Link between individual supply and market supply

Topic: Allocation of Resources – Supply

Learning objective

Understand how the quantity that a single producer is willing to supply at different prices (individual supply) combines to give the total quantity that all producers in the market are willing to supply at each price (market supply). Be able to explain movements along a supply curve, shifts of the supply curve, and the price elasticity of supply, and to relate supply to different economic systems and to supply‑side market failure.

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1. Individual & market supply

Individual supply

• Definition: The relationship, ceteris paribus, between the price of a good and the quantity that one firm is willing and able to produce and sell.
• Law of supply: When the price rises, the quantity supplied by the firm rises (and vice‑versa).
• Linear example: Q_s = a + bP, where
  • a = quantity supplied when price = 0 (vertical intercept)
  • b = change in quantity supplied for a one‑unit change in price (slope, b > 0)

Market supply

• Definition: The total quantity that all firms in a market are willing and able to supply at each possible price.
• Construction: Horizontally add (sum) the individual supply curves of every firm at each price level.
• General formula (n firms):
  Q_Ms = Σ_i=1ⁿ (a_i + b_iP) = (Σa_i) + (Σb_i)P
• Note: The same horizontal‑sum method works for any number of firms; the algebra simply extends to the required n.

Numerical illustration (two firms)

Price ($ per unit)	Firm A – Qs	Firm B – Qs	Market Qs
1	10	5	15
2	20	10	30
3	30	15	45
4	40	20	60
5	50	25	75

Plotting “Market Q_s” against price gives an upward‑sloping market‑supply curve.

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2. Movements along the supply curve

• A change in the price of the good causes a movement up or down along the same individual (or market) supply curve.
• Example (Firm A: Q_s = 10 + 10P):
  • At P = $2, Q_s = 30 units (point A).
  • If price rises to P = $4, Q_s = 50 units (point B) – a movement up the curve.
• All other factors (technology, input prices, expectations, etc.) are held constant (ceteris paribus).

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3. Shifts of the supply curve

A shift of the whole supply curve occurs when a factor **other than the price of the good** changes. The curve moves:

• Rightward (increase in supply): firms are willing to supply more at every price.
• Leftward (decrease in supply): firms are willing to supply less at every price.

Six common causes (Cambridge syllabus)

1. Change in input (factor) prices – e.g., a rise in the cost of raw material.
2. Technological improvement – e.g., new machinery that reduces production time.
3. Number of firms in the market – entry (rightward shift) or exit (leftward shift).
4. Expectations of future price changes – if firms expect higher future prices they may withhold supply now, shifting left.
5. Taxes, subsidies, or other government charges – a tax on inputs raises costs (leftward); a subsidy lowers costs (rightward).
6. Regulation (licences, quotas, environmental standards, etc.) – can restrict or encourage production.

Worked example – input tax

Firm A originally supplies:

Price ($)	Original Qs (units)	After $1/unit tax Qs (units)
2	20	15
3	30	20
4	40	25
5	50	30

The new schedule lies to the left of the original one, illustrating a leftward shift (decrease in supply).

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4. Price elasticity of supply (PES)

Definition

The percentage change in quantity supplied divided by the percentage change in price, holding all other factors constant.

Formula

\[ E_s = \frac{\%\Delta Q_s}{\%\Delta P} = \frac{\displaystyle \frac{Q_2-Q_1}{Q_1}}{\displaystyle \frac{P_2-P_1}{P_1}} \]

Elasticity categories (required by the syllabus)

Category	Value range	Typical example
Perfectly inelastic	Es = 0	Land – quantity supplied cannot change with price.
Inelastic	0 < Es < 1	Short‑run output of a factory operating at full capacity.
Unit‑elastic	Es = 1	Firm A’s schedule (see below).
Elastic	Es > 1	Fresh‑produce market where producers can quickly increase output.
Perfectly elastic	Es → ∞	Competitive market with excess capacity; producers will supply any quantity at a given market price.

Worked calculation – unit‑elastic

Using Firm A’s original schedule:

• Initial price, P₁ = $2 → Q₁ = 20 units.
• New price, P₂ = $3 → Q₂ = 30 units.

\[ \%\Delta P = \frac{3-2}{2}=0.50\;(50\%)\qquad \%\Delta Q_s = \frac{30-20}{20}=0.50\;(50\%) \] \[ E_s = \frac{0.50}{0.50}=1.0 \;\;(\text{unit‑elastic}) \]

Worked calculation – elastic (Eₛ > 1)

Suppose a horticultural firm can increase output from 40 to 70 units when price rises from $4 to $5.

\[ \%\Delta P = \frac{5-4}{4}=0.25\;(25\%)\qquad \%\Delta Q_s = \frac{70-40}{40}=0.75\;(75\%) \] \[ E_s = \frac{0.75}{0.25}=3.0 \;\;(\text{elastic}) \]

Worked calculation – inelastic (0 < Eₛ < 1)

A steel plant can only increase output from 200 to 210 units when price rises from $100 to $110.

\[ \%\Delta P = \frac{110-100}{100}=0.10\;(10\%)\qquad \%\Delta Q_s = \frac{210-200}{200}=0.05\;(5\%) \] \[ E_s = \frac{0.05}{0.10}=0.5 \;\;(\text{inelastic}) \]

Determinants of PES (Cambridge syllabus)

1. Availability of inputs: Easy, cheap access makes supply more elastic.
2. Time‑frame (short‑run vs. long‑run): In the long run firms can adjust plant size, hire/train staff, etc., so supply is more elastic.
3. Production capacity: Excess capacity → elastic; operating at full capacity → inelastic.
4. Mobility of factors of production: Highly mobile labour or capital increases elasticity.

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5. Supply and the economic system

• Market‑economy system: Private firms decide how much to produce, responding to profit‑maximising incentives and price signals. The market‑supply curve aggregates these decisions.
• Mixed‑economy system: The government may intervene to influence supply through:
  • Subsidies: Lower producers’ costs → rightward shift of supply.
  • Taxes or duties on inputs: Raise costs → leftward shift of supply.
  • Licences, quotas, or other regulatory limits: Restrict output → leftward shift.
  • Regulation (e.g., environmental standards): May increase costs (leftward) or, if it encourages innovation, could shift supply rightward.

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6. Supply‑side market failure

Market failure (supply side): A situation where the market does not allocate resources efficiently on the production side, leading to a socially undesirable level of output.

• External costs (negative externalities): Firms ignore social costs such as pollution, resulting in over‑supply.
• Public‑good characteristics of inputs: Essential inputs like basic research are under‑supplied because firms cannot capture all the benefits.
• Information asymmetry: Producers cannot accurately gauge consumer demand, causing mis‑allocation of resources.
• Monopoly power: A dominant firm restricts output below the competitive level to maximise profit, leading to under‑supply.

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Key points to remember

• The individual supply curve shows a firm’s response to price changes; the market supply curve is the horizontal sum of all individual curves and the method works for any number of firms.
• Movements along a supply curve are caused by price changes; shifts are caused by non‑price factors (input prices, technology, number of firms, expectations of future prices, taxes/subsidies, regulation).
• Price elasticity of supply measures how responsive quantity supplied is to price. Five categories are required: perfectly inelastic, inelastic, unit‑elastic, elastic, perfectly elastic.
• Determinants of PES include input availability, time‑frame (short‑run vs. long‑run), production capacity, and factor mobility.
• In a market economy, supply decisions are driven by profit‑maximising firms. In a mixed economy the government can shift supply through subsidies, taxes, licences/quotas, and regulation.
• Supply‑side market failures (externalities, public‑good inputs, information asymmetry, monopoly) justify government intervention to improve resource allocation.