eco200_uncertainty_fall2009

# eco200_uncertainty_fall2009 - ECO 200 Microeconomic Theory...

This preview shows pages 1–5. Sign up to view the full content.

ECO 200: Microeconomic Theory Lecture notes on uncertainty and demand for insurance 1 Fall 2008 Carlos J. Serrano 1 Lecture notes updated on Nov. 1, 2009 at 8.28pm 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Summary Uncertainty Probability, expected value and variance Von Neumann utility function and contingent consumption bundles Variance and preference towards risk Risk premium and certainty equivalent Demand for insurance Fair insurance 2
1 Uncertainty and demand for insurance 1.1 Uncertainty 1.1.1 Probability and Expected Value Let be the set of outcomes of a random variable . Fo simplicity, just consider that a random variable is a variable that can take random values in the set and only in . Assume that the number of elements in is f nite and equal to . De f nition 1 A probability is a function that maps outcomes in the set X to real numbers satisfying that X =1 ( )=1 Example 2 Suppose that there are two outcomes such { =100  =20 } ;andtha t ( )=Pr( )=0 3 and ( )=  ( )=0 7 Note that Pr( )+  ( )=1 An very useful application of the theory of probabilities is the calculation of an expected value. De f nition 3 The expected value is the probability weighted average of the payo f sassoc i - ated will all possible outcomes Example 4 Let { = 100  =20 } and  ( )=0 3 and  ( )=0 7 The expected value of the random variable is ( )=  ( ) +  ( ) =30+14=44 Sometimes it is useful to obtain measures of the dispersion of the random variable  This is particularly interesting when two random variables have the same expectation. The dispersion of a random variable is associated to risk. For instance, two mutual funds can o f er you the same expected return, but the risk can be di f erent. How do we measure

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
De f nition 5 Thevar ianceo farandomevar iab le is  ( )= [( ( )) 2 ]= X =1 (Pr( )( ( )) 2 ) As you can see the variance is a measure of the dispersion of the outcomes from the mean weighted by how likely the outcomes are. Example 6 Whenthenumbero fe lemen tsinSistwo ,then  ( )=  ( )( ( )) 2 +  ( )( ( )) 2 Example 7 Let { =100  =20 } and  ( )=0 3 and  ( )=0 7  ( )=0 3 (100 44) 2 +0 7 (20
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

eco200_uncertainty_fall2009 - ECO 200 Microeconomic Theory...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online