Re: Uncertainty - June 20
Posted by
anon_econ on
Jun 20, 2012; 1:52am
URL: http://discussion-forum.276.s1.nabble.com/Uncertainty-June-20-tp7578257p7578281.html
I see :-)
On Wed, Jun 20, 2012 at 5:53 AM, Amit Goyal [via Discussion forum]
<[hidden email]> wrote:
Hi Vasudha,
Your conclusion is correct and I could also see that you have right reasons is mind. The only thing that is missing is the convincing expressions. Here is how you prove it:
Given that the person is risk averse, his utility function for money will be a concave function.
Eu(Y + Z)
= E(Eu(Y + Z)|Y)
= pi(1) E(Eu(Y + Z)|Y = y(1)) + pi(2) E(Eu(Y + Z)|Y = y(2))
= pi(1) E(Eu(y(1) + Z)|Y = y(1)) + pi(2) E(Eu(y(2) + Z)|Y = y(2))
≤ pi(1) E(u(E(y(1) + Z)|Y = y(1))) + pi(2) E(u(E(y(2) + Z)|Y = y(2))) [By concavity of u(.)]
= pi(1) E(u(y(1))) + pi(2) E(u(y(2)))
= Eu(Y)
This automatically disproves (iii), (iv) and (v). For (i), just construct an example. As you said a risk loving person with appropriate choice of state space, pi, lotteries and utilities would do.