workout doubt

[tanudas]

5.5 (1) In her communications course, Nancy also takes two examina-
tions. Her overall grade for the course will be the maximum of her scores
on the two examinations. Nancy decides to spend a total of 400 minutes
studying for these two examinations. If she spends m1 minutes studying
for the first examination, her score on this exam will be x1 = m1/5. If
she spends m2 minutes studying for the second examination, her score on
this exam will be x2 = m2/10. Draw two or three \indifference
curves for Nancy. Draw a "budget line" showing the various combi-
nations of scores on the two exams that she can achieve with a total of 400
minutes of studying.


6.11 (0) Richard and Mary Stout have fallen on hard times, but remain
rational consumers. They are making do on $80 a week, spending $40 on
food and $40 on all other goods. Food costs $1 per unit. On the graph
below, use black ink to draw a budget line. Label their consumption
bundle with the letter A.
(a) The Stouts suddenly become eligible for food stamps. This means
that they can go to the agency and buy coupons that can be exchanged
for $2 worth of food. Each coupon costs the Stouts $1. However, the
maximum number of coupons they can buy per week is 10. On the graph,
draw their new budget line with red ink.


6.12 (2) As you may remember, Nancy Lerner is taking an economics
course in which her overall score is the minimum of the number of correct
answers she gets on two examinations. For the first exam, each correct
answer costs Nancy 10 minutes of study time. For the second exam, each
correct answer costs her 20 minutes of study time. In the last chapter,
you found the best way for her to allocate 1200 minutes between the two
exams. Some people in Nancy's class learn faster and some learn slower
than Nancy. Some people will choose to study more than she does, and
some will choose to study less than she does. In this section, we will ¯nd
a general solution for a person's choice of study times and exam scores as
a function of the time costs of improving one's score.

(a) Suppose that if a student does not study for an examination, he or
she gets no correct answers. Every answer that the student gets right
on the first examination costs P1 minutes of studying for the first exam.
Every answer that he or she gets right on the second examination costs
P2 minutes of studying for the second exam. Suppose that this student
spends a total of M minutes studying for the two exams and allocates
the time between the two exams in the most e±cient possible way. Will
the student have the same number of correct answers on both exams?___
Write a general formula for this student's overall score for the
course as a function of the three variables, P1, P2, and M: S =___
If this student wants to get an overall score of S, with the smallest possible
total amount of studying, this student must spend ___minutes
studying for the first exam and ____ studying for the second exam.

[Rajat]

Hi Tanudas,
I am totally new to ISI course and examination pattern so want to know, where did you find these questions? Are such questions asked in the entrance examination ?

I will be taking ISI examination next year. (desperately want to get familiar with the kind of questions that are asked)

[tanudas]

Rajat, these questions are from the Varian workbook. For questions on micro, it is more than sufficient.

[Rajat]

5.5(1)
we have m1=5(X1) and m2=10(X2)

also, m1+m2 = 400
=> (x1)+2(x2) = 80 . This is the budget line for Nancy (while it is intuitively easier to imagine the budget line: m1 + m2 = 400 )

Utility for Nancy is U = Max(X1,X2)

Drawing Indifference Curves
Imagine the curve X2 = X1 (a straight line at 45 degree passing through origin). For any X1, the indifference curve for Nancy will be all X2 points above the line X2 = X1. Simlarly, for any X2, the indifference curve will be all X1 points to the left of X2 = X1.
Thus the indifference curves are L-shaped with the corner lying on the line X2 = X1.
Optimal choice will be the will be the intersection of the indifference curve and the budget line