Calculation of PES using the formula

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Economics 0455 – Price Elasticity of Supply (PES)

Price Elasticity of Supply (PES)

1. Definition

The price elasticity of supply measures the responsiveness of the quantity supplied of a good to a change in its price, ceteris paribus.

2. Formula

The standard formula for PES is:

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

In algebraic terms, using initial and new values:

\$\text{PES} = \frac{\dfrac{Q2 - Q1}{Q1}}{\dfrac{P2 - P1}{P1}} = \frac{(Q2 - Q1) \times P1}{(P2 - P1) \times Q1}\$

Where:

  • \(Q_1\) = initial quantity supplied
  • \(Q_2\) = new quantity supplied
  • \(P_1\) = initial price
  • \(P_2\) = new price

3. Steps for Calculation

  1. Identify the initial and new price and quantity supplied.
  2. Calculate the change in quantity supplied \((Q2 - Q1)\) and the change in price \((P2 - P1)\).
  3. Compute the percentage changes:

    • \(\%\Delta Q = \dfrac{Q2 - Q1}{Q_1} \times 100\)
    • \(\%\Delta P = \dfrac{P2 - P1}{P_1} \times 100\)

  4. Divide \(\%\Delta Q\) by \(\%\Delta P\) to obtain PES.
  5. Interpret the result:

    • PES > 1 : supply is elastic.
    • PES = 1 : supply is unit‑elastic.
    • PES < 1 : supply is inelastic.

4. Worked Example

Suppose the price of wheat rises from \$200 per tonne to \$250 per tonne. The quantity supplied increases from 1,000 tonnes to 1,300 tonnes.

VariableInitial (1)New (2)
Price (\(P\))$200$250
Quantity Supplied (\(Q\))1,000 tonnes1,300 tonnes

Calculate the percentage changes:

\$\%\Delta Q = \frac{1,300 - 1,000}{1,000}\times 100 = 30\%\$

\$\%\Delta P = \frac{250 - 200}{200}\times 100 = 25\%\$

Now compute PES:

\$\text{PES} = \frac{30\%}{25\%} = 1.2\$

Interpretation: Since PES = 1.2 > 1, the supply of wheat is elastic in this price range.

5. Factors Influencing PES

  • Time period: Supply is more elastic in the long run because producers can adjust plant size, technology, and input use.
  • Availability of inputs: If inputs are readily available, firms can increase output quickly, leading to higher PES.
  • Spare production capacity: Firms operating below capacity can raise output without large cost increases.
  • Mobility of factors of production: Easy movement of labour and capital between industries raises PES.
  • Nature of the good: Perishable or highly specialized goods often have lower PES.

6. Summary Table

PES \cdot alueSupply ResponseTypical Situations
> 1Elastic – large change in quantity supplied for a given price changeLong‑run, excess capacity, many substitutes for inputs
= 1Unit‑elastic – proportional changeShort‑run with moderate flexibility
< 1Inelastic – small change in quantity supplied for a given price changeVery short‑run, limited inputs, specialized production

7. Suggested Diagram

Suggested diagram: A supply curve with two points (P₁,Q₁) and (P₂,Q₂) illustrating the calculation of PES using the slope method.

8. Quick Revision Questions

  1. Define price elasticity of supply.
  2. Explain why PES is usually higher in the long run than in the short run.
  3. Calculate PES given: \(P1 = £50\), \(P2 = £55\), \(Q1 = 200\) units, \(Q2 = 230\) units.
  4. Interpret a PES of 0.4 for a particular product.