Break Even and Shut Down Analysis (Math Problem Sample)

Break Even and Shut Down Analysis
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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
TVC = (50,000 x 80) + 400,000
TVC = $[4,000,000 + 400,000]
TVC = $4,400,000Average Variable Cost = Total Variable Cost / Units of Output per Day
AVC = TVC/Q
But Q = 200,000
AVC = $(4,400,000/200,000)
AVC = $22.0Average Total Cost = (Total Variable Cost +Total Fixed Cost) / Units of Output per Day
ATC = (TVC + TFC)/Q
ATC = $(4,400,000 + 1,000,000)/200,000
ATC = $27Worker Productivity = Units of Output per Day / Number of Workers 
WP = Q/L where Q = 200,000 and L = 50,000
WP = 200,000/50,000
WP = 4
Complete the Following: Calculate the firm’s profit or loss
Total Revenue – Total Costs = Profit
Profitability = TR-TC
But TR = PxQ while TC = TFC + TVC
TC = $5,400,000; TR = $(200,000x25) = TR = $5,000,000
Profit = $(5,000,000 – 5,400,000) = -$400,000
Hence, Loss = $400,000
Shut-down Analysis
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?
At TFC = $1,000,000, the firm is running at a loss since TC>TR, representing a loss of $400,000.
The Price, P = $25, Average Variable Costs (AVC) = $22.0
Since P > AVC (that is $25 >$22), the firm should therefore should not immediately shutdown, instead, it should continue to produce at this level of fixed costs.
With production the loss is $400,000
Or Fixed Costs minus (P-AVC)*Q = $1,000,000 - $600,000 = -$400,000
Without production or shutdown the loss is $1,000,000.
Since the shutdown loss is even more than the production loss ($1,000,000>$400,000), the firm should better produce at this level of fixed costs as opposed to shutting down (Froeb, 2014).
Break-Even Analysis
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.)
Break-even price: Pbe = ATCmin = $27
Break-even price: Pbe =Average Total Costmin,
Pbe= $27
Workers productivityOutput / number of workers = 200000 / 50000 = 4 units per dayTotal costs - $5.4 M 1M Fixed costat break even, TR = $5M = TCDecrease my total cost by $400,000Decreased in Workers = Decrease in TC/wage rate = $400,000 / $80 = 5000Labor force = 50,000 – 5,000 = 45000 workers
The company therefore will have to lay-off 5,000 workers, leaving 45,000 workers to produce the same quantity of output. Given a lower number of employees now working at the company, what is the change in worker productivity? ...