In her lastminute preparations for final exams a student has

In her last-minute preparations for final exams, a student has set aside five hours to split between studying for two subjects, finance and economics. Her goal is to maximize the average grade received in the two courses. (Note that maximizing the average grade and maximizing the sum of the grades are equivalent goals.) According to her best guesses, grades vary with study as follows: Study hours Finance Grade Study hours Economics Grade 0 70 0 75 1 78 1 81 2 83 2 85 3 88 3 87 4 90 4 89 5 92 5 90 a. List the marginal values of additional hours worked for each subject. b. How much time should the student spend studying each subject? c. c. Suppose the student also is taking an accounting exam and estimates that each hour of studying will raise her grade by three points. She has allotted two hours for studying accounting (in addition to the five hours already mentioned). Is this an optimal decision? Explain. (Assume her objective is to maximize her average grade across the three courses.)

Solution

Study hours Finance Grade Marginal Value Study hours Economics Grade Mearginal Value

0 70 0 0 75 -

1 78 3 1 81 6

2 83 5 2 85 4

3 88 5 3 87 2

4 90 2 4 89 2

5 92 2 5 90 1

b. Consumer is in equilibrium where marginal values for two subjcts are equal and sum of score of two subje t is maximum

Therefore, he is in equilibrium when he is spending 4 hours on Economics study and 1 hour on studying Finance because at this level Marginal values are equal.

Sum total in various combinations (5,0) (92,75) = 167

(4,1) (90,81) =171

(3,2) = (88,85) = 173

(2,3) = (83,87) = 170

(1,4) = (78,89) = 176

(0,5) = (70,90) = 160

Hence, he is in equilibrium when he is spending 1 hour in the study of Finance and 4 hours in the study of Economics.

c.

No, this is not an optimal decision. If he spends one hour on study of Finance, he can increase grades by 2 points which is less than 3. If he spends one hour on study of finance, he can increase his grades by 4. If he spends two hours on Economics, he can increase his grades by 6. If he divides two hours in this way that one hour is spent on Fiance and one on accounting then total increase in grades will be 4+3 = 7. . It could increase grade more than 6. Therefore, optimal decision is to spend 4 hours on the study of Fiance, 2 hours on the study of economics and 1 hour on the study of accounts.