Elasticity

Price Elasticity of Demand

A gas station raises its price from $3.50 to $4.00 per gallon. Weekly sales fall from 10,000 gallons to 9,500. That is a 14.3% price hike (midpoint method) and only a 5.1% drop in quantity. The ratio of those two numbers gives us price elasticity of demand (Ed):

Ed = % change in quantity demanded / % change in price

Here, Ed = -5.1% / 14.3% = -0.36. Take the absolute value: |Ed| = 0.36. Demand is inelastic. Drivers grumble but keep filling up.

The coefficient always comes out negative because demand curves slope downward. Economists drop the sign and work with |Ed|. One thing to watch: a straight-line demand curve does not have constant elasticity. The slope stays the same everywhere, but elasticity depends on the ratio P/Q, which changes at every point along the line.

The AP Microeconomics exam expects you to use the midpoint method for calculations. It eliminates the problem of getting a different answer depending on which price-quantity pair you start from. The formulas: %ΔQ = (Q2 - Q1) / ((Q1 + Q2)/2) and %ΔP = (P2 - P1) / ((P1 + P2)/2).

Elastic, Inelastic, and Unit Elastic

Novo Nordisk raises the price of insulin by 15%. Sales barely move. Louis Vuitton raises handbag prices by 15%. Plenty of shoppers walk away. The gap between those two reactions is the difference between elastic and inelastic demand.

|Ed| > 1 means elastic demand. Quantity changes more than proportionally to the price change. Buyers have substitutes, or they can wait, or the purchase is discretionary enough to skip.

|Ed| < 1 means inelastic demand. Quantity barely budges. Gasoline, electricity, prescription medications. Buyers absorb the price increase because they have no realistic alternative.

|Ed| = 1 means unit elastic demand. Percentage changes match exactly. On a linear demand curve, this occurs at the midpoint and nowhere else.

Two extreme cases round out the spectrum. Perfectly elastic demand (|Ed| = infinity) produces a horizontal curve. Any price increase above the market level sends quantity to zero. Perfectly inelastic demand (|Ed| = 0) produces a vertical curve. Price moves freely; quantity never changes.

The Total Revenue Test

A bookstore sells 500 copies a week at $12 each. Revenue: $6,000. Should the owner raise the price to $14? TR = P x Q, and when price goes up, P and Q pull revenue in opposite directions. Elasticity decides which force wins.

In the elastic range (|Ed| > 1), a price cut actually raises revenue. The surge in quantity more than compensates for the lower per-unit price. Netflix dropped its basic plan from $9.99 to $6.99 in certain markets during 2023 and saw subscriber counts jump enough to increase total revenue in those regions. Raise the price in this range and customers leave faster than the higher price can compensate.

In the inelastic range (|Ed| < 1), the math flips. A price cut hurts revenue because quantity barely responds. You collect less per unit on roughly the same volume. Pharmaceutical companies operate in this zone. They raise prices and revenue climbs because patients keep buying.

At unit elasticity (|Ed| = 1), revenue peaks. Any price movement in either direction reduces TR.

Determinants of Elasticity

Five factors explain most of the variation in elasticity across goods.

The availability of substitutes is the single biggest driver. Dasani competes with Aquafina, Fiji, tap water, and a dozen store brands. Demand is elastic. Your local electric utility faces no real competitor. Demand is inelastic.

Whether the good is a necessity or a luxury matters enormously. Nobody comparison-shops for an ambulance ride. A $300 increase in the price of a designer watch? That purchase gets postponed or dropped entirely. Necessities pin buyers in place. Luxuries give them room to say no.

Budget share plays a role. A 10% jump in the price of table salt costs a household maybe $0.40 a year. Unnoticeable. A 10% jump in rent reshapes an entire monthly budget. Goods that consume a larger fraction of income generate stronger reactions.

Time horizon changes things. When gas prices surged in 2022, drivers kept filling up (inelastic in the short run). Over the next two years, EV sales climbed 35% and public transit ridership recovered. Demand becomes more elastic as buyers find alternatives.

Market definition is the fifth factor. "Food" is inelastic. Nobody quits eating. "Organic blueberries from the farmer's market on Elm Street" is elastic. Plenty of substitutes exist at that level of specificity.

Cross-Price and Income Elasticity

Pepsi raises its price by 10%. Coke sales climb 7%. A printer drops from $200 to $150. Ink cartridge sales rise. These relationships need a different elasticity measure.

Cross-price elasticity of demand:

Exy = % change in Qd of good X / % change in price of good Y

The sign does the classifying. Positive Exy means the goods are substitutes (Coke and Pepsi, Uber and Lyft). When one gets more expensive, buyers switch to the other. Negative Exy means complements (printers and ink cartridges, hot dogs and buns). Cheaper printers drive more ink sales. A value near zero means the goods are unrelated.

For income changes rather than price changes:

Income elasticity (Ei) = % change in Qd / % change in income

Positive Ei marks a normal good. Within that category, goods with Ei > 1 are luxuries (demand grows faster than income -- think international vacations, designer clothing), and goods with 0 < Ei < 1 are necessities (demand grows, just more slowly -- groceries, basic utilities). Negative Ei flags an inferior good. As incomes rise, people buy less of it. Store-brand pasta gives way to Barilla once paychecks get bigger.

The AP exam puts heavy weight on reading a coefficient like -0.6 or +2.3 and classifying the good immediately.

Elasticity and the AP Exam

Elasticity questions appear on roughly 15-20% of the AP Microeconomics exam. The patterns repeat year after year:

Calculate |Ed| using the midpoint method from two price-quantity pairs. Classify demand as elastic, inelastic, or unit elastic based on the coefficient. Predict what happens to total revenue after a price change. Explain why one good has more elastic demand than another, citing specific determinants.

Free-response prompts tend to embed elasticity inside larger scenarios. A per-unit tax lands on a market and the question asks how the burden splits between buyers and sellers. That answer depends on relative elasticity of demand and supply. A firm facing inelastic demand raises its price, and the question asks why revenue still goes up.

Two mechanical skills get tested more than anything: the total revenue test and the midpoint formula. Nail the arithmetic and the reasoning follows.

Worked Example

A coffee shop sells large lattes at $5 each, moving 200 cups per week. The owner raises the price to $6. Weekly sales drop to 160 cups. Calculate the price elasticity of demand.

Percentage change in quantity (midpoint method):

%ΔQ = (160 - 200) / ((200 + 160) / 2) = -40 / 180 = -22.2%

Percentage change in price:

%ΔP = (6 - 5) / ((5 + 6) / 2) = 1 / 5.5 = 18.2%

Elasticity coefficient:

Ed = -22.2% / 18.2% = -1.22

Absolute value: |Ed| = 1.22.

Classification: |Ed| = 1.22 > 1, so demand is elastic over this price range. Buyers cut back more than proportionally to the price increase.

Revenue check: Before the hike, TR = $5 x 200 = $1,000. After, TR = $6 x 160 = $960. Revenue fell by $40. That confirms the elastic rule: when demand is elastic, a price increase reduces total revenue because the quantity drop outweighs the higher per-unit price.