Price Elasticity of Demand

How price elasticity works

Imagine the corner store raises the price of a candy bar from $1.00 to $1.10 — a 10% bump. If sales fall from 100 to 95 bars a day, quantity dropped 5%. Elasticity is −5% ÷ +10% = −0.5. Demand is inelastic: shoppers grumble but mostly still buy. Now do the same exercise with movie tickets, raising prices 10% and watching attendance fall 25%. Elasticity is −2.5, and demand is highly elastic — viewers stream Netflix instead.

The formal definition is:

PED = (percent change in quantity demanded) ÷ (percent change in price)
    = (ΔQ / Q) ÷ (ΔP / P)

Because the demand curve slopes downward, ΔQ and ΔP have opposite signs, and PED is negative for any normal good. By long convention, economists drop the minus sign in conversation — saying "the elasticity of cigarettes is 0.4" — but every formula and every regression carries the negative sign explicitly.

The number lives on a continuum:

     |PED|         Demand          What price hike does to revenue
   ─────────  ─────────────────  ──────────────────────────────────
        0      Perfectly inelastic   Revenue rises in lockstep with price
   0 to 1     Inelastic              Revenue rises (slower than price)
        1     Unit elastic            Revenue unchanged
   1 to ∞     Elastic                 Revenue falls
        ∞     Perfectly elastic      Revenue collapses to zero

Worked example: a cigarette tax

Suppose the empirical short-run elasticity of cigarette demand is −0.4 (the figure most often cited in tax-policy work, drawn from Chaloupka and Warner's surveys of dozens of studies). A pack costs $8.00 and 100 million packs are sold per month. Congress imposes a $2.00-per-pack excise tax, fully passed through to consumers, raising the price 25%.

Predicted change in quantity:

%ΔQ = PED × %ΔP
     = (−0.4) × (+25%)
     = −10%

New quantity = 100 million × 0.90 = 90 million packs/month

Tax revenue: $2.00 × 90 million = $180 million per month. Producer revenue (at the original $8 price): $8 × 90 million = $720 million, down from $800 million. Consumers pay $10 × 90 million = $900 million, up from $800 million. The government captures the full $2 wedge.

Now run the same tax on a more elastic good — say craft beer with PED ≈ −1.5. A 25% price hike now drops quantity 37.5%. Tax revenue per unit is the same $2, but only 62.5 million units sell. Revenue: $125 million, not $180 million. The lesson: governments tax inelastic goods because the base barely shrinks.

Real-world elasticities

Reported values vary by study, country, and time horizon, but the consensus ranges (drawn from BLS CPI elasticity work, the OECD's energy demand reviews, and the Tax Policy Center's sin-tax surveys) are:

Good	Short-run PED	Long-run PED	Why
Salt	−0.1	−0.1	No substitutes, tiny share of income
Gasoline	−0.25	−0.6	Cars are durable; long-run, drivers buy hybrids
Cigarettes	−0.4	−0.7	Addictive; quitting is slow but possible
Electricity (residential)	−0.3	−0.9	Long-run, homes get insulation and heat pumps
Beef	−0.7	−1.0	Many protein substitutes
Restaurant meals	−1.6	−2.3	Cooking at home is a near-perfect substitute
Foreign vacations	−1.8	−2.5	Discretionary; substitute is staying home
Coca-Cola (vs. all soda)	−3.8	−4.4	Pepsi sits one shelf over

Two patterns repeat: long-run elasticities are bigger than short-run ones, and brand-level elasticities (Coca-Cola) are bigger than category-level ones (sugary drinks). When a Pepsi costs the same and tastes similar, brand demand is highly elastic even when the category is not.

The demand curve, visually

A standard linear demand curve looks like this, with price on the vertical axis and quantity on the horizontal:

  P  ↑
     |\
     | \    ← elastic region (top half: |PED| > 1)
     |  \
     |   \
     |    \   ← unit elastic at the midpoint
     |     \
     |      \  ← inelastic region (bottom half: |PED| < 1)
     |       \
     +────────→ Q

This is the single most counter-intuitive fact about elasticity for beginners: even though the slope of a linear demand curve is constant, the elasticity changes at every point. At a high price, a $1 cut is a small percentage change but produces a large percentage rise in quantity (because quantities are tiny). At a low price, the same $1 cut is a huge percentage change producing only a small percentage rise. Elasticity ≠ slope.

Two extreme shapes anchor the intuition:

Perfectly inelastic            Perfectly elastic
(insulin, vertical line)      (perfect substitute, horizontal line)

P ↑                            P ↑
  |                              |
  |  |                           |─────────────  P*
  |  |                           |
  |  |                           |
  +──┴────→ Q                    +──────────→ Q

PED = 0                         PED = −∞

Variants: point vs arc, own vs cross

	Point elasticity	Arc (midpoint) elasticity
Formula	(dQ/dP)·(P/Q)	(ΔQ ÷ avg Q) ÷ (ΔP ÷ avg P)
Reference point	A single price-quantity pair	The midpoint of two pairs
Symmetric A→B vs B→A?	Only if Q and P are tiny	Yes, exactly
Best for	Calculus / theoretical work	Empirical / two-point data

Point elasticity is the calculus form: take the derivative dQ/dP and multiply by P/Q. It is the right answer for an infinitesimal price move and the building block of every regression model. Arc elasticity is the discrete version that economists use when they only have two price-quantity observations — a Tuesday-Wednesday price change at a grocery store, say. The midpoint formula is the unique discrete formula that returns the same number whether you compute the move forward or backward, which is why it became standard in textbooks.

Beyond price elasticity of demand, the same construction defines other elasticities: cross-price elasticity (response of one good's quantity to another good's price), income elasticity (response of quantity to income), and price elasticity of supply (response of quantity supplied to price). All four use the percent-change-divided-by-percent-change template.

What makes demand elastic

• Substitutes. The single biggest factor. A good with many close substitutes (Coca-Cola, butter, a particular airline route) is highly elastic; a good with no substitutes (insulin, postage stamps in 1960) is inelastic. Defining the market matters: "soft drinks" are less elastic than "Coca-Cola" because all sodas are substitutes for one another but very few drinks are substitutes for soda as a category.
• Necessity vs luxury. Necessities — food, electricity, basic medicine — are inelastic because you buy roughly the same amount whether they cost a little more or less. Luxuries are elastic because the alternative is simply not buying.
• Share of income. A 50% rise in salt prices is annoying but trivial; a 50% rise in rent is catastrophic and forces relocation. Goods that take a small slice of income are inelastic.
• Time horizon. Short-run demand is more inelastic than long-run demand because consumers cannot adjust capital and habits overnight. After OPEC's 1973 oil embargo, the U.S. gasoline elasticity in the first year was about −0.2; over the following decade, as fleet fuel economy rose from 14 to 23 mpg, the long-run elasticity moved closer to −0.7.
• Definition of "the good". Narrow definitions (this brand, this size, this store) are more elastic than broad ones (this category).

Common pitfalls

• Dropping the minus sign without saying so. "PED is 0.4" and "PED is −0.4" should mean the same thing in context, but in formulas the sign matters — if you forget it, your tax-revenue prediction has the wrong direction.
• Computing percent changes from the original instead of the average. Going from $10 to $12 is a 20% rise; going from $12 to $10 is a 16.7% fall. Using the simple formula gives different elasticities for the same two points. The midpoint formula avoids it.
• Confusing elasticity with slope. A linear demand curve has constant slope but variable elasticity. Two parallel demand curves can have wildly different elasticities at the same price.
• Using a single elasticity for all price ranges. Elasticity is a local property. The elasticity of gasoline demand at $4/gallon is not the elasticity at $8/gallon — at the higher price more substitutes (transit, EVs) become viable.
• Ignoring time. A study showing PED ≈ −0.2 for electricity might be measuring one-year response, missing the much larger five-year response when households replace appliances. Policy that needs a long-run elasticity but uses a short-run estimate will undershoot.
• Treating the entire industry's elasticity as one firm's elasticity. Industry demand for soft drinks may be inelastic, but Pepsi's own demand is highly elastic — its closest substitute is sitting one shelf over. Monopoly pricing models need firm-level elasticity, not industry-level.