<p></p><p>1.Mr. F. Slob (risk neutral) is thinking of joining a gym. He does not know whether he will have the resolve to frequent the gym once he has paid the membership fee. He could (i) do nothing, (ii) join now for a year and pay £400 membership fee, or (iii) opt for a £50 one month trial membership and decide at the end of the month whether to join for the rest of the year for an additional £400. If he turns out to like the gym, which happens with probability p, his benefit from membership is £800. </p><p>(a) 1.Draw a decision tree and find the optimal decision for all p </p><p>(b) Graph the EVPI as a function of p.</p><p>      </p><p>2.Toby is indifferent between $7 for sure and a lottery with a 50% chance of payoff<br/>zero and a 50% chance of payoff $20.<br/>(a) Show that this is consistent with Toby’s utility of money function U(x)=1-ax<br/>where a=0.93807.<br/>(b) Show that Toby prefers $1 for sure to a lottery with a chance p of payoff Z and<br/>1-p of payoff zero, for any positive Z, if p<0.06. </p>