- Tax incidence
- Subsidies
Sandwiches and gold
The last lecture promised to turn to the other side of the market: how strongly sellers respond to price. Here are two cases to compare.
Suppose the price of sandwiches in a city rises by 50%. Within days, cafés can buy more bread, make more fillings and take on more staff. Many more sandwiches appear. Now suppose the price of gold rises by 50%. Can the world's mines produce half as much gold again next month? No. Opening a new mine takes years, and the gold in the ground is only what nature put there. In the short run, very little extra gold appears.
Both are rises in price, and both are normal upward-sloping supply curves. The difference is how much sellers can respond. The PED, YED and XED lectures measured buyers. This lecture measures sellers, with the last member of the elasticity family.
Price elasticity of supply
Here is the quantity supplied. PES measures how strongly sellers change the quantity they offer when the price of the good changes, other things being equal.
Because a supply curve slopes upwards, price and quantity supplied move in the same direction. A higher price brings more onto the market, and a lower price brings less. So PES is positive, or zero, never negative. Unlike PED, there is no minus sign to drop.
The size is read the same way as PED:
- PES above 1: elastic supply. Quantity supplied changes by a larger percentage than price. Sellers respond strongly.
- PES below 1: inelastic supply. Quantity supplied changes by a smaller percentage than price. Sellers can respond only a little.
- PES = 1: unit elastic supply. The two percentages are equal.
- PES = 0: perfectly inelastic supply. The quantity cannot change at any price. The supply curve is vertical. Example: paintings by an artist who died long ago. No more can ever be made.
- PES infinite: perfectly elastic supply. Sellers will supply any quantity at one price, and nothing below it. The supply curve is horizontal. No real market is exactly like this, but some come close, such as a product that many firms can make at the same steady cost.
What makes supply elastic?
Every determinant comes down to one question: how easily can sellers produce more, or less, when the price changes?
- Time, the most important factor. In the very short run, the quantity is whatever is already made or grown, so supply is close to perfectly inelastic. Over weeks, firms can use overtime and run machines longer, so supply becomes more elastic. Over years, firms build new factories and new firms enter the market, so supply becomes more elastic still.
- Spare capacity. A factory with idle machines and workers can raise output quickly. A factory already running at full capacity cannot.
- Stocks. Goods that can be stored, such as rice in a warehouse, can be released when the price rises. Perishable goods, such as fresh strawberries, cannot wait for a better price.
- Ease of switching. A farmer whose land can grow several crops can switch to the one whose price has risen. A specialised factory cannot.
- Mobile inputs. If workers, machines and materials can move easily into the industry, supply expands quickly. If it needs rare skills or scarce materials, it does not.
- Length of production. Aircraft take years to build, houses many months, and a newly planted coffee bush a few years before its first harvest. Long production times make supply inelastic in the short run.
A steep supply curve and a flat supply curve both pass through the same point. Which one has the more elastic supply at that point?
Show the answer
The flat one. Along a flatter supply curve, a small change in price brings a large change in quantity, so sellers respond strongly: elastic supply. Along a steep curve, even a large price change brings only a small change in quantity: inelastic supply. Compare curves through the same point. A slope alone is not an elasticity, because elasticity uses percentage changes, and those depend on where on the curve you are.
Why PES decides what happens to prices
Here is where PES matters most. Suppose demand for a good rises. Buyers want more at every price. Will the market answer with more of the good, or with a higher price? The answer depends on supply.
Try it below. The same rise in demand meets supply curves with different elasticities.
Demand rises from D₁ to D₂: buyers want 40 more units at every price. Change the PES of the supply curve at the starting point. Watch how much of the change goes into price, and how much into quantity.
Demand rises by 40 units at every price, from a starting point of $10 and 100 units a week (an invented market). The result depends on the PES of supply:
| PES | New price | New quantity |
|---|---|---|
| 0 | $12.00 (+20%) | 100 (0%) |
| 0.5 | $11.60 (+16%) | 108 (+8%) |
| 1 | $11.33 (+13.3%) | 113.3 (+13.3%) |
| 4 | $10.67 (+6.7%) | 126.7 (+26.7%) |
| infinite | $10.00 (0%) | 140 (+40%) |
The less elastic the supply, the more of the rise in demand turns into a higher price, and the less into extra quantity.
Did you see the trade-off? With PES of 0, a rise in demand produces only a price rise of 20%, and not one extra unit. With PES of 4, the price rises less than 7%, and the quantity rises by more than a quarter. That is it. That is the whole idea. When supply is inelastic, a rise in demand mainly raises the price. When supply is elastic, it mainly raises the quantity.
This explains why the prices of farm products such as coffee and cocoa can jump sharply after a poor harvest or a rise in demand: supply cannot respond until the next growing season. Manufactured goods, made in factories that can add shifts, usually see steadier prices.
Worked examples
The price of coffee beans rises from $20 to $25 per kg. Over the next month, the quantity supplied rises from 1000 to 1150 tonnes. Find the PES (an invented example).
Price: . Quantity: .
PES = 15 ÷ 25 = 0.6. Inelastic: in a month, growers can sell some stored beans, but they cannot grow more coffee.
A factory making plastic chairs has half its machines idle. When the price of chairs rises by 10%, it raises output by 30%. Find the PES (an invented example).
PES = 30 ÷ 10 = 3. Elastic: spare capacity lets the factory respond quickly. Once all the machines are busy, its PES will fall.
In a city, the PES of rented flats over one year is 0.4 (an invented figure). Rents rise by 15%. Predict the change in the number of flats offered for rent.
% change in quantity supplied = PES × % change in price = .
A 15% rise in rent brings only 6% more flats within a year. Building takes time, so most of the adjustment comes through price.
The policy. In April 2013, England launched the Help to Buy Equity Loan. Buyers of newly built homes could borrow up to 20% of the price from the government, interest-free for five years, with only a 5% deposit. In February 2016, London received a more generous version, with loans of up to 40%. The aim was to help people buy homes and to get more homes built.
The prediction. The scheme raised demand for new-build homes. By the logic above, where housing supply is elastic, it should mostly raise the number of homes built. Where supply is inelastic, it should mostly raise prices.
What happened. A study of property sales from 2010 to 2019 (Carozzi, Hilber and Yu, Journal of Urban Economics, 2024) compared two kinds of area. In Greater London, where land is scarce and planning is slow, the scheme raised new-build prices by nearly 8% and had no detectable effect on how many homes were built. Near the border between England and Wales, where land is cheaper and building easier, it raised construction and had no noticeable effect on prices. There, the study compared the English side of the border with the Welsh side, where the scheme started later and had a lower price cap.
The verdict. Exactly the pattern PES predicts. The same policy raised quantity where supply was elastic, and raised prices where it was inelastic. In London, much of the help went into higher prices, which benefited sellers and developers more than the buyers the scheme was meant to help. Research on the United States finds the same contrast between cities: Albert Saiz (Quarterly Journal of Economics, 2010) estimated long-run housing supply elasticities for many cities. They were below 1 in the most land-constrained coastal cities, such as San Francisco (about 0.66), and above 3 in the least constrained inland ones.
Now sort some markets yourself.
For each case, decide whether supply is likely to be elastic or inelastic. Think about time, spare capacity, stocks and how long production takes.
Each case and its likely supply:
| Case | Supply |
|---|---|
| Fresh strawberries, the day after their price rises | inelastic |
| T-shirts from a factory with idle machines | elastic |
| Houses in a crowded city with slow planning permission | inelastic |
| Paintings by an artist who died long ago | inelastic (perfectly) |
| Bread from a bakery that can add a night shift | elastic |
| New passenger aircraft over the next six months | inelastic |
| Phone cases from a firm that can switch moulds in a day | elastic |
| Rice from a warehouse holding large stocks | elastic |
Three classic mistakes
Price and quantity supplied move in the same direction, so both changes have the same sign. If you get a negative PES, you have probably mixed up supply and demand, or used the wrong quantity.
PES describes a movement along the supply curve, caused by a change in the good's own price. A change in costs or technology shifts the whole supply curve, as the lecture on what shifts supply showed. That is not measured by PES.
"The PES of housing" has no single value. Supply over one month is almost fixed; over ten years it can be quite elastic. Always say over what period you are measuring.
Work each one on paper first. Open a hint only when you are stuck.
-
The price of mangoes rises by 20%, and the quantity supplied rises by 5%. Find the PES and describe supply.
Hint 1
PES = % change in quantity supplied ÷ % change in price.
Hint 2
5 ÷ 20.
Full answer
PES = 5 ÷ 20 = 0.25. Inelastic: mango trees cannot produce more fruit quickly.
-
A printing firm has a PES of 2.5. The price it can charge rises by 8%. By what percentage will it raise its output?
Hint 1
Rearrange: % change in quantity supplied = PES × % change in price.
Hint 2
.
Full answer
. Elastic supply: the firm responds strongly, perhaps because it has spare machines.
-
A farm supplies 4000 kg of tomatoes a week at $2.00 per kg. The price rises to $2.50, and the farm supplies 4400 kg. Find the PES. Then explain why the PES over the following season might be higher.
Hint 1
Find both percentage changes from the starting values.
Hint 2
Price +25%, quantity +10%.
Full answer
PES = 10 ÷ 25 = 0.4, inelastic. Over a season, the farm can plant more tomatoes, perhaps instead of another crop, so the quantity can respond more to the same price: PES rises with time.
-
Demand for concert tickets in a city rises, and the same rise happens in two markets: seats in one stadium with a fixed number of seats, and hotel rooms across a city with many hotels that have empty rooms. Using PES, predict what happens to price and quantity in each market. Which group of sellers gains most from the rise in demand, and why?
Hint 1
What is the PES for seats in a single stadium on one night?
Hint 2
Use the graph builder's lesson: inelastic supply turns a rise in demand into a higher price.
Full answer
Stadium seats: the number is fixed, so PES = 0. The whole rise in demand goes into a higher ticket price; the quantity stays the same. Hotel rooms: there is spare capacity, so supply is elastic. More rooms are filled, and prices rise only a little. The stadium (or whoever sells its tickets) gains most per unit from the extra demand, because with fixed supply every bit of extra demand turns into a higher price. This is the same reason the London part of Help to Buy mainly raised prices.
The four elasticities together answer a question every government and every business asks: if something changes, who adjusts, and by how much? PED, YED and XED describe buyers. PES describes sellers. Put PED and PES together, and you can predict how any change in a market will split between a change in price and a change in quantity.
That split is the key to the next topic. When a government taxes a good, or pays a subsidy, the effect on prices and quantities depends on these elasticities, and so does the answer to a surprising question: who really pays a tax? Help to Buy was a subsidy, and inelastic supply sent much of it to sellers. The lectures on tax incidence and subsidies will show why, on a diagram.
- Price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price, and it is positive or zero.
- Supply is elastic when PES is above 1, inelastic when it is below 1, perfectly inelastic when the supply curve is vertical and perfectly elastic when it is horizontal.
- Time is the most important determinant of PES, along with spare capacity, stocks, ease of switching, mobile inputs and the length of production.
- When supply is inelastic, a rise in demand mainly raises the price, and when supply is elastic, it mainly raises the quantity.
- England's Help to Buy scheme raised new-build prices in supply-constrained London but raised construction near the English–Welsh border, as PES predicts.