Suppose a student has no more than t minutes to write an examination consisting of two questions, 1 and 2. He receives A points if he gets question A correct and B points if he gets question 2 correct. He knows that if he spends s minutes in question 1 (a) the probability that he gets it correct is p (s); and (b) the probability that he gets the second one correct is q (t s): You know that p (s) is increasing in s and q (t s) is decreasing in s. In addition, assume there is no partial credit, and the student receives constant marginal utility for additional points.

(a) Derive the equilibrium conditions for his optimal allocation of time between the two questions.

(b) Does he put more or less time into the question he knows more about to start with?

(c) How is his allocation a§ected by a change in A and B?