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Thursday, March 31, 2011

How the law of increasing costs works

The 'law of increasing costs' is an economic concept that states production costs will increase if maximum output efficiency has already been reached with fixed inputs i.e. overhead and other expenses. Once maximum efficiency of production is reached, the law of increasing costs states the cost to produce more will increase thereby lowering profit margin via increasing costs.

Illustration of the law of increasing costs 


The law of increasing costs can be illustrated with the example of a restaurant's file mignon operation. In this operation, maximum efficiency or profit margin is attained when 3 chefs produce 12 filet mignons per hour when operating with maximum efficiency while the costs of cooking the meat is constant i.e. ingredients, electricity, and wages, then increasing the number of filet mignons cooked in one hour will cost a company more than producing less.

Inputs and outputs:

• 3 Chefs produce 12 filet mignons in 1 hour
• Electricity, ingredients and wages are constant
• The Chefs are working at maximum efficiency

If the above illustration costs a restaurant $91.00 divided as $15/hr per Chef, $3/filet and $10 for 1hour of electricity and overhead, the restaurant will have to increase this cost to produce more filet mignons. This will cost the restaurant more in overhead, wages and ingredients that could negatively offset maximum profitability via the increase in cost.

Costs:

• $3.00 per filet
• $10 of electricity and overhead per hour
• $15.00 hourly Chef wages

To illustrate further, the restaurant sells the filets for $9.50 each or $114.00 before tax for a profit of $23.00. If the restaurant wants to produce 15 filet mignons they will either have to hire 1 more chef, buy more filets and use more overhead. This additional increase will cost $15.00 for the Chef, $9.00 for the filets and $3.33 for electricity and overhead for a total of $27.33. 15 filets sold at $9.50 are $142.50 for an additional $27.33 of cost. The total cost is now $91.00 + $27.33=$118.33 and the profit is $142.50-$118.33=24.17. Thus the costs increase more than the profits to produce more filets confirming the law of increasing costs. Stated otherwise, with maximum efficiency at 12 filets/hour, the restaurant makes 25.27% of cost i.e. profit margin or 20.17% of total revenue whereas with 15 filets produced the restaurant only earns 20.43% of cost or 16.97% of revenue.

Validation of the law of increasing costs


The law of increasing costs can be both confirmed through cost adjustment profit margin comparisons. Moreover, in the world of business, costs only remain fixed for relative periods of time making the maximum efficiency in production also variable. This can be illustrated by adjusting an calculating profit margin for adjustments in Chef's time spent working and the number of Chefs. For example, if filet costs rise to $3.50 per filet due to a drought that causes feed costs to rise, then the maximum profit margin will remain at 12 filets as stated in the above example. This will be illustrated by comparing 2 separate adjustments in comparison to the original efficiency level or 'control' level above.

• Effect of filet cost increase on original efficiency

To illustrate how efficiency is stable at a certain rate regardless of Chefs used, time spent cooking and cost of filets the following examples are illustrative. If the Chefs produce 4 filets each per hour at the increased filet cost of $3.50, 12 filets will be produced as in the previous illustration. However, all other costs held constant this amounts to $114.00 in sales minus $97.00 in cost=$17.00=17.525% in profit for a 7.74% decrease in profit margin for a .50 cent rise in per unit cost.

• Effect of hiring a 4th Chef on profit margin

If a fourth Chef is hired, 15 filets will be produced at a cost of $60.00(wages) + $52.50 (filets)+$13.33 (overhead)=$125.83. At $9.50 per filet this new production of 15 filets yields $142.50 in sales. $142.50-125.83=16.67, which is 12.03% less profit margin.

• Effect of reducing time spent cooking on profit margin

Contrarily, if the Chefs only work for half an hour however, and produce only 6 filets, the cost goes down $22.50 in wages, $21 for filets, and $5.00 in electricity and overheard for a total cost of $48.50. Since the filets are sold for $9.50 each without adjusting for cost, the total sales will be $57.00 minus $48.50 in cost for a profit of $8.50=7.92% decrease in profit margin.

While reducing the cooking time decreases profit margin by a similar amount to holding all other variables constant except filet cost, the original example still yields a slightly greater efficiency i.e. 7.92%-7.74%=.18% difference in favor of the original method.

Despite the above validation of the law of increasing costs, there is still evidence the law is not absolute via certain additional adjustments and/or scenarios. For example, in instances, where increasing per unit cost has a multiplier effect on potential profit margin, the law of increasing costs does not apply. 

To illustrate this example, consider the application of exponential increase in output for linear increase in input. Since exponential increases are greater than linear increases, the efficiency will rise with linear increase in input. Moore's law and computing components (answers.yahoo.com) illustrate this point. As technology advances, output of computers increases more than the per unit cost in enhancing the technology.

The law of increasing costs is similar to the law of diminishing returns and can be illustrated using the law of diminishing returns that states costs will increase as evident in a decrease in returns when production levels surpass maximum profitability and/or efficiency levels of production. This article illustrated this law through the example of 3 Chefs producing filet mignon at a restaurant with costs held constant and adjusted. 

In all examples, the efficiency level was not contradicted. Nevertheless, the law of increasing cost is not absolute as evident in certain scenarios such as the application of exponential output via application of Moore's law to linear increase in cost input. While Moore's law itself is debatable, the example serves to illustrate cases of increased efficiency are possible when exponential or larger production is possible for a corresponding declining percentage increase in input costs.

Sources:

1. http://en.wikipedia.org/wiki/Diminishing_returns
2. http://answers.yahoo.com/question/index?qid=20060907234254AAULjAS
3. http://en.wikipedia.org/wiki/Moore's_law
4. http://mmcconeghy.com/students/supscruleof70.html