Re: problem code : 140609MICRO

Posted by vishruti on Jun 16, 2009; 6:50pm
URL: http://discussion-forum.276.s1.nabble.com/problem-code-140609MICRO-tp3075741p3088155.html

the expected wealth is (1-p) ( w - xq) + p ( w -xq - d +x)

we have to maximize expected wealth wrt x

then we have p = q from first order condition

the condition is reduced to u'(w - d + x*- x*) = u'(w - x*)

because at x* First order condition is -q(1-p)u'(w-x*q) + p(1-q)u'(w-D + x*(1-p)) = 0

now since u'(.) is a decreasing function this implies

w - d +x*(1-p) = w - x*p

hence x*  = d , the optimum level of insurance

and it is fair because the final wealth is w - pd , weather loss occurs or not and the insurer is insured completely