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Economics

I. Lesson Focus

This lesson defines and calculates the price elasticity of supply (PES), classifies supply responses into five elasticity categories, identifies the key determinants of supply elasticity (especially time), and demonstrates how supply elasticity interacts with demand elasticity to determine the economic incidence of taxes and subsidies. Candidates must master the midpoint (arc) formula, interpret vertical and horizontal supply curves, and apply elasticity concepts to real-world policy effects and market adjustments in both short-run and long-run scenarios.

II. The Problem

Certain agricultural products experience sharp price declines and reduced farmer revenue following bumper harvests, while some manufactured goods can rapidly expand output when input costs rise, resulting in only modest price increases. Why do different goods respond so differently to price changes? CFA exams frequently require candidates to calculate supply elasticity, classify it as elastic, inelastic, or unit elastic, and analyze how excise taxes or subsidies are shared between producers and consumers depending on relative elasticities. Without a precise understanding of the formulas and determinants, it is impossible to correctly predict policy outcomes or determine market clearing conditions.

III. Definition and Calculation of Price Elasticity of Supply

Price elasticity of supply (PES) measures the responsiveness of quantity supplied to a change in the good’s own price. The basic formula is:

$$ PES = \frac{\% \Delta Q_s}{\% \Delta P} = \frac{\Delta Q_s / Q_s}{\Delta P / P} $$

Because the supply curve normally slopes upward, PES is generally positive; absolute values are used for comparison.

Point vs. Arc Elasticity
- Point elasticity (for tiny changes): $ PES = \frac{dQ_s}{dP} \times \frac{P}{Q_s} $
- Arc (midpoint) elasticity — the version most commonly tested:

$$ PES = \frac{(Q_2 - Q_1)/((Q_2 + Q_1)/2)}{(P_2 - P_1)/((P_2 + P_1)/2)} $$

The midpoint method avoids bias from choosing different base points.

IV. Classification of Supply Elasticity

Supply responses are classified into five categories based on the absolute value of PES:

V. Major Determinants of Supply Elasticity

1. Time available for adjustment: The longer the time horizon, the greater the elasticity (short-run vs. long-run).
2. Mobility of factors of production: Easier factor reallocation increases elasticity.
3. Inventory levels: Goods with ample stocks have higher elasticity.
4. Flexibility of technology: Highly adaptable technologies (e.g., software) yield high elasticity; rigid technologies (e.g., heavy industry) yield low elasticity.
5. Cost structure: Industries with slowly rising marginal cost have higher elasticity.

Income Elasticity of Supply measures how quantity supplied responds to changes in producers’ income and is particularly relevant for agriculture and natural resources.

Cross-Price Elasticity of Supply is given by:

$$ CES = \frac{\% \Delta Q_{sA}}{\% \Delta P_B} $$

A positive value indicates substitute goods in production; a negative value indicates complementary goods in production.

VI. Supply Elasticity and Tax Incidence

The economic burden of a tax is shared between producers and consumers according to relative elasticities:

• The more elastic supply is, the larger the share of the tax borne by consumers.
• The less elastic supply is, the larger the share borne by producers.

The precise formulas are:
Producer burden share = $\frac{|E_d|}{|E_d| + E_s}$
Consumer burden share = $\frac{E_s}{|E_d| + E_s}$

The same logic applies (in reverse) to government subsidies.

Worked Cases

Case 1: Arc Elasticity Calculation

A good’s price rises from $10 to $15 while quantity supplied increases from 100 to 160 units. Calculate the price elasticity of supply using the midpoint method.

Solution:
$\Delta Q_s = 60$, $\Delta P = 5$
Average $Q = 130$, Average $P = 12.5$

$$ PES = \frac{60/130}{5/12.5} = \frac{0.4615}{0.4} = 1.154 $$

Conclusion: Supply is elastic.

Case 2: Perfectly Inelastic Supply and Taxation

An original artwork has perfectly inelastic supply (PES = 0). The government imposes a $100 per-unit tax. How is the tax burden shared?

Solution:
With PES = 0 the entire tax is borne by the seller. The buyer pays the same price; the seller’s net receipt falls by the full $100. This illustrates that taxes on goods with perfectly inelastic supply fall entirely on producers.

Case 3: Short-Run vs. Long-Run Elasticity and Tax Incidence

An industrial good has short-run PES = 0.6 and long-run PES = 2.5. Demand elasticity is 1.0. A $10 per-unit tax is levied. Calculate the producer’s share of the tax in both periods.

Solution:
Short-run producer share = $\frac{1.0}{1.0 + 0.6} = 0.625$ → bears $6.25$.
Long-run producer share = $\frac{1.0}{1.0 + 2.5} = 0.286$ → bears $2.86$.

Conclusion: Over time producers can adjust capacity and pass more of the tax burden forward to consumers.

Traps

Key Formulas

• Price elasticity of supply: $ PES = \frac{\% \Delta Q_s}{\% \Delta P} $
• Midpoint (arc) formula (must memorize)
• Producer tax burden share = $\frac{|E_d|}{|E_d| + E_s}$
• Long-run PES > Short-run PES
• PES = 0 → vertical supply; PES → ∞ → horizontal supply
• Cross-price elasticity of supply > 0 indicates substitutes in production

Practice Questions

Q1. If the price of a good rises by 10% and quantity supplied rises by 15%, the price elasticity of supply is:
A. 0.67
B. 1.5
C. 10
D. 15

Q2. Which of the following goods is most likely to have perfectly inelastic supply?
A. Smartphones
B. Gold jewelry
C. An original Van Gogh painting
D. Clothing

Q3. Supply elasticity is likely to be highest for:
A. Short-run output of heavy industrial products
B. Long-run output of software services
C. Agricultural products with minimal inventories
D. Chemically rigid production processes

Q4. A good has PES = 0.8 and PED = 1.2. After a per-unit tax is imposed, who bears the larger share?
A. Producers
B. Consumers
C. Both bear equal shares
D. Cannot be determined

Q5. Using the midpoint method, price rises from $20 to $30 and quantity supplied rises from 50 to 80 units. Supply elasticity is closest to:
A. 0.92
B. 1.09
C. 1.25
D. 1.50

Q6. If the cross-price elasticity of supply between two goods is –0.5, the goods are:
A. Substitutes in production
B. Complements in production
C. Independent
D. Luxury goods

Q7. A good has long-run PES = 2.0 and short-run PES = 0.5. After a government subsidy, in the long run:
A. Producers benefit more
B. Consumers benefit more
C. Both benefit equally
D. The subsidy has no effect

Q8. Which statement about supply elasticity is incorrect?
A. The longer the time period, the larger supply elasticity usually is
B. A perfectly elastic supply curve is horizontal
C. With unit elastic supply, total revenue remains constant
D. With perfectly inelastic supply, price changes do not affect quantity supplied

Answers

Takeaways

• The core formula for price elasticity of supply is the ratio of percentage changes; exams require the midpoint method.
• Primary determinants are time, production flexibility, and inventory availability.
• Long-run supply elasticity always exceeds short-run elasticity.
• The more elastic supply, the greater the share of any tax borne by consumers.
• Vertical supply curves have PES = 0; horizontal curves have PES = ∞ — never reverse them.
• Economic incidence of taxes or subsidies is determined jointly by supply and demand elasticities, not by legislation alone.