A Firm Uses 50,000 Workers To Produce 200,000 Units
A Firm Currently Uses 50000 Workers To Produce 200000 Units Of Outpu
A firm currently uses 50,000 workers to produce 200,000 units of output per day. The daily wage per worker is $80, and the price of the firm’s output is $25. The cost of other variable inputs is $400,000 per day. Assume that total fixed cost equals $1,000,000. Calculate the values for the following four formulas: Total Variable Cost = (Number of Workers x Worker’s Daily Wage) + Other Variable Costs 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 Worker Productivity = Units of Output per Day / Number of Workers. Complete the following: Calculate the firm’s profit or loss. Compare the firm’s output price and the calculated average variable cost and average total cost. Should the firm shut down immediately when the total fixed cost equals $1,000,000? If the firm can operate at a loss in the short run, how many employees need to be laid off for the company to break even? (Assume that after layoffs, the remaining workers maintain output at 200,000 units per day.) To calculate the number of workers to be laid off, divide the loss for the two situations by the daily wage per worker. Given a lower number of employees now working at the company, what is the change in worker productivity? Provide a report to management of the firm that discusses what should be done. Be sure to show your work to support the decision you outline in your report.
Paper For Above instruction
In analyzing the operational efficiency and financial viability of the firm, it is imperative to calculate key economic and managerial metrics, including total variable costs, average costs, productivity, and profit or loss scenarios. These calculations serve as the foundation for strategic decisions such as whether to continue operations, scale back, or shut down temporarily or permanently.
Calculating Total Variable Cost
The total variable cost (TVC) comprises the direct labor costs and other variable inputs. Given 50,000 workers each earning $80 daily, and additional variable costs amounting to $400,000, the calculation is as follows:
Total Variable Cost = (Number of Workers x Worker’s Daily Wage) + Other Variable Costs
= (50,000 x $80) + $400,000
= $4,000,000 + $400,000
= $4,400,000
Calculating Average Variable Cost and Average Total Cost
The average variable cost (AVC) per unit of output is determined by dividing total variable costs by units produced:
AVC = Total Variable Cost / Units of Output
= $4,400,000 / 200,000 units
= $22 per unit
The average total cost (ATC) includes both variable and fixed costs spread over the units produced:
Total Fixed Cost = $1,000,000
Total Cost (TC) = Total Variable Cost + Total Fixed Cost = $4,400,000 + $1,000,000 = $5,400,000
ATC = Total Cost / Units of Output
= $5,400,000 / 200,000
= $27 per unit
Calculating Worker Productivity
Worker productivity, expressed as units produced per worker, is calculated as:
Productivity = Units of Output / Number of Workers
= 200,000 / 50,000
= 4 units per worker per day
Profit or Loss Determination
The firm's total revenue (TR) is calculated by multiplying output units by the selling price:
TR = 200,000 units x $25 = $5,000,000
The total cost (TC) has been calculated as $5,400,000. Therefore, the profit or loss is:
Profit/Loss = TR - TC = $5,000,000 - $5,400,000 = -$400,000
The firm is incurring a loss of $400,000 per day under the current operations.
Assessment of Shutdown Decisions
Comparing the price per unit ($25) with the AVC ($22), the firm is covering its variable costs and some fixed costs but is still incurring a loss overall. In the short run, firms should continue operating if the price exceeds the AVC, because covering variable costs helps minimize losses and contributes toward fixed costs. Since the current price ($25) exceeds AVC ($22), it suggests that temporary closure may not be necessary, but the firm must explore cost reduction or revenue enhancement strategies.
Break-Even Analysis: Layoffs and Output Maintenance
The firm must analyze whether it is feasible to reduce workforce to decrease losses. To find the workforce level where the firm breaks even, we first determine the necessary total cost to match total revenue, which is $5,000,000. The total fixed costs ($1,000,000) remain unchanged, and variable costs reduce proportionally with layoffs.
Let x be the number of workers after layoffs:
Total Variable Cost after layoffs = (x x $80) + $400,000
Average Variable Cost (AVC) after layoffs = (Total Variable Cost for x workers) / 200,000 units
To break even, total costs must equal revenue:
Total Variable Cost + Fixed Cost = $5,000,000
(x x $80) + $400,000 + $1,000,000 = $5,000,000
Solving for x:
x x $80 = $5,000,000 - $1,400,000 = $3,600,000
x = $3,600,000 / $80 = 45,000 workers
Thus, the firm must reduce its workforce from 50,000 to approximately 45,000 employees, laying off 5,000 workers to break even.
Impact of Layoffs on Worker Productivity
After layoffs, assuming the firm maintains output at 200,000 units per day with 45,000 workers, the new productivity is:
New Productivity = 200,000 / 45,000 ≈ 4.44 units per worker per day
This indicates an improvement in individual worker productivity post-layoffs, reflecting a more efficient workforce aligned with the firm's cost-minimization strategies.
Management Recommendations
Given the current economic environment, the firm’s decision to continue operations hinges on multiple factors, including short-term profitability and long-term viability. The analysis demonstrates that with a workforce of 45,000, the firm can break even. The current operations, resulting in a loss, suggest the need to either increase efficiency or reduce workforce size. Since the firm is covering its AVC, short-term operation is justified to minimize losses, but strategic cost reductions are advisable.
Further, management should evaluate opportunities for increasing output prices, reducing costs (both fixed and variable), or improving productivity through technological upgrades and process improvements. Engaging in market expansion or diversifying product offerings could also enhance revenue streams. Importantly, maintaining a balanced workforce that optimizes productivity while controlling costs will be crucial for sustaining profitability.
In conclusion, layoffs of approximately 5,000 workers are necessary for the firm to reach break-even capacity, and productivity improvements will accompany this reduction. The firm should carefully strategize on costs and output efficiencies to enhance financial health while considering market conditions and operational constraints.
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