Question

In her communications course, Nancy takes two examinations. Her overall grade for the course will be the minimum of her scores on the two examinations. Nancy decides to spend a total 880 minutes studying for these two examinations. If she spends m, minutes studying for the first examination, her score on this exam will be x1 = m/5. If she spends m2 minutes studying for the second examination, her score on this exam will be X2 = m2/6. (a) Draw a "budget line” showing the various combinations of scores on the two exams that she can achieve with a total of 880 minutes of studying. The maximum score on each examination is 100. On the same graph, draw two indifference curves for Nancy. [10 marks) (b) Given that she spends a total of 880 minutes studying, Nancy will maximize her overall score by achieving a score of on the first examination and on the second examination. [6 marks) (c) Her overall score for the course will then be ___ [4 marks]

Answer 1

(a)

Total m = 880

where m = m1 + m2

Budget Constraint of Nancy: 880 = 5x1 + 6x2

6x2 = 880 - 5x1

x2 = 146.67 - 0.83x1

Slope of BC = 0.83

and since, the max score on each exam is 100. So, x1 <= 100 and x2 < = 100

Since, the overall score is the minimum of score obtained in two exams

So, Utility Function, U = Min (x1, x2)

। Tr KBc

(b)

at equilibrium, x1 = x2

Put x1 = x2 into the budget constraint,

880 = 5x1 + 6x1

x1* = 80 = x2*

So, Overall score is acheived by scoring 80 in each exams.

(c)

Overall Score is the minimum of two score = Min(80, 80) = 80

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