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Abatement Cost Curve Segment Tool

Integrate one caller-supplied linear marginal abatement-cost segment by the trapezoid rule.

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Description

Return incrementalQuantity = endQuantity-startQuantity and segmentCost = incrementalQuantity*(startMarginalCost+endMarginalCost)/2.

Average, incremental and marginal environmental costs answer different questions. A ratio over a finite reduction is a step average, while marginal cost describes an additional unit; meaningful comparisons need common periods, boundaries and units.

Return incrementalQuantity = endQuantity-startQuantity and segmentCost = incrementalQuantity*(startMarginalCost+endMarginalCost)/2.

When to use this tool

Use Abatement Cost Curve Segment when checking a supplied environmental cost contribution or comparison.

How to use the tool and how it works

  1. Enter startQuantity, endQuantity, startMarginalCost, endMarginalCost. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read incrementalQuantity, segmentCost. Use the output convention below.

Require endQuantity >= startQuantity. Return incrementalQuantity = endQuantity-startQuantity and segmentCost = incrementalQuantity*(startMarginalCost+endMarginalCost)/2. Marginal costs must be currency per quantity unit on a matching valuation basis.1

A complete environmental economic analysis compares benefits, costs, baselines and timing. Integrating one supplied cost segment supplies a local cost term rather than a complete policy evaluation.2

Input fieldMeaning and unitsAccepted input
startQuantityStart QuantityRequired. Finite number.
endQuantityEnd QuantityRequired. Finite number.
startMarginalCostStart Marginal CostRequired. Finite number.
endMarginalCostEnd Marginal CostRequired. Finite number.
Output fieldInterpretationReturned shape
incrementalQuantityIncremental QuantityRequired. Finite number.
segmentCostSegment CostRequired. Finite number.
json
{
  "input": {
    "startQuantity": 10,
    "endQuantity": 30,
    "startMarginalCost": 2,
    "endMarginalCost": 4
  },
  "output": {
    "incrementalQuantity": 20,
    "segmentCost": 60
  }
}

Limitations and assumptions

  • This trapezoidal integral assumes marginal cost varies linearly across the segment. Signed quantities and marginal costs are accepted, equal endpoints give zero cost, and one segment does not construct a complete abatement curve or determine a policy optimum.
  • Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Assemble comparable costs and effects across the full baseline and project, and distinguish financial costs from social costs before ranking alternatives.

References

  1. Calculation and input contract: environmental-economics/abatement-cost-curve-segment — tool.io

  2. Guidelines for Preparing Economic Analyses, 3rd edition — U.S. Environmental Protection Agency

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