Elasticity

Lessons

Senior 4 · Economics

Elasticity

4 lessons

Lesson 4 of 4

Price elasticity of supply

35 min

Can coffee farmers respond to a better price?

According to the National Bank of Rwanda (BNR), Rwanda's coffee exports in the fiscal year 2024–25 were about 20,509 tonnes, 24.5% more than the year before, and the average price received rose by 18.6%, to US$5.66 per kg. The year before, both had fallen: volume by 17.9% and price by 17.3%. It is tempting to conclude that farmers simply sell more when the price is higher. But a coffee tree takes years to bear fruit, and this year's crop was flowering long before this year's price was known. How quickly, and how far, sellers can respond to a price change is measured by the price elasticity of supply.

Definition

Price elasticity of supply (PES): the responsiveness of quantity supplied to a change in the good's own price, ceteris paribus:

\text{PES} = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}}

Because price and quantity supplied normally move in the same direction, PES is positive. For a straight-line supply curve $Q_{s} = c + d P$ , the point elasticity is

\text{PES} = d \times \frac{P}{Q}

Worked example 1: PES of the tomato supply curve

Unit 2's market supply is $Q_{s} = - 200 + 4 P$ .

Simple method, price rising from Frw 200 to Frw 300 (quantity from 600 to 1,000 kg):

\text{PES} = \frac{400}{600} \div \frac{100}{200} \approx 0.667 \div 0.5 \approx 1.33

Arc method over the same stretch:

\text{PES} = \frac{400}{800} \div \frac{100}{250} = 0.5 \div 0.4 = 1.25

Point method at Frw 300:

\text{PES} = 4 \times \frac{300}{1\,000} = 1.2

All three show elastic supply (PES above 1). This matches the rule below: the line cuts the price axis (at Frw 50), so it is elastic at every point.

1. Categories of PES

The straight-line rule. For $Q_{s} = c + d P$ , $\text{PES} = \frac{dP}{c + dP}$ . If the line starts on the price axis, $c$ is negative, the denominator is smaller than $d P$ , and PES is above 1. If it passes through the origin, $c = 0$ and PES is exactly 1, whatever the slope. If it starts on the quantity axis, $c$ is positive and PES is below 1.

Category	Value	Example
Perfectly inelastic	PES = 0	Fish already landed today; seats in a stadium on match day
Inelastic	$0 \lt \text{PES} \lt 1$	Coffee and tea in the short run; houses in central Kigali
Unit elastic	PES = 1	Any straight supply line through the origin
Elastic	$\text{PES} \gt 1$	Manufactured goods with spare capacity, such as plastic buckets
Perfectly elastic	PES = ∞	A small country buying at a fixed world price

2. What determines PES?

Time. Alfred Marshall distinguished the momentary (market) period, when supply is fixed; the short run, when output can change with existing machines and land; and the long run, when new capacity can be built and new firms can enter. Supply becomes more elastic as time passes.
Spare capacity. A factory working below capacity can raise output quickly.
Stocks. Goods that can be stored (maize in a silo, cement in a warehouse) can be released when prices rise.
Mobility of factors. If labour and machines can easily move from other uses, supply is elastic.
Gestation period. Coffee, tea and timber take years from planting to harvest, so their supply is inelastic.
Perishability. Fresh tomatoes and milk must be sold quickly, whatever the price.
Ease of entry and natural limits, such as the land area suitable for tea.

The diagram shows the same increase in demand in all three periods. With momentary supply the whole adjustment is in the price; in the long run most of it is in the quantity.

Worked example 2: can we read PES from export data?

BNR's annual report gives these changes for coffee exports (fiscal years ending in June):

Year	% change in volume	% change in unit price	Ratio
2023–24	$- 17.9$	$- 17.3$	$\frac{-17.9}{-17.3} \approx 1.03$
2024–25	$+ 24.5$	$+ 18.6$	$\frac{24.5}{18.6} \approx 1.32$

For tea in 2022–23, volume rose by 10% while the unit price fell by 6%, a ratio of about $- 1.7$ .

Evaluation: these ratios are not elasticities of supply. PES holds everything else constant, but harvests depend on rainfall, the age of the trees and inputs bought a year or more earlier, so each year's volume reflects a shift of the supply curve, not a movement along it. The negative ratio for tea is the clue: on a normal supply curve, PES cannot be negative. A real estimate would need many years of data and a statistical method that separates the effect of price from the effect of the weather.

3. Why PES matters

Farm price fluctuations: when supply is inelastic, any shift in demand, or a small shift in supply, causes large swings in price (Unit 4).
Tax incidence: the more inelastic the supply, the larger the share of a tax borne by producers.
Planning: the government must plan years ahead for goods with long gestation periods, such as electricity plants and skilled workers like doctors.
Housing and land: where supply is inelastic, a rise in demand mostly raises prices and rents.
Firms' strategy: keeping spare capacity and stocks lets a firm gain when prices rise.

Warning

A steep line is not always inelastic. Every straight supply line through the origin has PES = 1, steep or flat. Judge a straight supply line by where it meets the axes, not by its slope.

Tip

"Price axis = elastic; origin = one; quantity axis = inelastic." Extend a straight supply line until it meets an axis and read off its elasticity.

Important

Discuss. The government wants Rwanda's coffee exports to respond faster when world prices are high. Which determinants of PES could policy change, and which cannot be changed?

EconplusDal, "Price Elasticity of Supply (PES)". Watch for the factors that make supply elastic or inelastic, and for how time changes the answer.

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Practice

Define price elasticity of supply and state its formula.
When the price of eggs rises from Frw 150 to Frw 180, the quantity supplied rises from 8,000 to 9,200 a day. Calculate PES by the simple method and classify supply.
Supply is $Q_{s} = 50 + 2 P$ . Find PES at $P = 25$ and at $P = 100$ . Explain why both are below 1.
Supply is $Q_{s} = 3 P$ . Show that PES = 1 at every price.
Explain four determinants of PES, with Rwandan examples.
With a diagram, explain why the momentary, short-run and long-run effects of a rise in demand differ.
Explain why the supply of coffee is more inelastic than the supply of plastic buckets.
"The BNR data prove that the supply of coffee is elastic." Evaluate this claim.

Show answersHide answers

The responsiveness of quantity supplied to a change in the good's own price: PES = % change in quantity supplied ÷ % change in price.
$\frac{1\,200}{8\,000} \div \frac{30}{150} = 0.15 \div 0.2 = 0.75$ : inelastic.
At 25: $Q = 100$ , PES $= 2 \times \frac{25}{100} = 0.5$ . At 100: $Q = 250$ , PES $= 2 \times \frac{100}{250} = 0.8$ . The line meets the quantity axis (at 50), so PES is below 1 everywhere.
PES $= 3 \times \frac{P}{3P} = 1$ for any $P$ .
Any four: time (coffee trees need years); spare capacity (a cement plant below capacity); stocks (maize in storage); factor mobility; perishability (milk, tomatoes); ease of entry; natural limits (land suitable for tea).
Momentary: supply fixed, so the whole effect is a higher price. Short run: existing capacity is used more, so price rises less and quantity rises. Long run: new capacity and firms enter, so supply is elastic and price rises least while quantity rises most.
Coffee takes years to grow and depends on land and weather; plastic buckets can be made quickly with existing machines and widely available inputs, so output can rise fast when prices rise.
The claim fails: a ratio of 1.32 in one year compares changes that were mostly caused by the harvest (supply shifts), not by price; other things were not equal; the year before gives about 1.03, and tea in 2022–23 gives a negative ratio, impossible for a supply elasticity. Short-run coffee supply is in fact likely to be inelastic.

Quick check

A straight-line supply curve starts on the quantity axis. Its price elasticity of supply is…

Key points

PES = % change in quantity supplied ÷ % change in price; for $Q_{s} = c + d P$ , point PES $= d \frac{P}{Q}$ .
A straight supply line from the price axis is elastic, through the origin unit elastic, from the quantity axis inelastic.
Supply is more elastic with more time, spare capacity, stocks, mobile factors and easy entry; less elastic for perishable goods and crops with long gestation periods.
Inelastic supply explains large swings in farm prices; export data alone cannot measure PES because harvests shift supply.

1Can coffee farmers respond to a better price?

21. Categories of PES

32. What determines PES?

43. Why PES matters

Can coffee farmers respond to a better price?

1. Categories of PES

2. What determines PES?

3. Why PES matters