Mathematics for Management -- Supplementary Electronic Materials

Marginal Analysis & Approximation using Increments

After having worked through the electronic materials (set of notes and video clips), please self-evaluate your learning progress by completing the following quiz. Therefore, please check the correct answer of each of the given questions (single choice) and press the submit button after you completed all 10 questions. (Sometimes the page needs a reload such that the grading script starts to work.)

Your selections will persist so that you can review your answers in case you did not achieve the complete grade. At the bottom of the page you can also find the solution key.

1. The marginal cost at an output level of \(10\) is equal to

the slope of a line drawn tangent to the total cost curve at the output level of \(10\) the total cost of \(10\) units of output divided by \(10\) the average cost of \(10\) units of output. the slope of a ray drawn from the origin to the point on the total cost curve at an output level of \(10.\)

2. Given the following total utility schedule, what is the marginal utility if the third unit consumed? \[ \begin{array}{r || c c c c c} {\text{quantities consumed}} & 0 & 1 & 2 & 3 & 4 \\ \hline {\text{utility}} & 0 & 100 & 150 & 180 & 200 \end{array} \]

\( 20 \) \( 30 \) \( 60 \) \( 200 \)

3. Given the following total utility schedule, what is the marginal utility if the third unit consumed? \[ \begin{array}{r || c c c c c c} {\text{quantities consumed}} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline {\text{utility}} & 0 & 100 & 200 & 270 & 320 & 350 \end{array} \]

\( 1 \) \( 2 \) \( 3 \) \(4 \)

4. A firm produces \(500\) units per week. It hired \(20\) full-time workers (\(40\) hrs/week) at an hourly wage of \(15\) GEL. Raw materials are ordered weekly, and they cost \(10\) for ever unit produced. The weekly cost of the rent payment for the factory is \(2 250\) GEL. How do the overall costs break down?

Total variable cost is \( 17000\) GEL, total fixed cost is \( 2250\) GEL, and total cost is \( 19250\) GEL. Total variable cost is \(12000\) GEL, total fixed cost is \(7250\) GEL, and total cost is \(19250\) GEL. Total variable cost is \(5000\) GEL, total fixed cost is \(7250\) GEL, and total cost is \(19250\) GEL. Total variable cost is \(5000\) GEL, total fixed cost is \(2250\) GEL, and total cost is \(7250\) GEL.

5. A retailer has to pay \(9\) GEL per hour to hire \(13\) workers. If the retailer only needs to hire \(12\) workers, a wage rate of \(7\) GEL per hour is sufficient. What is the marginal cost of the \(13\)th worker?

\( 117 \) \( 9 \) \( 33 \) \( 84 \)

6. A company is producing \(15000\) units. At this output level, marginal revenue is \(22\) GEL, and the marginal cost is \(18\) GEL. The firm sells each unit for \(48\) GEL and average total cost is \(40\) GEL. What can we conclude from this information?

The company is making a loss. The company needs to cut production. The company needs to increase production. Not enough information is provided.

7. Given a revenue function \(R(x) = 15x - 0.08 x^2\) and a cost function \(C(x) = 25x + 0.13 x^2\). What is the corresponding marginal profit function?

\( 10 x + 0.21 x^2 \) \( 10 + 0.42 x \) \( -10 x - 0.21 x^2 \) \( -10 - 0.42 x \)

8. The cost of producing \(x\) copies of an edition of your newspaper is given by \(C(x) = 30 + 0.10x + 0.001 x^2\) GEL. Calculate the marginal cost if you have produced and sold \(500\) copies.

\( 1.1 \) GEL per additional day \( 1.1 \) GEL per additional \(500\) copies \( 1.1 \) GEL per additional copy \( 1.1 \) GEL

9. A firm is producing \(1000\) units at a total cost of \(5000\) GEL. If it were to increase production to \(1001\) units, its total cost would rise to \(5008\). What does this information tell you about the firm?

Marginal cost is \(5\) GEL, and average variable cost is \(8\) GEL. Marginal cost is \(8\) GEL, and average variable cost is \(5\) GEL. Marginal cost is \(5\) GEL, and average total cost is \(8\) GEL. Marginal cost is \(8\) GEL, and average total cost is \(5\) GEL.

10. A firm is producing \(20\) units with an average total cost of \(25\) GEL and marginal cost of \(15\) GEL. If it were to increase production to \(21\) units, which of the following must occur?

Marginal cost would decrease. Marginal cost would increase. Average total cost would decrease. Average total cost would increase.

Your grade is: __ of 10

In case you cannot find the correct answers even after reviewing the electronic materials again, please click on the "+" sign to read more.

Solution: 1a; 5b; 3c; 4a; 5c; 6c; 7d; 8c; 9d; 10c

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.