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Tracy, the movie theater manager, wants to analyze the data she collected. Tracey will estimate some values that she will need to help her analyze the data. The workers contribute to both the areas and have an estimated number of workers she should hire so that her theater business can earn and profit the most. These data were organized using tables with workers' days, the cost of items, and workers' wages. For Tracy to analyze these data, the shoe would need to estimate the following values: Marginal Product (MP, Average Product(AP), Average value product and marginal value product, and Total value product. With these values, they will play a vital role in her estimating the optimal theater level of workers(L). Which is the average product (AP) expressed as the per unit (TP) output produced. When looking at a marginal product, this is an additional output produced when a business manager hires one additional worker. Below is how their estimation explain:

AP= TP/L Looking at table 1, the value of AP when TP is 100, and the workers (L) is two is: AP = 100/2 = 50 Because TP is 400 and workers is four is: AP = 400/4 = 100 Looking at table 2 for theater movie tickets, TP is 227, and workers are one is: AP = 227/1 = 227 For table 2 movie tickets, TP did rise to 615, and workers are two is." AP = 615/2 = 307.5

Looking at the rest of the values of AP is determined with table 1 and also table 2. Here is how the marginal product is determined as: (Marginal product) MP = ∆TP = TPn - TPn-1 ∆L Ln - Ln-1 Because a change in TP is divided by the change in theater workers furthermore, in table 1, the TP changes from 0 to 100. Also, workers change from 0 to 2. MP= ∆TP = 100-0 = 100 = 50 ∆ L 2-0 2 MP is 50 TP will change from 100 to 400, and also workers change from 2 to 4, MP is MP = ∆ TP = 400-100 = 300 = 150 ∆ L 6-4 2 MP is 150. Also, TP changes from 400to 750, and theater workers change from 4 to 6. MP is: MP = ∆TP = 750 - 400 = 350 = 175 ∆L 8 -6 2 MP is 175. Also, when TP remains the same and workers changes from 20 to 22 MP is: MP = ∆TP = 1290 - 1290 = 0 = 0 ∆L 22- 20 2 MP =0

For table 2, for the theater movie tickets, the methods are similar to estimate the MP. Because when TPO varies from 227 to 615 and workers from 1 to 2 MP is; MP = ∆TP = 615 - 227 - 388 - 388 ∆L 2 - 1 1 When looking at table 2, because the variation in the labor remains the same, which is 1, MP will be similar because of the change in total products only. And because TP did not change, the MP is zero and is: TPN = 1800 and TP(n-1) = 18-00, MP=0. But if TP falls this decrease, PM is: TPn=1800, Tp(b-1) = 1789, MPO = 1800 - m1789 = -11 This will result in Mp becomes negative.

Now we are going to look at another column of total value (TVP). The total value will determine the dollar value of the total output. The total value gives the money value to the total product. Also, the AVP is similarly alone with the MVP. These are the dollar value for the AP and MP. These are the value of the money of workers' AP and MP, in this order. To estimate these is done by how you multiplication for the price of goods sold. And this is the value of TP workers within the theater concession stand for the items price and multiplied total product. Which is: TVP = TP P also: AVP=P AP ; MVP = MP P The diminishing will return, it shows in the production of the output. This is because when the input rises, so does the output. But in the long run, the rise in the output will begin to fall when there is a rise in labor/worker is hired. Using the DMR to analyze, Tracy will see the range of workers from where the DMR starts, indicating that the increment in output begins to fall after employing one or more labor. This will let her know when to stop hiring new workers in production also in sales. Furthermore, in the theater concession stands, DMR starts at the level of 6 workers, leading to a rise in the level of workers. This will result in the long run the falling of the MP or lower rise in TP. Looking at the movie tickets, DMR will start at a level of 2 workers. This is because when you raise the workers by one more, this will decrease MP.

When looking at the optimal level/number of workers, this is estimated at the level of the theater workers given is similar to the value of the extra product added to the total output by hired workers. So these are the last analysis for Tracy, the manager. The concession stands optimal level/number for the workers that should be at the same level where the wage and MVP are at $120. So if Tracy went and hired 18 workers at this level, MVP and wage are the same $120, and the number of popcorn buckets produced/sold will be equal to the total product 18 levels of workers, which is 1280. The movie ticket would be similar, Looking at the optimal level number when it comes to workers. Should be a level in line where the wage and MVP, which is $120. The number of movie tickets produced/sold will equal the total product at eight levels of the theater workers, at $1,800.

Reference

McEachern, W. A. (2019). Micro ECON6: Principles of microeconomics. Cengage Learning. https://online.vitalsource.com/#/books/9781337671828

Unit IV Assignment Worksheet

This worksheet is intended to help you develop the information you will use to complete your Unit IV Essay. You are expected to include the completed tables in your Unit IV Essay. The additional questions after the tables are intended to help you formulate your ideas concerning what you will write in your essay.

NOTE: Just completing this worksheet does not constitute completing the Unit IV Assignment. The information from the worksheet must be incorporated into your essay submission. Follow the instructions below.

Instructions:

1. Complete all parts of this Unit IV Assignment Worksheet.

2. Answer the questions listed after the tables; these will help you formulate your ideas for writing the essay part of this unit’s assignment. You are expected to expand on these questions in your writing.

3. Include the tables and your question responses from this worksheet as an appendix at the end of your essay.

On the following pages, you will be provided with tables showing the different levels of output that are possible as the number of workers used per day changes. Using the information you learned from this unit’s textbook readings for this class as well as the information in the Unit IV Lesson, include the following:

1. Complete the two tables below; one is for production of concession stand item sales while the other is for production of movie ticket sales.

2. Answer all of the questions listed below each table; as mentioned, these answers will help you when formulating your thoughts for the essay part of your Unit IV Assignment.

Number of Workers per Day

Concession Items Produced per Day

Average Product

Marginal Product

Average Price of Concession Items

Total Value Product

Average Value Product

Marginal Value Product

Price of Worker per Day

0

0

0

0

$8.00

$0

$0

$0

$120.00

2

100

50

50

$8.00

$800

$400

$400

$120.00

4

400

100

150

$8.00

$3,200

$800

$1,200

$120.00

6

750

125

175

$8.00

$6,000

$1,000

$1,400

$120.00

8

900

112.5

75

$8.00

$7,200

$900

$600

$120.00

10

1,025

102.5

62.5

$8.00

$8,200

$820

$500

$120.00

12

1,125

93.75

50

$8.00

$9,000

$750

$400

$120.00

14

1,200

85.71

37.5

$8.00

$9,600

$685.68

$300

$120.00

16

1,250

78.13

25

$8.00

$10,000

$625

$200

$120.00

18

1,280

71.11

15

$8.00

$10,240

$568.88

$120

$120.00

20

1,290

64.5

5

$8.00

$10,320

$516

$40

$120.00

22

1,290

58.63

0

$8.00

$10,320

$469.04

$0

$120.00

24

1,280

53.33

-5

$8.00

$10,240

$426.64

-$40

$120.00

Questions: Use these questions to help you formulate your ideas for writing the Unit IV Essay.

Using the information from the table you completed, answer the following questions:

1. At what number of workers used per day does the law of diminishing marginal returns begin? How did you determine this number?

The DMR (diminishing marginal returns) because it started with six workers in the theater concession stand. The result let the MP fall as more workers were hired after the six.

2. At what number of workers used per day does negative marginal returns begin? How did you determine this number?

When looking at the marginal returns, it becomes negative level 24 because workers as MP were negative at this level.

3. What similarities do you see between the shape of the Average Product curve and the Average Value Product Curve?

AP and AVP similarities are: (1) AP and AVP curves rise till the six levels of workers. (2) AP and AVP curves begin falling around the eight levels of workers and continue falling.

4. What similarities do you see between the Marginal Product curve and the Marginal Value Product curve?

MP and MVP curve similarities are such: (1) MP and MVP curves continue rising until the six levels of workers. (2) MP and MVP curve start falling around the eight levels of workers and did not stop falling until 20 levels of workers (3) MP and MVP curves become zero at around the 22 levels of workers and become negative at a similar level of workers that is 24.

5. What is the optimal number of workers per day to use at the theater’s concession stand to produce concession stand item sales? How did you determine this optimal number?

Levels 18 of workers, the marginal product value (MVP) equal to the workers wage, the total is $120. Therefore, resulting in the optimal level/number of workers is 18.

Number of Workers per Day

Movie Tickets Produced per Day

Average Product

Marginal Product

Average Price of Movie Tickets

Total Value Product

Average Value Product

Marginal Value Product

Price of Worker per Day

0

0

0

0

$10.00

$0

$0

$120.00

1

227

227

227

$10.00

$2,270

$2,270

$2,270

$120.00

2

615

307.5

388

$10.00

$6,150

$3,075

$3,880

$120.00

3

935

311.66

320

$10.00

$9,350

$3,116.60

$3,200

$120.00

4

1,185

296.25

250

$10.00

$11,850

$2,962.50

$2,500

$120.00

5

1,427

285.4

242

$10.00

$14,270

$2,854

$2,420

$120.00

6

1,631

271.83

204

$10.00

$16,310

$2,718.3

$2,040

$120.00

7

1,788

255.42

157

$10.00

$17,880

$2,554.2

$1,570

$120.00

8

1,800

225

12

$10.00

$18,000

$2,250

$120

$120.00

9

1,800

200

0

$10.00

$18,000

$2,000

$0

$120.00

10

1,789

178.9

-11

$10.00

$17,890

$1,789

-$110

$120.00

11

1,757

159.72

-32

$10.00

$17,570

$1,597.2

-$320

$120.00

12

1,679

139.91

-78

$10.00

$16,790

$1,399

-$780

$120.00

Questions: Use these questions to help you formulate your ideas for writing the Unit IV Essay.

Using the information from the table you completed, answer the following questions:

1. At what number of workers used per day does the law of diminishing marginal returns begin? How did you determine this number?

When looking at the DMR, it started at two workers in the theater concession working. The MP starts to fall when more employees/workers are hired after 2

2. At what number of workers used per day do negative marginal returns begin? How did you determine this number?

Marginal return was negative at the level of 10 levels of workers. And MP also becomes negative at this level.

3. What is the optimal number of workers per day to produce movie ticket sales? How did you determine this optimal level?

Levels eight of workers, the marginal product value is equal to (W) wage of workers, which is $120. Furthermore, the optimal number/level of workers is at eight.