Description
Return the signed local second-good-versus-first-good production-frontier slope and its opportunity-cost magnitude.
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.
Return the signed local second-good-versus-first-good production-frontier slope and its opportunity-cost magnitude.
When to use this tool
Use Production Possibility Frontier Local Slope when checking one explicit theoretical economic-model relationship.
How to use the tool and how it works
- Enter marginalProductFirst, marginalProductSecond. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read slope, opportunityCost. Use the output convention below.
Require positive marginalProductFirst and nonnegative marginalProductSecond. slope = -marginalProductSecond/marginalProductFirst; opportunityCost is the positive counterpart.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| marginalProductFirst | Marginal Product First | Required. Finite number; strictly above 0. |
| marginalProductSecond | Marginal Product Second | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slope | Second-good vertical output versus first-good horizontal output under the stated marginal-product convention. | Required. Finite number. |
| opportunityCost | Opportunity Cost | Required. Finite number. |
{
"input": {
"marginalProductFirst": 3,
"marginalProductSecond": 6
},
"output": {
"slope": -2,
"opportunityCost": 2
}
}Limitations and assumptions
- The returned convention treats second-good output on the vertical axis and first-good output on the horizontal axis under a resource shift dX = marginalProductFirst*dR and dY = -marginalProductSecond*dR. Axis reversal inverts the ratio; no full production frontier is estimated.
- 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
- Production Cost Returns Exponent
elasticity = ln(costScale)/ln(outputScale); superlinear tests elasticity > 1.
- Public Good Lindahl Share Balance
sumBenefits is the sum; residual = sumBenefits-marginalCost.