Break Even and Shut Down Analysis (Math Problem) - 550 Words

Break Even and Shut Down Analysis (Math Problem Sample) Content: Break Even and Shut Down AnalysisName:Institutional Affiliations:Date: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 firms 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 Workers 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/QBut Q = 200,000 AVC = $(4,400,000/200,000) AVC = $22.0Average Total Cost = (Total Variable Cost +Total Fixed Cost) / Units of Output per DayATC = (TVC + TFC)/QATC = $(4,400,000 + 1,000,000)/200,000ATC = $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 = 4Complete t he Following:Calculate the firms profit or lossTotal Revenue Total Costs = Profit Profitability = TR-TC But TR = PxQ while TC = TFC + TVC TC = $5,400,000; TR = $(200,000x25) = TR = $5,000,000Profit = $(5,000,000 5,400,000) = -$400,000Hence, Loss = $400,000Shut-down AnalysisCompare the firms 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 TCTR, representing a loss of $400,000. The Price, P = $25, Average Variable Costs (AVC) = $22.0Since 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 $400,000Or Fixed Costs minus (P-AVC)*Q = $1,000,000 - $600,000 = -$400,000Without production or shutdown the loss is $1,000,000. Since the shutdown loss is even more than the production loss ($1,000,00 0$400,000), the firm should better produce at this level of fixed costs as opposed to shutting down (Froeb, 2014). Break-Even AnalysisIf 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 = $27Break-even price: Pbe =Average Total Costmin, Pbe= $27Workers 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 workersThe 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? ...