Wednesday, April 13, 2011

The trouble with average costs as a performance indicator

There are two types of coal from the Southern Powder River Basin in Wyoming: 8800 BTU coal, and 8400 BTU coal. The 8800 and 8400 numbers refer to the amount of energy contained in one pound of coal. The coal is delivered by rail and barge to power plants that crush it, burn it, and use the heat to create steam that drives generators that produce electricity.

8400 coal produces about 5% less electricity per ton than 8800 coal, so when the price of 8400 falls below 95% of the price of 8800, the average cost of producing electricity with 8400 coal falls below the average cost of electricity from 8800 coal.

However, when a plant manager at a coal-burning power plant made the switch from 8800 to 8400, his power plant was "de-rated," which means that its electrical output fell by 5%. The conveyor belts and crushers were already working at capacity, so he could not put a bigger volume of coal through the plant.  This forced his parent company to replace the lost electricity with higher-cost natural gas, which was even more expensive than producing electricity with 8800 coal.

The reason that the plant manager made the mistake was due to his balanced scorecard performance evaluation metric which included the average cost of electricity that he produced.

This story illustrates several ideas in the book:
  • the Hidden Cost Fallacy: the manager should have considered the hidden cost of replacing the lost electricity (the opportunity cost of his decision to switch to 8400);
  • that average costs are not necessarily the relevant costs of a decision;
  • that problems arise when the incentives of a business unit are not aligned with the goals of the parent company.
  • that demand is more price elastic in the long run:  in the short run, it would take a bigger drop in the price of 8400 to induce a plant manager--one whose incentives were aligned with the profitability goals of the parent company--to switch to 8400 due to the lost electricity.  In other words, the substitution between the two types of coal (measured by the cross-price elasticity of demand) would be bigger in the long run, when the capacity of the plant can be changed, than in the short run, when it cannot.


  1. The 8400 and 8800 numbers refer to the amount of energy contained in one POUND of coal.

  2. thanks, I changed it, Luke

  3. This comment has been removed by the author.

  4. The correct math exists but people fetishize math and then use the wrong math, unfortunately. Then they think because they are using math it must be correct.

  5. Another observation is that this sort of bias is baked-in to the voting process (it measures at medians more than it does at the margin), so democracies are very prone to it.

  6. It was a awe-inspiring post and it has a significant meaning and thanks for sharing the information.Would love to read your next post too......
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