Description
Compare an observed factor-income share with a supplied Cobb-Douglas output elasticity.
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.
Compare an observed factor-income share with a supplied Cobb-Douglas output elasticity.
When to use this tool
Use Cobb Douglas Share Reference Gap when checking one explicit theoretical economic-model relationship.
How to use the tool and how it works
- Enter outputElasticity, observedFactorIncome, totalIncome. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read observedShare, gap. Use the output convention below.
Require positive totalIncome and nonnegative observedFactorIncome. observedShare = observedFactorIncome/totalIncome; gap = observedShare-outputElasticity.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| outputElasticity | Output Elasticity | Required. Finite number. |
| observedFactorIncome | Observed Factor Income | Required. Finite number; minimum 0. |
| totalIncome | Total Income | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| observedShare | Observed Share Unit: 1. | Required. Finite number. |
| gap | Signed difference from the stated reference, using compatible units. | Required. Finite number. |
{
"input": {
"outputElasticity": 0.3,
"observedFactorIncome": 40,
"totalIncome": 100
},
"output": {
"observedShare": 0.4,
"gap": 0.10000000000000003
}
}Limitations and assumptions
- The share can exceed one because supplied amounts are not reconciled. Comparing it with a Cobb-Douglas elasticity does not validate competitive factor pricing or estimate the production model.
- 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
Similar or alternative tools
- Cobb Douglas Marginal Rate Substitution Term
mrs = alpha*y/((1-alpha)*x), the positive MUx/MUy magnitude for x^alpha*y^(1-alpha).
- Cobweb Linear One Period Update
nextPrice = (demandIntercept-supplyIntercept-supplySlope*previousPrice)/demandSlope.