Description
mrs = alpha*y/((1-alpha)*x), the positive MUx/MUy magnitude for x^alpha*y^(1-alpha).
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.
mrs = alpha*y/((1-alpha)*x), the positive MUx/MUy magnitude for x^alpha*y^(1-alpha).
When to use this tool
Use Cobb Douglas Marginal Rate Substitution Term when checking one explicit theoretical economic-model relationship.
How to use the tool and how it works
- Enter x, y, alpha. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read mrs. Use the output convention below.
Require positive x and y and alpha in (0,1). mrs = alpha*y/((1-alpha)*x), the positive MUx/MUy magnitude for x^alpha*y^(1-alpha).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number; strictly above 0. |
| y | Y | Required. Finite number; strictly above 0. |
| alpha | Alpha | Required. Finite number; strictly above 0; strictly below 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| mrs | Mrs | Required. Finite number. |
{
"input": {
"x": 4,
"y": 6,
"alpha": 0.5
},
"output": {
"mrs": 1.5
}
}Limitations and assumptions
- The corresponding y-versus-x indifference-curve slope is negative mrs. This local ratio does not choose an optimal basket or validate preferences.
- 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 Share Reference Gap
Compare an observed factor-income share with a supplied Cobb-Douglas output elasticity.
- Ces Substitution Elasticity Parameter Crosswalk
elasticity = 1/(1-rho), using the CES convention with rho as the power on inputs inside the aggregator.