Price Elasticity of Supply: Midpoint Method, Worked Example

Tickets to one sold-out concert jump from $50 to $150. Not one extra seat appears. When the price of plain T-shirts rises, factories turn out far more within weeks. Both prices went up. One seller couldn't respond at all. Why? This is Module 2.4, price elasticity of supply.

Price elasticity of supply measures how strongly sellers respond to a price change, in percent terms. The formula mirrors demand: the percent change in quantity supplied divided by the percent change in price. In plain words: when price rises 1%, by what percent does quantity supplied rise? One difference. By the law of supply, price and quantity supplied move the same way, so the number is positive. No sign to drop.

Exam trap: if you get a negative supply elasticity, you flipped a direction. Price and quantity supplied should both rise or both fall. Same method rules as demand: percent changes, never raw changes, and the midpoint method when the question asks for it.

Worked example. T-shirts rise from $8 to $10, and weekly quantity supplied rises from 2,000 to 3,000 shirts.

Quick refresher from Module 2.3: percent change is the change divided by the starting value. Elasticity puts the quantity percent on top and the price percent on the bottom, then compares the answer with 1.

Percent change in price: the $2 change over the starting $8. That's +25%. Percent change in quantity supplied: 1,000 more shirts over the starting 2,000. That's +50%. Divide: 50% over 25% is 2. No units, since the percents cancel. 2 is bigger than 1, so supply is elastic. Each 1% rise in price brings about 2% more shirts.

Or justify it in words: quantity rose 50%, more than the 25% price rise, so supply is elastic. If quantity had risen by exactly 25%, the same as price, supply would be unit elastic.

So what just happened with the T-shirts? One: price rose 25%, from $8 to $10. Two: quantity supplied rose 50%, from 2,000 to 3,000. Three: 50 over 25 is 2, bigger than 1, so supply is elastic.

Quick refresher, the midpoint method: divide each change by the average of the two values. Price: the $2 change over $9, halfway between $8 and $10, is about 22%.

Quantity: the 1,000 change over 2,500, halfway between 2,000 and 3,000, is 40%. 40 over 22 is about 1.8, bigger than 1, so supply is still elastic.

So what just happened with the midpoint? One: we divided by averages, $9 and 2,500, not starting values. Two: price changed about 22% and quantity about 40%. Three: 40 over 22 is about 1.8, so supply is elastic with either method.

Now the concert. Price rose from $50 to $150: a $100 rise over $50, or +200%. Tripling is a 200% rise, not 300%. Seats stayed at 20,000, a 0% change. 0% over 200% is 0. That's perfectly inelastic supply.

So what just happened at the stadium? One: the price tripled, a 200% rise. Two: the seats stayed at 20,000, a 0% change. Three: 0 over 200 is 0, so supply is perfectly inelastic: seats don't respond at all.

The ranges use the same benchmark as demand: 1, where quantity supplied changes by the same percent as price. Above 1, supply is elastic. Below 1, it's inelastic. Exactly 1, it's unit elastic. Perfectly inelastic supply is a vertical line: a fixed quantity no matter the price, like tonight's stadium seats. Perfectly elastic supply is a horizontal line: at that price, sellers will supply any amount, and below it, none. Think of plain paper cups that many factories can make at the same cost.

Exam trap: vertical means zero response, so elasticity is 0, not infinite. And through the same point, a steeper supply curve is less elastic.

So what just happened with the extremes? One: vertical supply means a fixed quantity: elasticity is 0, perfectly inelastic. Two: horizontal supply means any amount at one price: elasticity is infinite, perfectly elastic. Three: through the same point, steeper means less elastic.

What makes supply more elastic? First, inputs. If extra inputs are cheap and easy to get, or can be pulled over from other uses, sellers can expand output fast. College Board's name for this is the price of alternative inputs. The cheaper and easier the inputs, the more elastic the supply. A shirt factory buys more cotton and adds a shift. A stadium can't buy more seats for tonight, so its supply is inelastic. If a good needs an input that's hard to get more of, like farmland in one small valley, its supply is less elastic.

The second factor is time. Right after a price jump, sellers are stuck with what they have, so supply is steep. Give them time and they adjust. An apple grower can't grow more apples this week, but she can plant trees that bear fruit in a few years. Even the concert can respond over time: the promoter adds a second show or books a bigger stadium. So long-run supply is more elastic than short-run supply. Drawn through the same point, the long-run curve is flatter.

Exam trap: more time means flatter, not steeper. Short run, steep. Long run, flat.

So what just happened over time? One: right after a price jump, sellers are stuck, so supply is steep. Two: with time, the grower plants trees and the promoter adds shows. Three: long-run supply is flatter and more elastic.

That answers the hook. Tonight's stadium has a fixed input and no time, so its supply is vertical. When demand jumped, price did all the moving. With elastic supply, like T-shirts, a jump in demand raises quantity a lot and price only a little.

So what just happened when demand jumped? One: the stadium can't add seats tonight, so its supply is vertical and only the price rose. Two: T-shirt supply is elastic, so quantity rose a lot and price only a little.

You'll use this again in Module 2.8A, where supply and demand elasticities decide who really pays a tax.

Quick check. The price of fresh flowers rises 10%, and quantity supplied rises 4%. A) 2.5, elastic. B) 0.4, inelastic. C) -0.4, inelastic. D) 0.4, elastic.

B. 4 over 10 is 0.4, less than 1, so inelastic. A is the flipped ratio: quantity always goes on top. C has the wrong sign, since supply elasticity is positive.

A furniture maker has one workshop. Five years after a price jump, it has built a second. Compared with right after the jump, its supply is: A) less elastic and steeper. B) more elastic and flatter. C) perfectly inelastic. D) unit elastic no matter what.

B. More time means more ways to respond, so supply gets more elastic and flatter. A has time backwards.

Recap: supply elasticity is percent change in quantity supplied over percent change in price, and it's positive. Vertical means zero response. Easy inputs and more time make supply more elastic. Next: Module 2.5, Income Elasticity and Cross-Price Elasticity.