If a person if she writes the right answer for question #1, she will get A point

Question

If a person if she writes the right answer for question #1, she will get A points. The same condition for question #2 with B points.

But she only has t minutes for the exam. If she spends s minutes on the Q#1, (assume all her time is used up) then the probability that she gets Q#1 correct is p(s) and the Q#2 correct is q(t - s). p() is increasing (strictly) and concave. q() is also increasing (strictly) and concave. Let's assume no partial points are given and she gets constant marginal utility for additional credits.

(1) What are the equilibrium conditions for her optiomal allocation of time between Q#1 and Q#2? (Derive them)

(2) How does a change in A or B affect her allocation?

Explanation / Answer

Total marks on the exam are derived as

T = p(s) * A + q(t-s) * B

At equilibrium, the derivative of T would be equal to zero .

Differentiatin the equation , we get

0 = p`(s) A +(-) q`(t-s) *B

or, the equilibrium condition is

A/B = q`(t-s) / p`(s)

Since both the functions are strictly increasing and concave,

Any increase in one variable (A or B) will decrease the allocation to the same question respectively

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.