Description
followerQuantity = max(0,(demandIntercept-marginalCost-slope*leaderQuantity)/(2*slope)).
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.
followerQuantity = max(0,(demandIntercept-marginalCost-slope*leaderQuantity)/(2*slope)).
When to use this tool
Use Stackelberg Follower Reaction Point when checking one explicit theoretical economic-model relationship.
How to use the tool and how it works
- Enter demandIntercept, slope, marginalCost, leaderQuantity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read followerQuantity. Use the output convention below.
Require positive slope and nonnegative leaderQuantity. followerQuantity = max(0,(demandIntercept-marginalCost-slope*leaderQuantity)/(2*slope)).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| demandIntercept | Demand Intercept | Required. Finite number. |
| slope | Slope | Required. Finite number; strictly above 0. |
| marginalCost | Marginal Cost | Required. Finite number. |
| leaderQuantity | Leader Quantity | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| followerQuantity | Follower Quantity | Required. Finite number. |
{
"input": {
"demandIntercept": 100,
"slope": 2,
"marginalCost": 20,
"leaderQuantity": 10
},
"output": {
"followerQuantity": 15
}
}Limitations and assumptions
- This is the follower best-response point under linear inverse demand and constant marginal cost. Leader optimization, capacity limits and real strategic behavior are not solved.
- 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
- Slutsky Income Effect Single Good
incomeEffect = -quantity*incomeDerivative, the income contribution to the good's own-price derivative under this sign convention.
- Tax Incidence Elasticity Share Term
consumerShare = supplyElasticity/sum; producerShare = demandElasticityMagnitude/sum.