Joe Bloggs, who is risk-averse, is a contestant on the ‘Open the Box’ quiz show. The worst and best outcomes on the show are £1,000 and £9,000. What is the lower bound for Joe’s utility U value of £4000? It is known that Joe is indifferent between an offer of £4000 from the quiz-master and the show offering probabilities of 0.3 and 0.7 for the worst and best outcomes respectively.

What is the lower bound of Joe’s utility value for an offer of £5000 from the quiz-master?

(Hint: utility U values for risk-averse are greater than those for risk-indifferent)

(Answer: U(4000) ≥ 0.375; U(5000) ≥ 0.76 )