Social Insurance
Social Insurance
ECON 3440
What Is Insurance?
An insurance premium is money paid to an entity so that an individual paying the premium will be insured against adverse events. The premium is paid in return for a guarantee of compensation given a specified adverse event (illness, death, auto accident, home fire, disability, etc.).
ECON 3440 - Prof. Wassall
Expected Value and Fair Premiums
Suppose that in 2009 Emily has a 1/10 chance of serious illness and resulting disability, and a 9/10 chance of good health. If illness strikes, she has to stop working for several months and loses
$30,000 of her $50,000 annual salary.
The Expected Value of her 2009 income:
EV = (0.1) * ($20,000) + (0.9)*($50,000) =
$47,000
An actuarially fair premium would charge
Emily the expected value of her loss, or $3,000.
ECON 3440 - Prof. Wassall
Why Would Emily Buy Insurance?
(A)
(B)
(C)
Income if She
Stays
Healthy
Income if
She Gets
Sick
Expected
Value
Insurance
Options
Income
Probability of Staying
Healthy
Probability of Getting
Sick
Lost
Income if
She Gets
Sick
Option 1: No
Insurance
$50,000
9 in 10
1 in 10
$30,000
$50,000
$20,000
$47,000
Option 2: Full
Insurance
($3,000 premium to cover $30,000 in losses $50,000
9 in 10
1 in 10
$30,000
$47,000
$47,000
$47,000
Actuarially Fair Insurance Policy
ECON 3440 - Prof. Wassall
Why Would Emily Buy Insurance?
Risk aversion. Emily, and most of us, are risk-averse. Our expected utility of income received when outcomes are uncertain is less than when the same income is earned with certainty. Consumption Smoothing. The translation of consumption from periods when consumption is high, and thus has low marginal utility, to periods when consumption is low, and thus has high marginal utility. The fundamental result of basic insurance theory is that individuals will demand full insurance in order to fully smooth their consumption across states of the world.
ECON 3440 - Prof. Wassall
Risk Aversion and
ECON 3440
What Is Insurance?
An insurance premium is money paid to an entity so that an individual paying the premium will be insured against adverse events. The premium is paid in return for a guarantee of compensation given a specified adverse event (illness, death, auto accident, home fire, disability, etc.).
ECON 3440 - Prof. Wassall
Expected Value and Fair Premiums
Suppose that in 2009 Emily has a 1/10 chance of serious illness and resulting disability, and a 9/10 chance of good health. If illness strikes, she has to stop working for several months and loses
$30,000 of her $50,000 annual salary.
The Expected Value of her 2009 income:
EV = (0.1) * ($20,000) + (0.9)*($50,000) =
$47,000
An actuarially fair premium would charge
Emily the expected value of her loss, or $3,000.
ECON 3440 - Prof. Wassall
Why Would Emily Buy Insurance?
(A)
(B)
(C)
Income if She
Stays
Healthy
Income if
She Gets
Sick
Expected
Value
Insurance
Options
Income
Probability of Staying
Healthy
Probability of Getting
Sick
Lost
Income if
She Gets
Sick
Option 1: No
Insurance
$50,000
9 in 10
1 in 10
$30,000
$50,000
$20,000
$47,000
Option 2: Full
Insurance
($3,000 premium to cover $30,000 in losses $50,000
9 in 10
1 in 10
$30,000
$47,000
$47,000
$47,000
Actuarially Fair Insurance Policy
ECON 3440 - Prof. Wassall
Why Would Emily Buy Insurance?
Risk aversion. Emily, and most of us, are risk-averse. Our expected utility of income received when outcomes are uncertain is less than when the same income is earned with certainty. Consumption Smoothing. The translation of consumption from periods when consumption is high, and thus has low marginal utility, to periods when consumption is low, and thus has high marginal utility. The fundamental result of basic insurance theory is that individuals will demand full insurance in order to fully smooth their consumption across states of the world.
ECON 3440 - Prof. Wassall
Risk Aversion and