Profit: normal profit, sub-normal profit and supernormal profit

Profit, Cost and Revenue – AS 7.5 (Cambridge IGCSE/A‑Level)

1. Cost concepts

Costs are the value of resources used in production. The syllabus requires the following measures:

Cost	Definition	Formula
Fixed Cost (FC)	Cost that does not vary with the level of output (e.g. rent, salaries of permanent staff).	$FC$
Variable Cost (VC)	Cost that varies directly with output (e.g. raw materials, hourly wages).	$VC(Q)$
Total Cost (TC)	Sum of fixed and variable costs.	$TC = FC + VC$
Average Fixed Cost (AFC)	Fixed cost per unit of output.	$AFC = \dfrac{FC}{Q}$
Average Variable Cost (AVC)	Variable cost per unit of output.	$AVC = \dfrac{VC}{Q}$
Average Total Cost (ATC)	Total cost per unit of output; ATC = AFC + AVC.	$ATC = \dfrac{TC}{Q}=AFC+AVC$
Marginal Cost (MC)	Additional cost of producing one more unit of output.	$MC = \dfrac{\Delta TC}{\Delta Q}$

Shape of the short‑run cost curves

• U‑shaped AVC and ATC: they fall as output rises (spreading of fixed costs and increasing marginal returns) and then rise because of diminishing marginal returns.
• MC curve cuts both AVC and ATC at their minimum points – the “intersection rule”. This occurs because when MC is below AVC (or ATC) the average cost falls, and when MC is above the average cost the average cost rises.
• AFC continuously falls as $Q$ increases because $FC$ is constant.

Numerical example

Let $FC = £1{,}000$ and $VC = 5Q$ (where $Q$ is output in units).

• $TC = 1{,}000 + 5Q$
• $AFC = \dfrac{1{,}000}{Q}$
• $AVC = 5$ (constant)
• $ATC = \dfrac{1{,}000}{Q}+5$ – falls sharply at low $Q$, flattens as $Q$ grows.
• $MC = \dfrac{dTC}{dQ}=5$ (horizontal line).

2. Revenue concepts

Revenue is the money received from selling output.

Revenue	Definition	Formula
Total Revenue (TR)	Price multiplied by quantity sold.	$TR = P \times Q$
Average Revenue (AR)	Revenue per unit of output.	$AR = \dfrac{TR}{Q}=P$ (in perfect competition $AR$ equals price).
Marginal Revenue (MR)	Additional revenue from selling one more unit.	$MR = \dfrac{\Delta TR}{\Delta Q}$

Price‑taking vs price‑setting markets

• Perfect competition: the firm is a price taker; $P$ is given, so $AR = MR = P$.
• Monopoly / monopolistic competition: the firm faces a downward‑sloping demand curve; consequently $MR < AR$.

3. Production function and product concepts (short‑run)

The short‑run production function shows the relationship between the variable input (usually labour) and output when at least one input (capital) is fixed.

Product concept	Definition	Formula
Total Product (TP)	Total output produced for a given quantity of the variable input.	$TP = f(L)$
Average Product (AP)	Output per unit of the variable input.	$AP = \dfrac{TP}{L}$
Marginal Product (MP)	Additional output from one more unit of the variable input.	$MP = \dfrac{\Delta TP}{\Delta L}$

• When MP is rising, each extra worker adds more output than the previous one; this makes MC fall because the same extra output costs less labour.
• When MP reaches its maximum and starts to fall (law of diminishing marginal returns), MC begins to rise. Hence the characteristic U‑shape of the MC curve.
• The point where MP = $ \dfrac{1}{\text{price of labour}} $ corresponds to the minimum of the AVC curve.

4. Profit concepts

Profit ($\pi$) is the difference between total revenue and total cost, measured **including both explicit and implicit costs**.

Profit type	Condition (formula)	Economic interpretation
Normal profit	$\pi = TR - TC = 0$  (i.e. $TR = TC$ when all implicit costs are included)	All explicit and implicit costs (including the entrepreneur’s opportunity cost) are covered. The firm is indifferent between staying in the industry and leaving – long‑run equilibrium in perfect competition.
Sub‑normal profit (loss)	$\pi < 0$  (i.e. $TR < TC$)	The firm does not cover its total costs. In the long run it will exit the market unless conditions improve.
Super‑normal profit	$\pi > 0$  (i.e. $TR > TC$)	Revenue exceeds both explicit and implicit costs. This signals that resources are earning more than their next‑best alternative, attracting entry in competitive markets (which erodes the profit) or indicating market power in imperfect markets.

Profit‑maximising rule

• The profit‑maximising output $Q^{*}$ satisfies $MR = MC$. At this point the extra revenue from the last unit equals the extra cost of producing it.
• If $MR > MC$, expanding output raises profit; if $MR < MC$, reducing output raises profit.
• After locating $Q^{*}$, compare $TR$ and $TC$ (or price $P$ with $ATC$) to determine whether the profit is normal, sub‑normal or super‑normal.

Shutdown rule (short‑run)

• If price falls below average variable cost ($P < AVC$) the firm cannot cover its variable costs and will **shut down** in the short run.
• If $AVC \le P < ATC$, the firm continues to produce (it covers variable costs and part of fixed costs) but incurs a loss equal to $ATC - P$ per unit.

5. Short‑run equilibrium in different market structures

Market	Condition for equilibrium	Profit outcome (short‑run)
Perfect competition	$MC = MR = P$ (horizontal demand)	Super‑normal profit if $P > ATC$, normal profit if $P = ATC$, loss if $ATC > P > AVC$ (continue operating) or shutdown if $P < AVC$.
Monopoly	$MR = MC$ and $P$ is read from the demand curve (so $P > MC$)	Can sustain super‑normal profit because entry is blocked; loss occurs only if $P < ATC$ at the profit‑maximising output.
Monopolistic competition	$MR = MC$ with a downward‑sloping demand	Same three profit possibilities as perfect competition, but in the long run super‑normal profit attracts entry and drives profit to normal.

Long‑run production and cost

Returns to scale (definition)

Returns to scale describe how output changes when **all** inputs are increased proportionally.

Returns to scale	Definition (input change → output change)	Effect on long‑run average cost (LRAC)
Increasing Returns to Scale (IRS)	Doubling all inputs more than doubles output.	LRAC falls as output expands (economies of scale).
Constant Returns to Scale (CRS)	Doubling all inputs exactly doubles output.	LRAC is flat (horizontal) over this range.
Decreasing Returns to Scale (DRS)	Doubling all inputs less than doubles output.	LRAC rises as output expands (diseconomies of scale).

Economies and diseconomies of scale

• Economies of scale – reduction in average cost when a firm expands output (IRS region). Main sources:
  • Technical – larger, more efficient plant & machinery.
  • Managerial – specialisation of staff and better supervision.
  • Financial – access to cheaper capital and bulk borrowing.
  • Marketing – bulk buying of inputs, larger advertising reach.
• Diseconomies of scale – increase in average cost when a firm becomes too large (DRS region). Typical causes:
  • Coordination and communication problems.
  • Loss of employee motivation and higher absenteeism.
  • Excessive bureaucracy and slower decision‑making.

Minimum Efficient Scale (MES)

The lowest output at which a firm can exploit all possible economies of scale and achieve the minimum point of the LRAC curve. In a perfectly competitive market entry continues until firms operate at or near the MES, resulting in normal profit.

Long‑run cost curves

• All inputs are variable; the firm can choose the plant size that minimises cost.
• The envelope of all possible short‑run ATC curves forms the Long‑run Average Cost (LRAC) curve. The LRAC is typically U‑shaped, reflecting IRS at low output, CRS in the middle, and DRS at high output.
• Where LRAC is falling the firm enjoys economies of scale; where it is rising the firm faces diseconomies.

Long‑run equilibrium (perfect competition)

• Profit‑maximising condition: $P = MC = LRAC$ at the minimum of the LRAC curve.
• Result: only normal profit survives; any super‑normal profit would attract entry, any loss would cause exit.

Long‑run equilibrium (monopoly)

• Profit‑maximising condition: $MR = MC$ and, because the monopolist faces a downward‑sloping demand curve, $P > MC$.
• Entry is blocked, so the monopoly can sustain super‑normal profit in the long run.

Summary of profit types

Profit type	Condition (in £)	Economic significance
Normal profit	$\pi = 0$ ($TR = TC$ including implicit costs)	All opportunity costs are covered; industry is in long‑run equilibrium.
Sub‑normal profit (loss)	$\pi < 0$ ($TR < TC$)	Firm does not cover total costs; it will exit in the long run unless conditions improve.
Super‑normal profit	$\pi > 0$ ($TR > TC$)	Revenue exceeds all costs; attracts entry in competitive markets or indicates market power in imperfect markets.

Key diagrams (suggested for Paper 2)