A firm currently uses 50,000 workers to produce 120,000 units of output per day. The daily wage per worker is $100, and the price of the firm's output is $48. The cost of other variable inputs is $400,000 per day. (Note: Assume that output is constant at the level of 120,000 units per day.)

Assume that total fixed cost equals $900,000. Calculate the values for the following four formulas:

Total Variable Cost = (Number of Workers x Worker’s Daily Wage) + Other Variable Costs
Total Costs = Total Variable Costs + Total Fixed Costs
Total Revenue = Price * Quantity
Average Variable Cost = Total Variable Cost / Units of Output per Day
Average Total Cost = (Total Variable Cost + Total Fixed Cost) / Units of Output per Day
Complete the following:

Calculate the firm’s profit or loss. Is the firm making a profit or a loss?
Explain the Short Run Shut Down Rule. Should this firm shut down? Please explain.

To calculate the values for the given formulas, we can use the provided information.

1. Total Variable Cost:
Given:
- Number of workers = 50,000
- Worker's daily wage = $100
- Other variable costs = $400,000

We can calculate the total variable cost using the formula:
Total Variable Cost = (Number of Workers x Worker’s Daily Wage) + Other Variable Costs

Substituting the values:
Total Variable Cost = (50,000 x $100) + $400,000
Total Variable Cost = $5,000,000 + $400,000
Total Variable Cost = $5,400,000

2. Total Costs:
Given:
- Total Variable Costs = $5,400,000
- Total Fixed Costs = $900,000

We can calculate the total costs using the formula:
Total Costs = Total Variable Costs + Total Fixed Costs

Substituting the values:
Total Costs = $5,400,000 + $900,000
Total Costs = $6,300,000

3. Total Revenue:
Given:
- Price = $48
- Quantity/Units of output per day = 120,000

We can calculate the total revenue using the formula:
Total Revenue = Price * Quantity

Substituting the values:
Total Revenue = $48 * 120,000
Total Revenue = $5,760,000

4. Average Variable Cost:
Given:
- Total Variable Cost = $5,400,000
- Units of Output per Day = 120,000

We can calculate the average variable cost using the formula:
Average Variable Cost = Total Variable Cost / Units of Output per Day

Substituting the values:
Average Variable Cost = $5,400,000 / 120,000
Average Variable Cost = $45

Average Total Cost:
Given:
- Total Variable Cost = $5,400,000
- Total Fixed Cost = $900,000
- Units of Output per Day = 120,000

We can calculate the average total cost using the formula:
Average Total Cost = (Total Variable Cost + Total Fixed Cost) / Units of Output per Day

Substituting the values:
Average Total Cost = ($5,400,000 + $900,000) / 120,000
Average Total Cost = $6,300,000 / 120,000
Average Total Cost = $52.50

To determine whether the firm is making a profit or loss, we need to calculate the profit:

Profit = Total Revenue - Total Costs
Profit = $5,760,000 - $6,300,000
Profit = -$540,000 (negative value)

The firm is making a loss of $540,000.

Now, let's explain the Short Run Shutdown Rule:

The Short Run Shutdown Rule states that a firm should shut down if its revenue is insufficient to cover its variable costs. In other words, if a firm is unable to generate enough revenue to cover at least its variable costs, it should temporarily halt its operation to minimize losses.

In this case, the firm's total revenue is $5,760,000, which is higher than its total variable costs of $5,400,000. Therefore, the firm is able to cover its variable costs but is still making a loss.

Whether the firm should shut down depends on various other factors, such as whether it expects the loss to be temporary or more long-term, market conditions, future prospects, and operational efficiency. This decision is ultimately up to the management of the firm.

To calculate the values, we'll go step-by-step:

Step 1: Calculate Total Variable Cost (TVC)

TVC = (Number of Workers x Worker’s Daily Wage) + Other Variable Costs

Given:
Number of Workers = 50,000
Worker’s Daily Wage = $100
Other Variable Costs = $400,000 per day

TVC = (50,000 x $100) + $400,000
TVC = $5,000,000 + $400,000
TVC = $5,400,000

Step 2: Calculate Total Costs (TC)

TC = Total Variable Costs + Total Fixed Costs

Given:
Total Variable Costs (TVC) = $5,400,000
Total Fixed Costs = $900,000

TC = $5,400,000 + $900,000
TC = $6,300,000

Step 3: Calculate Total Revenue (TR)

TR = Price * Quantity

Given:
Price = $48
Quantity = 120,000 units

TR = $48 * 120,000
TR = $5,760,000

Step 4: Calculate Average Variable Cost (AVC)

AVC = Total Variable Cost / Units of Output per Day

Given:
Total Variable Cost (TVC) = $5,400,000
Units of Output per Day = 120,000 units

AVC = $5,400,000 / 120,000
AVC = $45

Step 5: Calculate Average Total Cost (ATC)

ATC = (Total Variable Cost + Total Fixed Cost) / Units of Output per Day

Given:
Total Variable Cost (TVC) = $5,400,000
Total Fixed Cost = $900,000
Units of Output per Day = 120,000 units

ATC = ($5,400,000 + $900,000) / 120,000
ATC = $45 + $7.5
ATC = $52.5

Now, let's answer the questions:

To calculate the firm's profit or loss, we need to subtract Total Costs (TC) from Total Revenue (TR):
Profit = TR - TC
Profit = $5,760,000 - $6,300,000
Profit = -$540,000

The firm is making a loss of $540,000.

The Short Run Shut Down Rule states that a firm should shut down if its revenue is not enough to cover its variable costs. In this case, the firm's average variable cost (AVC) is $45 per unit, and the price per unit is $48. Since the price is higher than the AVC, the firm should not shut down.

However, it's important to note that the firm is making a loss. If the firm anticipates that it will continue making losses in the long run, it might consider shutting down to avoid further losses.