a) Anna has utility function over her net income U (I ) = √I. Anna rides the train to work every day where she spends a lot of money on the train tickets. Some days the thought of cheating and not paying for the train ticket crosses her mind. However she knows that there is a ¼ probability of being caught in a given day if she cheats, and that the cost of the fine is $36. Her daily income is $100. What is the maximum amount that she will be willing to pay for one day train ticket? [Hint: by paying that amount she avoids the risk of getting a fine!]. b) Phil also faces the same dilemma every single day. But he has a utility function U(I)=I. His daily income is also $100. If the price of one day train ticket is 9.25, will Phill cheat or buy the train tickets? Will Anna cheat or buy the train tickets for this price?
