Lerato can play squash better than tennis. If she were to enter an amateur squash championship she would have a 70% chance of winning the tournament...

Lerato can play squash better than tennis. If she were to enter an amateur squash championship she would have a 70% chance of winning the tournament and receive R900 as prize money. If, on the other hand, she were to enter an amateur tennis championship, her winning chances would be reduced to 30%, but she would stand to win more than double the prize money at R2,500. 

If Lerato were to enter either one of the championships but does not win the trophy, she would still receive R100 just for participating and irrespective of how far she goes through the draw. 

Lerato's utility function is  √ , where U=utility and I =income. 

Answer the following questions. Show all the steps involved in your calculations and explain your answers. 

(a) Calculate Lerato's expected income from playing squash and tennis respectively. 

(b) Calculate Lerato's expected utility from playing squash and tennis respectively. 

(c) Given the form of Lerato's utility function, is she risk loving, risk neutral or risk averse? 

(d) Calculate the variances (ie standard deviations) associated with the payoffs of playing tennis and squash, respectively. 

(e) Calculate the variances (ie standard deviations) associated with the utility of playing tennis and squash, respectively. 

(f) Based on your answers to the questions (a) to (e), advise Lerato on which tournament to enter.