A firm currently uses 40,000 workers to produce 180,000 units of output per day. The daily wage per worker is $100, and the price of the firm's output is $28. The cost of other variable inputs is $500,000 per day. (Note: Assume that output is constant at the level of 180,000 units per day.) Assume that total fixed cost equals $1,200,000. 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. Provide a report to the management of the firm that discusses what should be done. Be sure to show your work to support the decision that you outline in your report.

To answer these questions, let's calculate the values for the given formulas step by step:

1. Total Variable Cost:
We are told that the firm currently employs 40,000 workers, and the daily wage per worker is $100. The formula for total variable cost is:
Total Variable Cost = (Number of Workers x Worker’s Daily Wage) + Other Variable Costs

Other Variable Costs are given as $500,000 per day, and the number of workers is 40,000.
Total Variable Cost = (40,000 workers x $100 daily wage) + $500,000
Total Variable Cost = $4,000,000 + $500,000
Total Variable Cost = $4,500,000

Therefore, the Total Variable Cost is $4,500,000.

2. Total Costs:
The formula for total costs is:
Total Costs = Total Variable Costs + Total Fixed Costs

We are given that the Total Fixed Costs are $1,200,000, and the Total Variable Costs are $4,500,000.
Total Costs = $4,500,000 + $1,200,000
Total Costs = $5,700,000

Therefore, the Total Costs are $5,700,000.

3. Total Revenue:
The formula for total revenue is:
Total Revenue = Price * Quantity

We are given that the price of the firm's output is $28, and the quantity (units of output per day) is 180,000.
Total Revenue = $28 * 180,000
Total Revenue = $5,040,000

Therefore, the Total Revenue is $5,040,000.

4. Average Variable Cost:
The formula for average variable cost is:
Average Variable Cost = Total Variable Cost / Units of Output per Day

We have already calculated the Total Variable Cost as $4,500,000, and the Units of Output per Day are 180,000.
Average Variable Cost = $4,500,000 / 180,000
Average Variable Cost = $25

Therefore, the Average Variable Cost is $25.

5. Average Total Cost:
The formula for average total cost is:
Average Total Cost = (Total Variable Cost + Total Fixed Cost) / Units of Output per Day

We know that the Total Variable Cost is $4,500,000, the Total Fixed Cost is $1,200,000, and the Units of Output per Day are 180,000.
Average Total Cost = ($4,500,000 + $1,200,000) / 180,000
Average Total Cost = $5,700,000 / 180,000
Average Total Cost = $31.67

Therefore, the Average Total Cost is $31.67.

Now, let's analyze the firm's profit or loss and answer the question about shut down:

Profit or Loss:
Profit or Loss = Total Revenue - Total Costs

Total Revenue = $5,040,000 and Total Costs = $5,700,000

Profit or Loss = $5,040,000 - $5,700,000
Profit or Loss = -$660,000

The negative profit value indicates a loss of $660,000.

Short Run Shut Down Rule:
The Short Run Shut Down Rule states that a firm should shut down if the price is below the minimum average variable cost. In this case, the Average Variable Cost is $25.

Since the price of the firm's output is $28 (higher than the Average Variable Cost), the firm should not shut down based on the Short Run Shut Down Rule.

Report and Recommendations:
Based on the calculations and analysis:

- The firm is making a loss of $660,000.
- The firm should not shut down in the short run as the price is higher than the average variable cost.

However, considering the loss and the decision to continue production, the firm should closely evaluate its cost structure and explore options to reduce costs. This could involve renegotiating wage rates, optimizing the use of other variable inputs, or finding efficiencies in the production process.

It is also advisable for the management to conduct a thorough market analysis to assess demand conditions and consider strategies to increase the price or quantity of output, such as expanding the customer base or product diversification.

Regular monitoring of costs, revenues, and market dynamics is essential to ensure the long-term viability and profitability of the firm.