<blockquote>
  <p>Consider a society of individuals who receive an income of \$10, 000 pesos if they are healthy and \$100 pesos if they are sick. There are two types of individuals: some who get sick with a probability of p and others who are sick with probability of p′ bigger than p. There are equal numbers of
  individuals of each type in the population. All individuals are CRRA expected utility maximizers
  with the relative risk-aversion coefficient equal to 1</p>
  
  <p>a) supposing insurance companies can observe the agents’ types, what are the actuarially fair
  rates they would charge each type for insurance?</p>
</blockquote>

<p>a) R1= p, R2=p´ </p>

<blockquote>
  <p>b) supposing insurance companies can’t observe the types, what would be the actuarially fair rate
  they would charge if every individual were obliged to buy insurance ?</p>
</blockquote>

<p>b) R=1/2p+1/2p´ </p>

<blockquote>
  <p>c) if only full insurance is available, which agents would insure at the rate in (b)? Does your
  answer depend on the probabilities of being sick?</p>
</blockquote>

<p>c) Individuals who are sick because they have p´bigger than p </p>

<blockquote>
  <p>d) given your answer in (c), would the insurance companies be willing to offer such a rate if
  individuals were free to choose, whether to buy insurance or not?</p>
</blockquote>

<p>d) No, because they only attract sick customers. </p>

<blockquote>
  <p>e) if an insurance company could offer people who choose not to be insured in (c) a partial insurance contract, can it profitably do so? What is the most insurance that can be offered.</p>
</blockquote>

<p>e) By incentive compatibility constraint</p>

<blockquote>
  <p>f) is your answer in (e) Pareto efficient? If not, could the inefficiency be resolved by forcing
  everybody to buy insurance? Explain</p>
</blockquote>

<p>I can not answer f) Pareto efficiency</p>

CC BY-SA 4.0
2019-05-20T15:55:26.490Z
Why don't you show us what you have done so far?
Bayesian
CC BY-SA 4.0
2019-05-20T16:00:21.017Z
a) R1= p,  R2=p´       b) R=1/2p+1/2p´      c) Individuals who are sick  because they have p´bigger than p          d) No, because they only attrack sick customers.     e) By incentive compatibility constraint
bernda
<microeconomics>
I can not answer f) Pareto efficiency
bernda
# I can not answer f) Pareto efficiency

(Asked by: username_0 on 2019-05-20)

> Consider a society of individuals who receive an income of \$10, 000 pesos if they are healthy and \$100 pesos if they are sick. There are two types of individuals: some who get sick with a probability of p and others who are sick with probability of p′ bigger than p. There are equal numbers of
> individuals of each type in the population. All individuals are CRRA expected utility maximizers
> with the relative risk-aversion coefficient equal to 1
>
> a) supposing insurance companies can observe the agents’ types, what are the actuarially fair
> rates they would charge each type for insurance?

a) R1= p, R2=p´

> b) supposing insurance companies can’t observe the types, what would be the actuarially fair rate
> they would charge if every individual were obliged to buy insurance ?

b) R=1/2p+1/2p´

> c) if only full insurance is available, which agents would insure at the rate in (b)? Does your
> answer depend on the probabilities of being sick?

c) Individuals who are sick because they have p´bigger than p

> d) given your answer in (c), would the insurance companies be willing to offer such a rate if
> individuals were free to choose, whether to buy insurance or not?

d) No, because they only attract sick customers.

> e) if an insurance company could offer people who choose not to be insured in (c) a partial insurance contract, can it profitably do so? What is the most insurance that can be offered.

e) By incentive compatibility constraint

> f) is your answer in (e) Pareto efficient? If not, could the inefficiency be resolved by forcing
> everybody to buy insurance? Explain

I can not answer f) Pareto efficiency

**Tags:** microeconomics

> **Comments:**
> **username_1**: Why don't you show us what you have done so far?  
> **username_0**: a) R1= p,  R2=p´       b) R=1/2p+1/2p´      c) Individuals who are sick  because they have p´bigger than p          d) No, because they only attrack sick customers.     e) By incentive compatibility constraint  

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## 0 answers

