Questions: A worker costs 60 a day, and the firm has fixed costs of 120. Use this information to fill in the column for total cost Fill in the column for marginal cost in the previous table. (Hint: MC = (Delta TC)/(Delta Q).) Fill in the column for average total cost in the previous table. (Hint: ATC = TC/Q.) Which of the following statements are true about the patterns found in this table? Check all that apply. - Average total cost is not U-shaped. - Marginal product rises at first, then declines. - When marginal product is rising, marginal cost is also rising. - When marginal cost is less than average total cost, average total cost is falling.

A worker costs 60 a day, and the firm has fixed costs of 120. Use this information to fill in the column for total cost

Fill in the column for marginal cost in the previous table. (Hint: MC = (Delta TC)/(Delta Q).)

Fill in the column for average total cost in the previous table. (Hint: ATC = TC/Q.)

Which of the following statements are true about the patterns found in this table? Check all that apply.

- Average total cost is not U-shaped.
- Marginal product rises at first, then declines.
- When marginal product is rising, marginal cost is also rising.
- When marginal cost is less than average total cost, average total cost is falling.

Transcript text: A worker costs $\$ 60$ a day, and the firm has fixed costs of $\$ 120$. Use this information to fill in the column for total cost Fill in the column for marginal cost in the previous table. (Hint: $M C=\frac{\Delta T C}{\Delta Q}$.) Fill in the column for average total cost in the previous table. (Hint: $A T C=\frac{T C}{Q}$.) Which of the following statements are true about the patterns found in this table? Check all that apply. - Average total cost is not U-shaped. - Marginal product rises at first, then declines. - When marginal product is rising, marginal cost is also rising. - When marginal cost is less than average total cost, average total cost is falling.

Solution

To address the questions, let's first fill in the missing values in the table using the given formulas and information.

Total Cost (TC)

The total cost is the sum of fixed costs and variable costs. The fixed cost is \$120, and each worker costs \$60 per day. Therefore, the total cost for each number of workers is calculated as follows:

0 workers: \$120 (fixed cost)
1 worker: \$120 + \$60 = \$180
2 workers: \$120 + 2(\$60) = \$240
3 workers: \$120 + 3(\$60) = \$300
4 workers: \$120 + 4(\$60) = \$360
5 workers: \$120 + 5(\$60) = \$420
6 workers: \$120 + 6(\$60) = \$480
7 workers: \$120 + 7(\$60) = \$540

Marginal Cost (MC)

Marginal cost is calculated using the formula $ MC = \frac{\Delta TC}{\Delta Q} $, where $ \Delta TC $ is the change in total cost and $ \Delta Q $ is the change in output.

From 0 to 1 worker: $ MC = \frac{180 - 120}{15 - 0} = \frac{60}{15} = 4.00 $
From 1 to 2 workers: $ MC = \frac{240 - 180}{40 - 15} = \frac{60}{25} = 2.40 $
From 2 to 3 workers: $ MC = \frac{300 - 240}{75 - 40} = \frac{60}{35} = 1.71 $
From 3 to 4 workers: $ MC = \frac{360 - 300}{120 - 75} = \frac{60}{45} = 1.33 $
From 4 to 5 workers: $ MC = \frac{420 - 360}{150 - 120} = \frac{60}{30} = 2.00 $
From 5 to 6 workers: $ MC = \frac{480 - 420}{165 - 150} = \frac{60}{15} = 4.00 $
From 6 to 7 workers: $ MC = \frac{540 - 480}{170 - 165} = \frac{60}{5} = 12.00 $

Average Total Cost (ATC)

Average total cost is calculated using the formula $ ATC = \frac{TC}{Q} $.

1 worker: $ ATC = \frac{180}{15} = 12.00 $
2 workers: $ ATC = \frac{240}{40} = 6.00 $
3 workers: $ ATC = \frac{300}{75} = 4.00 $
4 workers: $ ATC = \frac{360}{120} = 3.00 $
5 workers: $ ATC = \frac{420}{150} = 2.80 $
6 workers: $ ATC = \frac{480}{165} \approx 2.91 $
7 workers: $ ATC = \frac{540}{170} \approx 3.18 $

Analysis of Statements

Average total cost is not U-shaped.
- This statement is incorrect. The average total cost decreases initially and then starts to increase, which is characteristic of a U-shaped curve.
Marginal product rises at first, then declines.
- This statement is correct. The marginal product increases from 15 to 45 and then decreases to 5.
When marginal product is rising, marginal cost is also rising.
- This statement is incorrect. When the marginal product is rising (from 15 to 45), the marginal cost is actually falling (from 4.00 to 1.33).
When marginal cost is less than average total cost, average total cost is falling.
- This statement is correct. When MC < ATC, the ATC is decreasing, which is evident from the table.