Chapter 7, Problem 7RQ

a

To determine

Average point for each week and reason for lower average after 1^st week.

Answer to Problem 7RQ

The average was always lower than his current week’s quiz because when Marginal cost is less than the Average cost is less than the Average Cost, then the AC also comes down.

Explanation of Solution

Given information:

The grading is based on 10 weekly quizzes, where each quiz has a maximum of 100 points. Late Bloomer receives a 10 in the first quiz and gets an increment of 10 points in each successive test ending with a 100 in the final quiz of the year.

Late Bloomers average after the weeks starting from the 1st week:

  $1^{st}$ Week Average;

10

  $2^{nd}$ Week $score=20$ , $2^{nd}$ Week Average;

  $\begin{array}{l}=\frac{10+20}{2}\\ =15\end{array}$

  $3^{rd}$ Week $score=30$ , $3^{rd}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30}{3}\\ =20\end{array}$

  $4^{th}$ Week $score=40$ , $4^{th}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30+40}{4}\\ =25\end{array}$

  $5^{th}$ Week $score=50$ , $5^{th}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30+40+50}{5}\\ =30\end{array}$

  $6^{th}$ Week $score=60$ , $6^{th}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30+40+50+60}{6}\\ =35\end{array}$

  $7^{th}$ Week $score=70$ , $7^{th}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30+40+50+60+70}{7}\\ =40\end{array}$

  $8^{th}$ Week $score=80$ , $8^{th}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30+40+50+60+70+80}{8}\\ =45\end{array}$

  $9^{th}$ Week $score=90$ , $9^{th}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30+40+50+60+70+80+90}{9}\\ =50\end{array}$

  ${10}^{th}$ Week $score=100$ , ${10}^{th}$ Week Average;

  $\begin{array}{l}=\frac{10+20+30+40+50+60+70+80+90+100}{10}\\ =55\end{array}$

After this week, his average was always lower than his current week’s quiz because when Marginal cost is less than the Average cost is less than the Average Cost, then the AC also comes down.

Economics Concept Introduction

Introduction:

Marginal cost is the addition to total cost when one more unit of output is produced.

Total cost is the sum of fixed and variable cost spent by the firm to produce the output.

b)

To determine

Average point for each week after professorial gift.

Answer to Problem 7RQ

All the average points were increased after professorial gift.

Explanation of Solution

Given information:

The grading is based on 10 weekly quizzes, where each quiz has a maximum of 100 points. Late Bloomer receives a 10 in the first quiz and gets an increment of 10 points in each successive test ending with a 100 in the final quiz of the year.

If 40 points are added to his score, then his weekly averages would be:

  $1^{st}$ Week Average;

  $\begin{array}{l}=40+10\\ =50\end{array}$

  $2^{nd}$ Week $score=20$ , $2^{nd}$ Week Average;

  $\begin{array}{l}=\frac{50+20}{2}\\ =35\end{array}$

  $3^{rd}$ Week $score=30$ , $3^{rd}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30}{3}\\ =33.33\end{array}$

  $4^{th}$ Week $score=40$ , $4^{th}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30+40}{4}\\ =35\end{array}$

  $5^{th}$ Week $score=50$ , $5^{th}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30+40+50}{5}\\ =38\end{array}$

  $6^{th}$ Week $score=60$ , $6^{th}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30+40+50+60}{6}\\ =41.66\end{array}$

  $7^{th}$ Week $score=70$ , $7^{th}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30+40+50+60+70}{7}\\ =45.71\end{array}$

  $8^{th}$ Week $score=80$ , $8^{th}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30+40+50+60+70+80}{8}\\ =50\end{array}$

  $9^{th}$ Week $score=90$ , $9^{th}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30+40+50+60+70+80+90}{9}\\ =54.44\end{array}$

  ${10}^{th}$ Week $score=100$ , ${10}^{th}$ Week Average;

  $\begin{array}{l}=\frac{50+20+30+40+50+60+70+80+90+100}{10}\\ =59\end{array}$

Economics Concept Introduction

Introduction:

The average was always lower than his current week’s quiz because when Marginal cost is less than the Average cost is less than the Average Cost, then the AC also comes down.

c)

To determine

Reason for U-shaped averages and its lowest point.

Explanation of Solution

Late Bloomer’s weekly averages are showing a U shape because the fixed marks get reduced over subsequent weeks and variable score keeps increasing over the subsequent weeks. So till the point that the fall in fixed marks is greater than the increase in the variable marks, the average keeps on decreasing then when the rise in variable marks becomes greater than the fall in fixed marks, the average starts increasing. The lowest average during the term was 33.33.

Economics Concept Introduction

Introduction:

The average was always lower than his current week’s quiz because when Marginal cost is less than the Average cost is less than the Average Cost, then the AC also comes down.

d)

To determine

Reason for U-shaped curve due to presence of fixed cost.

Explanation of Solution

This presence of fixed 40 marks lead to an increase of average in the initial part which is initially concentrated over a few quizzes in the beginning. Hence, increasing the average by a big way and then the effect subsequently keeps decreasing and the effect of increase in variable marks takes over, thereby leading to a U shaped curve.

Economics Concept Introduction

Introduction:

The average was always lower than his current week’s quiz because when Marginal cost is less than the Average cost is less than the Average Cost, then the AC also comes down.