ln(15.000) = 9.594
In this option the smokers choose policy L because it gives the highest utility 9.602 > 9.598>
9.594
3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller leidenab123. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $11.31. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67866 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now