Is price elasticity of supply ever negative?

PES is typically non‑negative because price and quantity supplied usually move in the same direction. Negative values indicate data errors or non‑standard situations.

Arc vs point elasticity—when should I use which?

Use arc elasticity for finite changes between two points to avoid base bias. Use point elasticity for small changes or when estimating at a point using a derivative.

Why does PES differ across time horizons?

In the short run capacity is fixed so supply is less responsive (lower PES). Over longer horizons firms can add capacity and PES increases.

How do taxes or subsidies affect PES readings?

Tax or subsidy wedges shift effective producer prices; the observed responsiveness can differ from underlying technical elasticity. The calculator shows an adjusted view.

What if price or quantity doesn’t change?

Arc elasticity is undefined if both points have the same price or quantity. The tool warns you and suggests a minimal perturbation or the point formula.

Price Elasticity of Supply (PES) Calculator

Compute arc and point PES, visualize supply shifts, and estimate long‑run responsiveness with regression. Run batch CSVs, cap capacity, model tax or subsidy wedges, and export clean charts and reports. Built with AngularJS and Bootstrap, optimized for speed, accessibility, education, and SEO‑friendly structured data to help users and teams. Deliver clarity, confidence, and repeatability.

P₁ ({{vm.currency}})

Q₁ ({{vm.qUnit}})

P₂ ({{vm.currency}})

Q₂ ({{vm.qUnit}})

Currency

Quantity unit

Horizon

Max capacity ({{vm.qUnit}})

Tax/Subsidy wedge (%)

Applied to producer price for adjusted view.

Sensitivity (±% around P₁)

−10%{{vm.sensitivity}}%+10%

{{vm.horizon}} context: {{vm.horizonNote}}

Result {{vm.classBadge.label}}

PES = {{vm.es | number:3}}

(Arc method by default)

ΔP: {{vm.deltaP.sign}} {{vm.formatPrice(vm.deltaP.abs)}} ({{vm.deltaP.pct | number:2}}%)
ΔQ: {{vm.deltaQ.sign}} {{vm.formatQty(vm.deltaQ.abs)}} ({{vm.deltaQ.pct | number:2}}%)
Adjusted for wedge: {{vm.taxPct || 0}}%
Capacity binding: Q₂ capped at {{vm.formatQty(vm.capacity)}}.

Saved scenarios

#	Label	P₁	Q₁	P₂	Q₂	PES	Class
{{$index+1}}		{{vm.formatPrice(s.p1)}}	{{vm.formatQty(s.q1)}}	{{vm.formatPrice(s.p2)}}	{{vm.formatQty(s.q2)}}	{{s.es \| number:3}}	{{s.classLabel}}

%Δ Price

%Δ Quantity

Tax/Subsidy wedge (%)

PES = {{vm.esPct | number:3}}

Direct percent mode (no units required). Adjusted view for wedge: {{vm.taxPctPctMode||0}}%.

Elasticity (target Eₛ)

Given

Enter %Δ Price

Enter %Δ Quantity

Upload CSV (columns: label,P1,Q1,P2,Q2)

Example row: Widget A,100,1000,110,1150

#	Label	P₁	Q₁	P₂	Q₂	PES	Class
{{$index+1}}	{{row.label}}	{{vm.formatPrice(row.p1)}}	{{vm.formatQty(row.q1)}}	{{vm.formatPrice(row.p2)}}	{{vm.formatQty(row.q2)}}	{{row.es \| number:3}}	{{row.classLabel}}
Mean PES						{{vm.batchStats.mean \| number:3}}

Estimate long‑run PES from a time series using a simple log–log regression on (P, Qs). Upload CSV with columns: P,Q.

Upload CSV (P,Q)

Log–log estimate

β (PES): {{vm.regression.beta | number:3}}
Intercept: {{vm.regression.intercept | number:3}}
R²: {{vm.regression.r2 | number:3}}
n: {{vm.regression.n}}

How it works

Arc elasticity between two points uses the midpoint formula to avoid base bias:

E_s = (ΔQ / \bar{Q}) / (ΔP / \bar{P}),  where  \bar{Q}=(Q₁+Q₂)/2,  \bar{P}=(P₁+P₂)/2.

Point elasticity approximates responsiveness at a point: E_s ≈ (ΔQ/ΔP) × (P/Q) for small changes. For real data with finite changes, arc is generally preferred.

Range	Classification
0	Perfectly inelastic
0 < Eₛ < 1	Inelastic
= 1	Unitary
> 1	Elastic
∞	Perfectly elastic

Tips

Set a realistic max capacity; near capacity, supply becomes less responsive.
Use the sensitivity slider to see how small price moves translate to quantity responses with your estimated Eₛ.
For policy analysis, apply a tax/subsidy wedge to see an adjusted view.

Quick FAQ

Is PES negative?

PES is usually ≥ 0. Negative values imply issues with data or unusual contexts.

Arc vs point?

Arc for finite changes; point for small changes around a baseline.

Short‑run vs long‑run?

Capacity is fixed in the short run; more flexible long run → higher PES.

What if ΔP=0?

Elasticity is undefined. Nudge values slightly or switch to point formula.

Exports

CSV of inputs & outputs
PNG chart snapshot
PDF one‑pager summary

About This Calculator and the PES Formula

The Price Elasticity of Supply (PES) measures how responsive quantity supplied is to a change in price. This tool implements both the arc (midpoint) method for finite changes and a point approximation for very small changes. Use Two‑Point (Arc) when you know before/after prices and quantities; use Percent Mode for quick ratio checks; and the Target Solver to ask “what change in price would be needed for a desired change in supply,” or vice versa. In practice, PES depends on production flexibility, input availability, storage, and—crucially—time horizon. In the short run, capacity is often fixed, so firms can’t ramp output much; in the long run, investment and reallocation make supply more elastic.

Formulas. The arc (midpoint) elasticity avoids base bias by dividing changes by the average level: E_s = (ΔQ/\bar{Q}) / (ΔP/\bar{P}), where \bar{Q}=(Q₁+Q₂)/2 and \bar{P}=(P₁+P₂)/2. The point approximation at a baseline (P,Q) uses E_s ≈ (ΔQ/ΔP) × (P/Q) for small movements. The calculator also includes an optional ad valorem tax/subsidy wedge so you can observe how a policy‑adjusted producer price changes the measured responsiveness.

Mode	Inputs	Typical use‑case
Two‑Point (Arc)	P₁, Q₁, P₂, Q₂	Compare two observed states and avoid base bias.
Percent Mode	%ΔP, %ΔQ	Quick sense‑check or when only percentage changes are known.
Point Approximation	P₁, Q₁ plus small ΔP	Local sensitivity around a current operating point.
Regression (log–log)	Time series of P, Q	Estimate long‑run elasticity from historical data (β ≈ PES).

Mode

Inputs

Typical use‑case

Two‑Point (Arc)

P₁, Q₁, P₂, Q₂

Compare two observed states and avoid base bias.

Percent Mode

%ΔP, %ΔQ

Quick sense‑check or when only percentage changes are known.

Point Approximation

P₁, Q₁ plus small ΔP

Local sensitivity around a current operating point.

Regression (log–log)

Time series of P, Q

Estimate long‑run elasticity from historical data (β ≈ PES).

Interpreting Results

After you enter values, the calculator reports a coefficient and a plain‑English verdict. Values between 0 and 1 indicate inelastic supply; equal to 1 is unitary; greater than 1 indicates elastic supply. The capacity field lets you cap Q₂ to reflect an operational ceiling—near capacity, additional price increases barely raise output, pushing PES downward. The tax/subsidy control applies a wedge to price received by producers, which can change the observed responsiveness for policy simulations.

Range	Classification	Example intuition
0	Perfectly inelastic	Output fixed (e.g., very short‑run with rigid capacity).
0 < Eₛ < 1	Inelastic	Limited flexibility; modest output response to price.
= 1	Unitary	Proportional: 1% price → 1% quantity.
> 1	Elastic	Ample capacity or scalability; strong response.
∞	Perfectly elastic	Producers supply any amount at a going price (theoretical).

Range

Classification

Example intuition

Perfectly inelastic

Output fixed (e.g., very short‑run with rigid capacity).

0 < Eₛ < 1

Inelastic

Limited flexibility; modest output response to price.

= 1

Unitary

Proportional: 1% price → 1% quantity.

> 1

Elastic

Ample capacity or scalability; strong response.

∞

Perfectly elastic

Producers supply any amount at a going price (theoretical).

Workflow tips. Start with a realistic short‑run scenario and save it. Use the sensitivity slider to nudge price around P₁ and observe implied Q₂ based on your estimated coefficient. For planning, add a long‑run scenario with a higher capacity and compare. Upload product‑level rows via Batch to compute elasticity per SKU and export the results for analysis. With historical data, use the Regression tab: fit a simple log–log line to obtain β (the slope), which approximates long‑run PES; inspect R² to gauge fit quality. Finally, export a PDF one‑pager that captures inputs, classification, and the chart for sharing with teammates or stakeholders.