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Mathematics & Economics

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Math Problem

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# Break Even and Shut Down Analysis (Math Problem Sample)

Instructions:

Task: Conduct Break even and shut down analysis (Costs, Revenues, and Workers productivity)

source..Content:

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 &g...

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