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Worked-example setupScope and assumptions
- Harbor is original fiction; each pair uses aligned weekly endpoints for one defined customer segment and holds focal-good own price and other modeled determinants fixed.
- The packet stipulates relationships for instruction; it does not supply an observational or causal estimate.
- Product direction is explicit: coffee quantity responds to tea price, and cereal quantity responds to milk price.
- Period
- Two comparable fictional weekly scenarios for each product pair
- Units
- USD per driver-good unit; focal-good units per week; unit-free cross-price elasticity
- Rounding
- Full precision internally; elasticities displayed to four decimals
Harbor's fictional packet contains two different response directions.
Coffee quantity responding to tea price
Tea price rises from $4 to $5. Coffee demand rises from 100 to 112 units per week.
coffee quantity change = 12 / 106 = 11.3208%
tea price change = 1 / 4.5 = 22.2222%
cross-price elasticity = +0.5094
The positive sign supports coffee as a substitute for tea in this segment and range. It does not prove that tea is equally strong as a substitute for coffee; that reverses numerator and denominator products and needs separate evidence.
Cereal quantity responding to milk price
Milk price rises from $4 to $5. Cereal demand falls from 100 to 90 units.
cereal quantity change = -10 / 95 = -10.5263%
milk price change = 1 / 4.5 = 22.2222%
cross-price elasticity = -0.4737
The negative sign supports cereal as a complement to milk under the packet's conditions. Classification comes from sign. The fact that both magnitudes are below one does not turn either relationship into “unrelated.”
Stop before the legal and strategic conclusions
Brand, use, location, switching cost, bundles, availability, customer segment, and time can change both coefficients. A real competition analysis would need current law, market-definition evidence, supply response, entry, contracts, multi-product behavior, and institutional authority. A pricing plan would add own-price demand, costs, capacity, competitor response, uncertainty, and governance.
The two coefficients classify stipulated relationships. They do not prove a legal market, market power, realized sales, revenue, profit, or cash.
Verified calculation · economics foundations analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- midpoint elasticities
- 2 fields
Inspect data
{
"cereal_response_to_milk_price": {
"driver_end": 5,
"driver_name": "milk_price_usd_per_unit",
"driver_start": 4,
"relationship": "cross_price_demand",
"response_end": 90,
"response_name": "cereal_units_demanded_per_week",
"response_start": 100
},
"coffee_response_to_tea_price": {
"driver_end": 5,
"driver_name": "tea_price_usd_per_unit",
"driver_start": 4,
"relationship": "cross_price_demand",
"response_end": 112,
"response_name": "coffee_units_demanded_per_week",
"response_start": 100
}
}Recomputed result
| Measure | Value |
|---|---|
| cereal response to milk price negative signed elasticity | 1 |
| cereal response to milk price signed elasticity | -0.4737 |
| coffee response to tea price positive signed elasticity | 1 |
| coffee response to tea price signed elasticity | 0.5094 |