2 pages/≈550 words
Mathematics & Economics
Break Even and Shut Down Analysis (Math Problem Sample)
Task: Conduct Break even and shut down analysis (Costs, Revenues, and Workers productivity)source..
Break Even and Shut Down Analysis
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
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 &g...
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