1. A football fan has a utility of wealth U(w) = (w 1). a) Show that the football fan is: i) non-satiated and, ii) risk averse [2 marks] b) Calculate the coefficient of relative risk aversion and explain what this result conveys. [2 marks] Before the UEFA Champions League starts, the football fan intends to place bets on two teams winning the trophy: Paris Saint Germain and Chelsea. The table below shows the fan's regular betting house pay-outs for a 1 bet on each of these teams, and the football fan's estimated probabilities of each team winning. Team Paris Saint Germain Chelsea Winning pay-out per 1 bet 4.0 1.0 Probability of winning 0.2 0.7 The football fan has a total wealth of 100 and they will be all of their wealth on this championship. Negative bets are not allowed. The pay-out is the total amount of money given back to the customer by the betting house if they win the bet. c) Calculate the amount they should bet on each team to maximise their expected utility of wealth. [5 marks) d) Calculate the expected utility from wealth resulting from the bets in part c). [2 marks] e) Compare the expected utility from the bets with the utility of the football fan's initial wealth. Explain why they are different [4 marks) 1) State whether the football fan would put their money on these two teams winning the UEFA Championship at the pay-outs offered. Explain your answer. [2 marks) [Total: 17 marks) 1. A football fan has a utility of wealth U(w) = (w 1). a) Show that the football fan is: i) non-satiated and, ii) risk averse [2 marks] b) Calculate the coefficient of relative risk aversion and explain what this result conveys. [2 marks] Before the UEFA Champions League starts, the football fan intends to place bets on two teams winning the trophy: Paris Saint Germain and Chelsea. The table below shows the fan's regular betting house pay-outs for a 1 bet on each of these teams, and the football fan's estimated probabilities of each team winning. Team Paris Saint Germain Chelsea Winning pay-out per 1 bet 4.0 1.0 Probability of winning 0.2 0.7 The football fan has a total wealth of 100 and they will be all of their wealth on this championship. Negative bets are not allowed. The pay-out is the total amount of money given back to the customer by the betting house if they win the bet. c) Calculate the amount they should bet on each team to maximise their expected utility of wealth. [5 marks) d) Calculate the expected utility from wealth resulting from the bets in part c). [2 marks] e) Compare the expected utility from the bets with the utility of the football fan's initial wealth. Explain why they are different [4 marks) 1) State whether the football fan would put their money on these two teams winning the UEFA Championship at the pay-outs offered. Explain your answer. [2 marks) [Total: 17 marks)
