Worked-example setupScope and assumptions
- The $50/900 and $70/700 endpoints lie on Linden's same stipulated weekly demand line; no demand determinant shifts between them.
- The midpoint method and signed coefficient are computed first; the conventional demand magnitude is then reported separately.
- Endpoint price-times-quantity is described as a conditional model product, not recognized seller revenue, profit, cash, or a recommendation.
- Period
- One representative fictional week at each endpoint
- Units
- USD per qualifying chair; qualifying chairs per week; unit-free elasticity
- Rounding
- Full precision internally; proportional changes and elasticity displayed to four decimals
Linden's stipulated demand line gives 900 chairs per week at $50 and 700 at $70. The slope is -10 chairs per week per dollar. That is not the elasticity; it carries units and does not scale either change.
Build the midpoint control table
| Component | Change | Midpoint | Proportional change |
|---|---|---|---|
| Quantity demanded | 700 - 900 = -200 | (900 + 700) / 2 = 800 | -25.0000% |
| Own price | $70 - $50 = $20 | ($50 + $70) / 2 = $60 | 33.3333% |
signed elasticity = -0.25 / 0.333333... = -0.75
conventional demand magnitude = 0.75
The negative sign records opposite movement. The magnitude is below one, so demand is inelastic over this arc. Reversing the endpoints gives positive percentage denominators where these are negative and preserves the same signed coefficient and magnitude.
Test the conditional endpoint product
If the modeled quantities are sold at those prices, with no rationing, shift, discount, return, tax, or quality change:
$50 × 900 = $45,000
$70 × 700 = $49,000
change = +$4,000
That direction is consistent with an inelastic demand arc: price changes proportionally more than quantity in the opposite direction. It is not a price recommendation and does not establish profit.
Quantity demanded is not a sale. Recognized revenue requires seller identity, contract, performance, transaction price, completed transfer, returns and variable consideration evidence, period, and applicable authority. Cash adds a collection event. The elasticity calculation closes none of those ledgers.
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
- 1 field
Inspect data
{
"linden_demand_arc": {
"driver_end": 70,
"driver_name": "usd_per_chair",
"driver_start": 50,
"relationship": "price_demand",
"response_end": 700,
"response_name": "chairs_demanded_per_week",
"response_start": 900
}
}Recomputed result
| Measure | Value |
|---|---|
| absolute elasticity | 0.75 |
| conventional price elasticity of demand | 0.75 |
| driver midpoint | 60 |
| driver proportional change | 0.3333 |
| ending total revenue | 49,000 |
| inelastic | 1 |
| response midpoint | 800 |
| response proportional change | -0.25 |
| signed elasticity | -0.75 |
| starting total revenue | 45,000 |
| total revenue change | 4,000 |