Description
secondQuantity = (income-firstPrice*firstQuantity)/secondPrice; priceDerivative = -firstQuantity/secondPrice.
A budget constraint links prices, quantities and a monetary resource. An axis intercept, residual or local share contribution describes one aspect of that constraint and does not independently solve preferences or determine actual affordability.
secondQuantity = (income-firstPrice*firstQuantity)/secondPrice; priceDerivative = -firstQuantity/secondPrice.
When to use this tool
Use Budget Frontier Single Price Derivative when checking one supplied basket, budget-line or resource-allocation term.
How to use the tool and how it works
- Enter income, firstPrice, secondPrice, firstQuantity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read secondQuantity, priceDerivative. Use the output convention below.
Require positive firstPrice and secondPrice and nonnegative income and firstQuantity. secondQuantity = (income-firstPrice*firstQuantity)/secondPrice; priceDerivative = -firstQuantity/secondPrice.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| income | Income | Required. Finite number; minimum 0. |
| firstPrice | First Price | Required. Finite number; strictly above 0. |
| secondPrice | Second Price | Required. Finite number; strictly above 0. |
| firstQuantity | First Quantity | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| secondQuantity | Second Quantity | Required. Finite number. |
| priceDerivative | Price Derivative | Required. Finite number. |
{
"input": {
"income": 100,
"firstPrice": 10,
"secondPrice": 5,
"firstQuantity": 3
},
"output": {
"secondQuantity": 14,
"priceDerivative": -0.6
}
}Limitations and assumptions
- The derivative holds income, first quantity and second price fixed. Negative second quantity is retained rather than enforcing basket feasibility or solving demand.
- 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 the complete feasible set and an appropriate choice model for optimization, rationing or welfare questions.
References
Similar or alternative tools
- Budget Line Axis Intercept
intercept = budget/price, the maximum single-good quantity if all budget is spent at that price.
- Budget Share Compensated Change
initialExpenditure = initialShare*expenditure; shareContribution = price*suppliedCompensatedQuantityChange/expenditure.