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Loss Minimization

Firms will not immediately stop production if the firm becomes unprofitable. As long as the loss is less by operating than by stopping production the firm will continue to produce even though it is incurring a loss; that is, total revenue is greater than total variable cost, but total revenue is less than total cost. The firm will discontinue production if total revenue drops below total variable cost, or if fixed inputs become variable inputs with the passage of time.

 

Firms do not earn a profit at all times. Occasionally, a firm will incur a loss, that is, total cost exceeds total revenue. But how should a manager react at that time? Should the manager stop operating the firm? Should the manager continue to operate the business even though the firm is incurring a loss?

The general response is that a manager may continue to operate a business in the short-run even though it is incurring a loss. The reason is that if a firm stops operating, it is still incurring its fixed costs, that is, the cost associated with the fixed inputs. Fixed inputs were described in another section as "inputs that cannot be changed in the time period being considered by the manager."  Restated, in the short run, there is not enough time to expand the fixed input (such as construct another building) or there is not enough to time contract or reduce the fixed input (such as sell a manufacturing facility).

In the short run, the cost of the fixed input (e.g., depreciation, maintenance, interest on debt associated with the asset, opportunity cost on equity invested in the asset) is going to be incurred whether or not the business is being operated.

Variable costs, on the other hand, drop to zero when the business is shut down because the variable inputs are no longer being purchased, e.g., some utilities, fuel, and labor.

The manager's decision is "is the business "better off" continuing to operate and thereby earning some revenue but incurring variable and fixed costs, or is the business "better off" to stop operating, earn no revenue, incur no variable cost, but continue to incur fixed cost."

The answer is "as long as the business is generating enough revenue to pay all variable cost and some fixed cost, the business will incur a smaller loss than if the business shut down and paid none of its fixed cost."

Operate the business as long as TR > TVC, even though TR < TC.

Graph 26 (Minimizing Loss by Continuing to Operate)

Graph 27 (Minimizing Loss by Ceasing to Operate)

An alternative statement that arrives at the same decision or outcome is "operate the business as long as the price of the output (Py) is greater than the average variable cost (AVC).

 

How long will a business operate at a loss?

This is a tricky question. First, if revenue drops further so it is less than variable cost, the manager will cease operation.  This idea also can be expressed as cease operating the business when the price of output drops below average variable cost.

Second, what if revenue does not drop any further? Will the business continue to operate at a loss for an indefinite time? The answer is "no" but the reason, as explained by economic theory, may not be immediately clear.

The assumption is that the manager is thinking about the short run; that is, a time period wherein there is time to vary the level of some inputs (variable inputs) but there is not enough time to vary other inputs (fixed inputs). As the manager thinks about a longer time period, more inputs become variable and more cost become variable. As more cost become variable, the revenue needs to pay a greater portion of the total cost to justify continuing to operate at a loss.

Another way to describe a fixed input/cost becoming a variable input/cost is to consider a long-term (fixed?) asset that needs to be replaced because it is worn out. This long-term asset that needs to be replaced is no longer a fixed input, but is now a variable input and the cost of the replacement asset is now a variable cost. The need to replace a long-term asset shifts fixed cost to variable cost. Needing to replace a worn out piece of major equipment is an example of a long-term asset that is now a variable input/cost.

Graph 28 (Passage of Time Shifts Fixed Inputs/Fixed Costs into Variable Inputs/Variable Costs)

Even without a change in revenue, an unprofitable firm will cease operation when there is enough time to sell or consume its fixed assets.

The manager will cease operation when enough time has passed that fixed inputs/costs are now considered variable inputs/costs and the revenue is not enough to pay all the costs that are now variable.

 

In summary: a business will continue to produce in the short-run even though the firm is experiencing a loss (i.e., Py < ATC; TR < TC) as long as the price of output exceeds average variable cost (Py > AVC; TR > TVC).  Restated, a business will operate to minimize loss as long as TR exceeds TVC. In this situation, all variable costs and  some portion of fixed cost are being paid; when the firm ceases operation, none of the fixed cost is paid.

When revenue is not enough to pay total variable cost, the firm will stop producing.

 

Numeric Example of Loss Minimization

A numeric example may help illustrate the concept of loss minimization.  The first table in the following section is based on the data presented previously on the pages titled Production Function and Numeric Example.  Several columns were added:  average variable cost (AVC) and average total cost (ATC).  A row for no production  (no variable input is used and no output is produced) also was added.  This first table illustrates a profitable firm.

As explained earlier, profit is maximized where MR = MC. Also note that no production would cause the firm to incur a loss equal to its fixed cost ($50 in this example).

 

Table. Revenue, Cost and Profit for Stage II of Firm Earning a Profit

Qty. of Var. Input Qty. of Output          
. (X) . (Y or TPP) Py or MR
Total Revenue Px TVC TFC TC Profit MC AVC ATC
0 0 $0 $18 $0 $50 $50 -$50 ???? ????
11
54
   $270 $18 $198 $50 $248 $22 $3.67 $4.59
$5 $4.50
11.25 55 $275 $18 $202.50 $50 $252.50 $22.50 $3.68 $4.59
$5 $4.50
11.5 56 $280 $18 $207 $50 $257 $23 $3.70 $4.59
$5 $4.50
11.75 57 $285 $18 $211.50 $50 $261.50 $23.50 $3.71 $4.59
$5 $4.50
12 58 $290 $18 $216 $50 $266 $24 $3.72 $4.59
$5 $6
12.33 59    $295 $18 $222 $50 $272 $23 $3.76 $4.61
$5 $6
12.66 60 $300 $18 $228 $50 $278 $22 $3.80 $4.63
$5 $6
13 61    $305  $18 $234 $50 $284 $21 $3.84 $4.66
$5 $9
13.5 62   $310 $18 $243 $50 $293 $17 $3.92 $4.73
$5 $9
14 63 $315 $18 $252 $50 $302 $13 $4.00 $4.79
    $5 $18
15 64 $320 $18 $270 $50 $320 $0 $4.22 $5.00
$5 ????
16 64 $320 $18 $288 $50 $338 -$18 $4.50 $5.28

 

The second table illustrates a firm that is operating to minimize its loss due to a drop in the price of the output ($4.50 rather than $5).  The firm will continue to operate by using 1 or 12 units of variable input, producing 54 to 58 units of output, and incurring a loss of $5 for the production period.  This is still better than a $50 loss that would be incurred if the firm shut down.  Note that Py exceeds AVC and that TR is greater than TVC when the firm is minimizing loss.

 

Table. Revenue, Cost and Profit for Stage II of Firm Minimizing Loss

Qty. of Var. Input Qty. of Output          
. (X) . (Y or TPP) Py or MR
Total Revenue Px TVC TFC TC Profit MC AVC ATC
0 0 $0 $18 $0 $50 $50 -$50 ???? ????
11
54
   $243 $18 $198 $50 $248 -$5 $3.67 $4.59
$4.50 $4.50
11.25 55 $247.50 $18 $202.50 $50 $252.50 -$5 $3.68 $4.59
$4.50 $4.50
11.5 56 $252 $18 $207 $50 $257 -$5 $3.70 $4.59
$4.50 $4.50
11.75 57 $256.50 $18 $211.50 $50 $261.50 -$5 $3.71 $4.59
$4.50 $4.50
12 58 $261 $18 $216 $50 $266 -$5 $3.72 $4.59
$4.50 $6
12.33 59    $265.50 $18 $222 $50 $272 -$6.50 $3.76 $4.61
$4.50 $6
12.66 60 $270 $18 $228 $50 $278 -$8 $3.80 $4.63
$4.50 $6
13 61    $274.50  $18 $234 $50 $284 -$9.50 $3.84 $4.66
$4.50 $9
13.5 62   $279 $18 $243 $50 $293 -$14 $3.92 $4.73
$4.50 $9
14 63 $283.50 $18 $252 $50 $302 -$18.50 $4.00 $4.79
    $4.50 $18
15 64 $288 $18 $270 $50 $320 -$32 $4.22 $5.00
$4.50 ????
16 64 $288 $18 $288 $50 $338 -$50 $4.50 $5.28

 

The third table in this section illustrates that the firm will cease production due to a continued drop in the price of its output (now the price of the output is $3.50).  Producing the minimum amount for Stage 2 (54 units) will result in a loss of $59 for the production period.  Not operating incurs a loss of only $50.  Time to shut down production.  Note that the Py is less than AVC and that TR is less than AVC when the firm ceases to operate.

 

Table. Revenue, Cost and Profit for Stage II of Firm Ceasing Production due to Revenue Decrease

Qty. of Var. Input Qty. of Output          
. (X) . (Y or TPP) Py or MR
Total Revenue Px TVC TFC TC Profit MC AVC ATC
0 0 $0 $18 $0 $50 $50 -$50 ???? ????
11
54
   $189 $18 $198 $50 $248 -$59 $3.67 $4.59
$3.50 $4.50
11.25 55 $192.50 $18 $202.50 $50 $252.50 -$60 $3.68 $4.59
$3.50 $4.50
11.5 56 $196 $18 $207 $50 $257 -$61 $3.70 $4.59
$3.50 $4.50
11.75 57 $199.50 $18 $211.50 $50 $261.50 -$62 $3.71 $4.59
$3.50 $4.50
12 58 $203 $18 $216 $50 $266 -$63 $3.72 $4.59
$3.50 $6
12.33 59    $206.50 $18 $222 $50 $272 -$65.50 $3.76 $4.61
$3.50 $6
12.66 60 $210 $18 $228 $50 $278 -$68 $3.80 $4.63
$3.50 $6
13 61    $213.50  $18 $234 $50 $284 -$70.50 $3.84 $4.66
$3.50 $9
13.5 62   $217 $18 $243 $50 $293 -$76 $3.92 $4.73
$3.50 $9
14 63 $220.50 $18 $252 $50 $302 -$81.50 $4.00 $4.79
    $3.50 $18
15 64 $224 $18 $270 $50 $320 -$96 $4.22 $5.00
$3.50 ????
16 64 $224 $18 $288 $50 $338 -$114 $4.50 $5.28

 

The final table in this section illustrates a firm that will cease production due to the passage of time in which fixed inputs (fixed cost) transform to variable inputs (variable cost).  In this situation, the firm ceases operation even though the price of the output ($4.50) drops no further.  Note that TR is less than TVC and that Py is less than AVC at the boundary between Stages 1 and 2 (that is, 54 units of output).  Even though the TC has not changed from a previous table ($248), some fixed inputs and costs have shifted to variable, and there is less loss by ceasing operation ($5 v. $5.10).

 

Table. Revenue, Cost and Profit for Stage II of Firm Ceasing Production due to Passage of Time

Qty. of Var. Input Qty. of Output          
. (X) . (Y or TPP) Py or MR
Total Revenue Px TVC TFC TC Profit MC AVC ATC
0 0 $0 $22.10 $0 $5 $5 -$5 ???? ????
11
54
   $243 $22.10 $243.10 $5 $248.10 -$5.10 $4.50 $4.59
$4.50 $4.50
11.25 55 $247.50 $22.10 $248.63 $5 $253.63 -$6.13 $4.52 $4.61
$4.50 $4.50
11.5 56 $252 $22.10 $254.15 $5 $259.15 -$7.15 $4.54 $4.63
$4.50 $4.50
11.75 57 $256.50 $22.10 $259.68 $5 $264.68 -$8.18 $4.56 $4.64
$4.50 $4.50
12 58 $261 $22.10 $265.20 $5 $270.20 -$9.20 $4.57 $4.66
$4.50 $6
12.33 59    $265.50 $22.10 $272.57 $5 $277.57 -$12.07 $4.62 $4.70
$4.50 $6
12.66 60 $270 $22.10 $279.93 $5 $284.93 -$14.93 $4.67 $4.75
$4.50 $6
13 61    $274.50  $22.10 $287.30 $5 $292.30 -$17.80 $4.71 $4.79
$4.50 $9
13.5 62   $279 $22.10 $298.35 $5 $303.35 -$24.35 $4.81 $4.89
$4.50 $9
14 63 $283.50 $22.01 $309.40 $5 $314.40 -$30.90 $4.91 $4.99
    $4.50 $18
15 64 $288 $22.10 $331.50 $5 $336.50 -$48.50 $5.18 $5.26
$4.50 ????
16 64 $288 $22.10 $353.60 $5 $358.60 -$70.60 $5.53 $5.60

 

Thought Question -- increase production when output price drops?

  • Will a manager always decrease production when the price of the output declines? Why? How does this decision relate to the manager's other goals? How does this decision relate to the manager's perception about 1) the value of the manager's labor, 2) the manager's trade-off between time away from work and the manager's goal for family income, and 3) the manager's willingness and ability to assume risk?
  • An example from years ago. A dairy farmer was being interviewed about a recent drop in the price of milk. The farmer was asked what he will do in response to the drop in price. He said, "I guess I will milk more cows." This is inconsistent with economic theory. Was the farmer wrong? Is theory wrong? Is theory only "telling part of the story?"
    • HINT -- the farmer may have goals of 1) earning a certain level of net income (perhaps $60,000 annually to be used for family living expenses) and 2) then to stop working each day.  When the price of milk drops and net income drops, the farmer will give up some daily "time off" (the second goal) to milk additional cows to achieve the first goal of $60,000 net income (the first goal).  Students of economics must take the time to recognize the assumptions that underpin the theoretical concepts and their applications. 

 

Summary: How much to Produce

  • Marginal Value Product (MVP) -- additional revenue that results from using one more unit of variable input
  • Marginal Input Cost (MIC) -- additional cost that arises from using one more unit of variable input
  • Decision rule:  use additional units of variable input as long as the additional revenue (MVP) exceeds the additional cost (MIC)
  • Marginal Cost (MC) -- additional cost that arises from producing one more unit of output
  • Marginal Revenue (MR) -- additional revenue that results from producing and selling one more unit of output
  • Decision rule:  produce additional output as long as revenue from the additional output (MR) exceeds the cost of producing additional output (MC)
  • The marginal value product (MVP) in stage II is that firm's demand for the variable input; that is, as the price of variable input decreases, the firm will increase its use of the variable input.
  • The marginal cost (MC) above average variable cost is that firm's supply of the output; that is, as the price of the output increases, the firm will produce a larger quantity of the output.
  • Do not produce where total physical product is maximized unless the variable input is free or the price for the output is infinite (neither condition is likely).
  • Produce in the short-run (that is, some inputs are fixed and some inputs are variable) even though the firm is suffering a loss as long as revenue exceeds total variable cost.  In such a situation, although all costs are not being paid, at least all variable costs are being paid and some fixed cost.  This is better than not producing at all because without any production, none of the fixed cost will be paid.

 

Managers may also want to consider the economic theory that explains deciding how to produce and what to produce.

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