The firm currently uses 50,000 workers to produce 200,000 units of output per da

Question

The 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 * 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
Then, assume that total fixed cost equals $3,000,000, and recalculate the values of the four variables listed above.
For both cases, calculate the firm’s profit or loss.

For both sets of calculations, compare the firm’s output price and the calculated average variable cost and average total cost. Should the firm shutdown immediately when the total fixed cost equals $1,000,000? Should the firm shut down immediately when the total fixed cost equals $3,000,000?
For one of the cases, if the firm can operate at a loss in the short-run, how many employees need to be laid off in order for the company to break even? 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? Is the change in worker too large, and the firm should shut down immediately? Or in your opinion, can the workers increase their productivity, assuming that the units of output per day remain fixed at 200,000 units, so that the firm operates at a breakeven state?

Explanation / Answer

TFC = $1M -----> TVC = $4.4M ($4M for wages (50,000 workers x $80 per worker) + $400,000 other variable inputs AVC = $22 (TVC of $4.4M / 200,000 units) ATC = $27 (TVC $4.4M + TFC $1M / 200,000 units) Worker productivity = 4 (200,000 units / 50,000 workers) Profit/Loss = $400,000 loss (total revenue of 200,000 units x $25 price = $5M minus total cost of $5.4M (total cost can be calculated either by taking ATC times 200,000 units or by taking TVC plus TFC) TFC = $3M -----> TVC unchanged at $4.4M AVC unchanged at $22 ATC = $37 ($4.4M TVC + $3M TFC / 200,000 units) Worker productivity unchanged at 4 Profit/Loss = $2.4M loss (total revenue remains at $5M; total cost = $7.4M) The shutdown rule = if a firm can cover total variable costs at some level of production in the short run, it should continue to operate. Fixed costs are irrelevant in the short run because they are sunk costs. The firm receives $25 with variable costs of $22 per unit, so it can cover variable costs; it should not shut down immediately (both) break even (workers): TFC = $1M -----> $400,000 / $80 per worker, or 5,000; lay off 5,000 workers = workforce of 45,000 TFC = $1M -----> $2,400,000 / $80 per worker, or 30,000; lay off 30,000 workers = workforce of 20,000 All of this assumes that the production remains at 200,000 units per day (due to information given) new worker productivity to: TFC = $1M -----> = 4.4 (as opposed to 4) found by (200,000 units x new workforce of 45,000) TFC = $3M -----> = 10 (as opposed to 4) found by (200,000 units times the new workforce of 20,000) TFC = $1M -----> is likely to occur; it is asking remaining employees to increase production by 11% (4.4/4, then times 100). This level of increase happens all the time during a recession. TFC = $3M -----> is not likely to occur; it is asking remaining employees to increase production by 250% (10/4, then times 100). This means that break-even is not possible in the short run, but that does not mean that the firm should immediately shut down; only variable costs are relevant in the short run.

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