Relationship between Average Product and Marginal Product

UMGC – Rota u. Landstuhl Economics 203

Fall (ii) 2020 Exercise 4

Exercise 4 (25 points; 15 points individual; 10 point class (bonus) if each question answered in good faith;

due at beginning of Week 5 class)

Last Name, First Name:

Individual Score: (- = + /15

Class Score: + /10

Total Score: + /25

1. Question #1 Score (-0) = + /3

(On the relationship betweenAverage Product, and Marginal Product) (2 points)

Suppose the production function for a local hops grower is as follows:

Number of units of labor
Bushels of Hops produced

1
20

2
92

3
200

4
320

5
400

6
440

7
440

8
400

(a) What is the average product of labor when four units of labor is used?(Remember: AP = TP/L)

(.4 points)(-

Answer:Average Product =320/4

=80

(b) What is the marginal product of labor when between five and six units of labor are used?(Remember: MP = ∆TP/∆L) (.4 points)(-

Answer:Marginal Product =440-400

=40

Answer:

(d) At what level of output does average product equal marginal product? (.4 points)(-

Answer:When 5 units of labor are employed both average product and marginal product are 80

(e) When marginal product equals zero, what happens to total product? (.2 points) (-

Answer:The total product remains the same

At what level of output does this occur? (.2 points) (-Answer:When 7 units of labor is employed Marginal product is zero and total product is 440

2. Question #2 Score = (- = + /3.0

(On the relationship between marginal this and marginal that) (2 points)

(a) Suppose instead of 6 quizzes over 8 weeks our class had 10 quizzes over 12 week. And that each quiz was worth 100 points instead of 10 points. So you start off the semester well, but then your grades begin to slip a little until you recover later on, finishing the term with a bang. Specifically, your ten course grades are shown in the table below.

Quiz number
Quiz Score
Cumulative Quiz Score
Average Quiz Score
Marginal Quiz Score

1
82
82
82
–

2
74
156
78
74

3
68
224
74.7
68

4
72
296
74
72

5
77
373
74.6
77

6
83
456
76
83

7
86
542
77.4
86

8
88
630
78.75
88

9
90
720
80
90

10
100
820
82
100

(i) Fill in each of the blank cells in the Table above. (.75 points; .025 per cell)(-

(ii) Your grades begin to improve with your fourth quiz grade. Does your average quiz grade begin to increase with your fourth quiz grade as well? Why or why not? (.75 points)(-

Answer:The average quiz score began improving with 5th quiz grade.

(b) Suppose your friend’s Spring (ii) term-specific GPA (grade point average) is higher than her Spring (i) term-specific GPA. But that her overall (cumulative) GPA fell. Your friend then tells you that a mistake must have been made. Assuming the records are accurate, explain to your friend why this is possible. (.5 points)(-

Answer:

3. Question #3 Score = (- = + /3.0

(On costs!) Fill in the Table below. (It’s fun!) (See key below Table.)Round any values with decimal to one decimal place. (2 points; .0625 points per correct cell)

Q
TC
FC
VC
AC = ATC
AFC
AVC
MC

0
$80
80
0
______
_______
_______
_______

10
120
80
40
12
8
4
$4= ∆TC/∆Q = ∆VC/∆Q

20
$200
80
120
10
4
6
8

30
320
80
$240
10.7
2.7
8
12

40
480
80
400
12
2
10
16

50
680
80
600
$13.60
1.6
12
$20= ∆TC/∆Q = ∆VC/∆Q

Key: Q = output; TC = total cost; VC = variable cost; FC = fixed cost; AC = average total cost = TC/Q; AFC = average fixed cost = FC/Q; AVC = average variable cost = VC/Q; MC = marginal cost = ˙∆TC/∆Q = ∆VC/∆Q (so remember, ∆Q from 0 to 10 =10, from 10 to 20 = 10, etc.)(Hint: see red! Also, ask yourself, if Q = 0, what is VC?)

4. Question #4 Score = (- = + /3.0

(On explicit and implicit costs)

Suppose you’re considering owning your own restaurant. To do so, you’ll have to resign from your current job that pays $46,000 per year and cash in your life savings of $200,000, which you have invested in mutual funds that return an average of 6% per year. You estimate that you’ll have to spend $4000 during the year to maintain the equipment so that it maintains its market value of $200,000. It turns out that you currently own a building that you plan to use for your restaurant, which you currently rent out to others for $2500 per month. Finally, you anticípate that during the year you’ll spend $50,000 on food, $40,000 for labor, and $14,000 for utilities and supplies.

Compute the economic costs of operating the restaurant during the first year, making sure to identify the explicit and implicit costs. This total, by the way, is the amount of revenues you will need to achieve a zero economic profit.

Answer:

5. Question #5 Score = (- = + /3.0

For each of the UMUC events below (a)- (e), identify, as indicated, whether MC (marginal cost), AVC (average variable cost), AFC, (average fixed cost) and AC (average total cost) increase, decrease, or remain the same. For this exercise, think of the number of classes taught as the output, so that all variable costs are related to what’s necessary to produce an additional class. (2 points; .4 points per question; .1 point per answer)

Notes: Marginal Cost (MC)(For any given unit of output, if the cost of a variable input rises, so does the MC, which means, by the way, that the MC curve shifts up (to the left).)

Average Variable Cost (AVC)(Note: if MC rises, so does AVC and AC, which means, by the way, that the AVC and AC curves shift up,)

Average Fixed Cost (AFC) (If AFC rises, AC (averge total cost) also rises.)

(a) UMUC increases per-class payments to adjunct faculty.(-

Marginal Cost (MC) Answer:

Average Variable Cost (AVC) Answer: