Consider a contest between two competitors, A and B, for a prize totaling $50.Holding the effort of contestant B constant, consider the decision by contestant A between "high" effort, costing $7, and "low" effort, costing $4.Suppose the probability that A will win is .60 if she chooses high effort, and .40 if she chooses low effort.

(a)Suppose first that the reward scheme is "all or nothing."That is, whichever contestant wins receives the entire prize of $20.Show that contestant A will choose high effort.

(b)Now suppose a graduated prize is put in place, where the winner receives $30 and the loser receives $20.Show that contestant A now chooses low effort.