Question

Nimbus, Inc., makes brooms and then sells them door- to-door. Here is the relationship between the number of workers and Nimbus's output during a given day: Workers 0 1 2 3 4 5 6 7 Output 0 20 50 90 120 140 150 155 1. Calculate marginal products for each labor level. What pattern do you see? How might you explain it? 2. A worker costs $100 a day, and the firm has fixed costs of $200. Use this information to calculate total costs for each output level. 3. Calculate average total cost. What pattern do you see? 4. Calculate marginal cost. What pattern do you see? 5. Compare marginal product marginal cost. Explain the relationship. 6. Compare average total cost with marginal cost. Explain the relationship.

Answer 1

This answer explains the concepts of marginal product, total costs, average total cost, marginal cost, and their patterns in the context of Nimbus, Inc.'s broom production. The answer focuses on the relationship between diminishing returns, marginal product, and marginal cost, as well as the relationship between average total cost and marginal cost.

Step-by-step explanation:

1. To calculate the marginal product, you need to find the change in output when the number of workers increases by one. We can see from the data provided that the marginal product follows a pattern of diminishing returns. As the number of workers increases, the output initially increases at a higher rate, but then starts to increase at a slower rate.

2. To calculate the total costs for each output level, you need to add the cost of labor (number of workers multiplied by the cost per worker) to the fixed costs. For example, when there are 0 workers, the total cost is $200 (fixed cost). When there are 1 worker, the total cost is $300 (fixed cost + labor cost of $100). And so on.

3. The average total cost can be calculated by dividing the total cost by the output level. You will see that the average total cost initially decreases as the output level increases, reaches a minimum point, and then starts to increase.

4. The marginal cost can be calculated by finding the change in total cost when the output level increases by one. You will notice that the marginal cost initially decreases, reaches a minimum point, and then starts to increase.

5. Comparing the marginal product and marginal cost, you will observe that as the marginal product decreases, the marginal cost increases. This is because of diminishing returns. When the marginal product is high, each additional worker adds a significant output, resulting in a lower marginal cost. However, as the marginal product decreases, each additional worker contributes less to the output, making the marginal cost higher.

6. Comparing the average total cost and marginal cost, you will see that the average total cost is at its minimum point when the marginal cost intersects it. This is because when the marginal cost is below the average total cost, adding one more unit of output reduces the average total cost. Conversely, when the marginal cost is above the average total cost, adding one more unit of output increases the average total cost.

Answer 2

Nimbus, Inc. Brooms Production Analysis:

1. Marginal Product:

Workers Output Marginal Product

0 0 -

1 20 20

2 50 30

3 90 40

4 120 30

5 140 20

6 150 10

7 155 5

Pattern: Marginal product increases until 3 workers, then starts decreasing. This is diminishing marginal returns, where each additional worker adds less output.

2. Total Cost:

Output Total Cost

0 $200

20 $300

50 $400

90 $500

120 $600

140 $700

150 $800

155 $900

3. Average Total Cost:

Output Average Total Cost

0 -

20 $15

50 $8

90 $5.56

120 $5

140 $5

150 $5.33

155 $5.81

Pattern: Average total cost decreases until reaching a minimum at 4 workers, then starts increasing.

4. Marginal Cost:

Output Marginal Cost

0 $200

20 $100

50 $100

90 $100

120 $100

140 $100

150 $100

155 $100

Pattern: Marginal cost remains constant at $100.

5. Comparison:

Marginal product starts decreasing when marginal cost is still constant. This means that even though each additional worker adds less output, the cost per additional unit remains the same.

When marginal product falls below marginal cost, it indicates inefficiency, as the cost of producing each additional unit exceeds the additional revenue it generates.

6. Comparison:

Average total cost initially decreases, indicating economies of scale due to more efficient production with more workers.

When average total cost starts increasing, it indicates diseconomies of scale, meaning additional workers lead to inefficiencies and higher costs per unit.

Average total cost intersects with marginal cost at the minimum efficient scale, where cost per unit is the lowest.