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2.6

Elasticity of supply

Unit 2 · Microeconomics · SL and HL

Price elasticity of supply (PES) measures how quickly and how far producers can respond to a price change. It explains why hotel room prices on Bali soar in peak season while t-shirt prices barely move, and why food and commodity prices are so volatile. The calculation is short; the marks are in explaining the determinants, especially time.

🎯What you need to be able to do

  • Define and calculate PES, and interpret values from zero to infinity.
  • Draw relatively elastic and inelastic supply, and perfectly elastic, perfectly inelastic and unit elastic supply.
  • Explain the determinants of PES: time, mobility of factors of production, unused capacity, ability to store, and the rate at which costs increase.
  • Calculate a change in price or quantity supplied from PES data.
  • HL Explain why the PES for primary commodities is generally lower than for manufactured products.

📚The economics

Price elasticity of supply

PES measures the responsiveness of quantity supplied to a change in the price of the good.

\[ \text{PES} = \frac{\%\Delta Q_s}{\%\Delta P} \]

Price and quantity supplied move in the same direction, so PES is positive.

PES = 0
perfectly inelastic: fixed quantity (seats in a stadium on match day, original paintings).
0 < PES < 1
relatively inelastic: %ΔQs < %ΔP. Most farm products in the short run.
PES = 1
unit elastic: any straight-line supply curve through the origin.
PES > 1
relatively elastic: %ΔQs > %ΔP. Many manufactured goods.
PES = ∞
perfectly elastic: firms supply any quantity at one price.
Two supply curves. On the left a flat supply curve, where a price rise from P1 to P2 gives a large rise in quantity supplied. On the right a steep supply curve, where the same price rise gives a small rise in quantity supplied.
Relatively elastic and relatively inelastic supply.
Three supply diagrams with constant PES: a horizontal line (perfectly elastic), a vertical line (perfectly inelastic), and two straight lines of different slope both starting at the origin (unit elastic).
Every straight-line supply curve through the origin has PES = 1, whatever its slope.

Determinants of PES

  • Time — the most important. Right after a price rise, output may be fixed (momentary period). In the short run, firms can add variable inputs such as labour and overtime. In the long run, they can build new capacity and new firms can enter. Supply becomes more elastic as the time period lengthens.
  • Mobility of factors of production: if labour and capital can move easily between uses, supply responds quickly. A garment factory can switch from shirts to face masks; a skilled surgeon cannot be trained in a month.
  • Unused (spare) capacity: firms with idle machines and workers can increase output quickly, so supply is elastic. In a recession, spare capacity is common; at full capacity, supply becomes inelastic.
  • Ability to store: if goods can be stored cheaply (rice, cement, canned goods), firms can release stocks when prices rise: elastic supply. Perishable goods (fresh fish, flowers, hotel rooms on a given night) cannot be stored: inelastic supply.
  • Rate at which costs increase: if producing more raises costs only slightly, supply is elastic; if costs rise quickly with extra output (overtime pay, costlier inputs, diminishing returns), firms need a large price rise to supply more: inelastic.
Three supply curves through the same starting point at price P1. After a price rise to P2, the vertical momentary supply curve shows no change in quantity, the short-run supply curve shows a moderate increase, and the flatter long-run supply curve shows a large increase.
The same price rise brings a larger supply response the longer producers have to adjust.

Why primary commodities have low PES HL

  • Long production periods: crops take a season to grow; oil palms take about three years to bear fruit and cocoa longer; new mines take years to open.
  • Immobile factors: land suited to one crop or a specific mine cannot be switched quickly.
  • Limited storage: many agricultural products are perishable.
  • Natural limits: weather and land availability cap output.

Manufactured goods can usually be produced faster, with more mobile factors and spare capacity, so their PES is higher. Combined with the low PED of commodities (2.5), inelastic supply and demand mean that any shift causes large price swings: a poor harvest sends prices soaring, a bumper one makes them crash. This price volatility makes farmers’ incomes and commodity exporters’ export earnings unstable, and is one reason governments intervene with buffer stocks, price floors and diversification.

✏️Worked example

(a) The price of cocoa beans rises from $20 to $25 per kg. In the following year, quantity supplied by a cooperative rises from 400 to 450 tonnes. Calculate PES and comment.
(b) The PES of cement is 2.5. Its price rises by 6%. Calculate the change in quantity supplied.
(c) A furniture maker currently supplies 800 chairs a month. PES = 1.2. Calculate the price rise needed to raise supply to 920 chairs.

(a) %ΔP = 5 ÷ 20 = +25%; %ΔQs = 50 ÷ 400 = +12.5%.

\[ \text{PES} = \frac{12.5\%}{25\%} = 0.5 \]

Supply is price inelastic: cocoa trees take years to mature, so in one year farmers can only harvest existing trees more intensively.

(b) %ΔQs = PES × %ΔP = 2.5 × 6% = +15%.

(c) %ΔQs = 120 ÷ 800 = 15%, so %ΔP = 15% ÷ 1.2 = 12.5%.

Check it. PES should be positive; if you get a negative number, a price or quantity has been subtracted the wrong way round. In (c), 12.5% × 1.2 = 15% ✓.
Judging PES by steepness alone. A steep straight line through the origin still has PES = 1. Look at where the supply curve meets the axes: a straight line starting on the price axis is elastic (PES > 1); one starting on the quantity axis is inelastic (PES < 1).

📝Practise

Work through these on paper, then reveal the answer.

1. [2 marks, Paper 2 style] Define the term price elasticity of supply.
A measure of the responsiveness of quantity supplied of a good to a change in its price, calculated as the percentage change in quantity supplied divided by the percentage change in price.
2. [2 marks, Paper 2 style] The price of a smartphone model rises by 8% and quantity supplied rises by 20%. Calculate PES.
PES = 20% ÷ 8% = 2.5: price elastic supply.
3. [4 marks, Paper 2 style] Using a demand and supply diagram, explain why hotel room prices in a tourist resort rise sharply in the peak season.
The number of rooms is fixed in the short run and a room-night cannot be stored, so supply is highly price inelastic (a steep or vertical supply curve). In peak season demand shifts right. Because quantity supplied can hardly increase, the adjustment falls almost entirely on price: a large price rise with a small increase in rooms let. Diagram: steep S, D1 and D2, large rise P1 to P2, small rise Q1 to Q2.
4. Explain why the supply of fresh fish is more price inelastic than the supply of canned fish.
Fresh fish is perishable: it cannot be stored, so the day’s catch must be sold whatever the price, and the catch depends on weather and boats at sea. Canned fish can be stored, so firms hold stocks and release more when the price rises; they also have factory capacity that can run extra shifts. So canned fish supply responds more to price.
5. HL Explain why a country dependent on exporting one agricultural commodity experiences unstable export revenues.
Commodity supply is price inelastic (long growing periods, immobile land, perishability) and demand is price inelastic (necessities, few substitutes). Supply is also hit by weather shocks. With both curves steep, a shift in supply or demand produces a large change in price and hence in revenue. A good harvest can even reduce revenue if prices fall more than proportionately. So export earnings, government tax revenue and farmers’ incomes swing from year to year, making planning and investment difficult.
6. A firm operating at full capacity faces a sudden increase in demand. Explain how its PES differs in the short run and the long run.
In the short run it has no spare capacity, so it can only raise output through overtime and extra shifts, which raise marginal costs quickly: supply is inelastic, and most of the demand increase shows up as a higher price. In the long run, it can invest in new machinery and premises, and other firms can enter the market, so supply becomes much more elastic and the price falls back towards its original level.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • Khan Academy — Price elasticity of supply and its determinants.
  • UNCTAD — State of Commodity Dependence reports on commodity-dependent developing countries.
  • World Bank Commodity Markets Outlook — the “Pink Sheet” of monthly commodity prices, to see volatility for yourself.