Elasticity Logchange Residual Tool

Description

quantityLogChange = ln(quantityAfter)-ln(quantityBefore); predictedLogChange = elasticity*(ln(priceAfter)-ln(priceBefore)); residual is observed minus predicted.

An economic model specifies how quantities, prices or marginal values relate under stated assumptions. A derivative, reaction function or first-order-condition term is a local model object rather than an empirical finding or complete equilibrium solution.

quantityLogChange = ln(quantityAfter)-ln(quantityBefore); predictedLogChange = elasticity*(ln(priceAfter)-ln(priceBefore)); residual is observed minus predicted.

When to use this tool

Use Elasticity Logchange Residual when checking one explicit theoretical economic-model relationship.

How to use the tool and how it works

Enter quantityBefore, quantityAfter, priceBefore, priceAfter, elasticity. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read quantityLogChange, predictedLogChange, residual. Use the output convention below.

Require positive before/after quantities and prices. quantityLogChange = ln(quantityAfter)-ln(quantityBefore); predictedLogChange = elasticity*(ln(priceAfter)-ln(priceBefore)); residual is observed minus predicted.^[1]

Input field	Meaning and units	Accepted input
quantityBefore	Quantity Before	Required. Finite number; strictly above 0.
quantityAfter	Quantity After	Required. Finite number; strictly above 0.
priceBefore	Price Before	Required. Finite number; strictly above 0.
priceAfter	Price After	Required. Finite number; strictly above 0.
elasticity	Elasticity	Required. Finite number.

Output field	Interpretation	Returned shape
quantityLogChange	Quantity Log Change	Required. Finite number.
predictedLogChange	Predicted Log Change	Required. Finite number.
residual	Residual	Required. Finite number.

json

{
  "input": {
    "quantityBefore": 1,
    "quantityAfter": 2,
    "priceBefore": 1,
    "priceAfter": 2,
    "elasticity": 1
  },
  "output": {
    "quantityLogChange": 0.6931471805599453,
    "predictedLogChange": 0.6931471805599453,
    "residual": 0
  }
}

Limitations and assumptions

This applies a supplied constant log-elasticity relationship. It does not estimate elasticity, correct confounding or interpret the residual as a causal demand shock.
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

Use a complete model, defensible parameter estimates and suitable identification before drawing empirical or policy conclusions.

References

Calculation and input contract: economics/elasticity-logchange-residual — tool.io

Similar or alternative tools

Marginal Product Elasticity Term
elasticity = suppliedMarginalProduct*inputQuantity/outputQuantity; if the direct product overflows or spuriously underflows, reorder multiplication with the input/output ratio.
Ces Substitution Elasticity Parameter Crosswalk
elasticity = 1/(1-rho), using the CES convention with rho as the power on inputs inside the aggregator.