25 marks

My von neumann morgenstann utility function over wealth is sqrt w. I am betting on my favourite football team (FFC) to win in a particular match. I think the probability of FFC winning is 0<-p<-1. If they win, my wealth will be wg and if they lose it will be wb. Explain all please.

a) 5 marks.

Am i risk averse or not? Write formula for my expected utility as a function of wg,wb and p.

b)7 marks.

If p=0.25, wg=1600 and wb=900. What certain amount of wealth gives same utility as expected utility of the bet? Calculate risk premium of the bet

c)7 marks

If my initial wealth is w and i think about how much, x, to bet of FFC winning, i think they will win with probability p. If bookmakers offer odds of q to 1 on FFC winning. For each 1 dollar i bet, i get dollar q plus 1 dollar if they win and loses if they lose. Write formula for my expected utility as a function of w,x,p and q. Use this to write conditions for optimal choice of x.

d) 6 marks

if w=1000$ and p=0.25. using answers before, how much will i bet if i am offered offs q=4? explain