Big picture
A firm turns inputs (labour, capital, land) into output. To decide how much to produce, it needs to know three things: how output changes as it adds inputs (production), what the output costs (cost), and what it earns from selling it (revenue). The firm maximises profit where the extra revenue from one more unit equals its extra cost: MR = MC.
From this decision we derive the supply curve, which shows how much firms are willing to sell at each price. Tables, diagrams and the relationships between curves are tested heavily.
Learning goals
Explain the production function and the short and long run.
Calculate and explain total, average and marginal product, and the law of variable proportions.
Explain returns to scale.
Calculate and explain short-run costs and the relationships between them.
Explain total, average and marginal revenue under perfect and imperfect competition.
Explain producer's equilibrium using the MR = MC approach.
Explain supply, its determinants, the law of supply, and movement versus shift.
Calculate price elasticity of supply by the percentage and geometric methods.
Core ideas
1. Production function
The production function shows the technical relationship between physical inputs and physical output: Q = f(L, K).
Short run: at least one factor (usually capital) is fixed; output changes by varying the variable factor (labour).
Long run: all factors can be varied.
2. Total, average and marginal product
Total product (TP): total output from a given amount of the variable factor.
Average product (AP) = TP ÷ L.
Marginal product (MP) = change in TP from one more unit of the variable factor: MPn = TPn − TPn−1.
Worked example (capital fixed, labour variable)
Labour | TP | MP | AP |
|---|---|---|---|
1 | 10 | 10 | 10 |
2 | 24 | 14 | 12 |
3 | 36 | 12 | 12 |
4 | 44 | 8 | 11 |
5 | 48 | 4 | 9.6 |
6 | 48 | 0 | 8 |
7 | 44 | −4 | 6.29 |
3. Law of variable proportions (returns to a factor)
When more units of a variable factor are combined with a fixed factor, TP first increases at an increasing rate, then at a diminishing rate, and finally falls.
Phase | TP | MP | In the example |
|---|---|---|---|
I: Increasing returns to a factor | Rises at an increasing rate | Rises | Labour 1 to 2 (MP rises from 10 to 14) |
II: Diminishing returns to a factor | Rises at a diminishing rate, reaching its maximum | Falls but stays positive, reaching zero | Labour 3 to 6 (MP falls from 12 to 0; TP is maximum at 48) |
III: Negative returns to a factor | Falls | Negative | Labour 7 (MP = −4) |
Reasons: in Phase I, the fixed factor is better utilised and specialisation improves; in Phase II, the fixed factor becomes scarce relative to the variable factor; in Phase III, too many workers crowd the fixed factor and get in each other's way. A rational producer operates in Phase II.
Relationships between TP, AP and MP: TP is maximum when MP = 0; TP falls when MP is negative; when MP > AP, AP rises; when MP = AP, AP is at its maximum; when MP < AP, AP falls.
4. Returns to scale
Returns to scale describe how output changes when all inputs are increased in the same proportion (a long-run concept).
Type | Meaning | Example |
|---|---|---|
Increasing returns to scale | Output rises by a greater proportion | Inputs doubled, output triples |
Constant returns to scale | Output rises by the same proportion | Inputs doubled, output doubles |
Diminishing returns to scale | Output rises by a smaller proportion | Inputs doubled, output rises by 50% |
5. Short-run costs
Cost | Meaning |
|---|---|
Total fixed cost (TFC) | Costs that don't change with output (rent, salaries of permanent staff, interest); incurred even at zero output |
Total variable cost (TVC) | Costs that change with output (raw materials, wages of casual labour, power) |
Total cost (TC) | TFC + TVC |
Average fixed cost (AFC) | TFC ÷ Q; falls continuously as output rises |
Average variable cost (AVC) | TVC ÷ Q |
Average cost (AC) | TC ÷ Q = AFC + AVC |
Marginal cost (MC) | Change in TC from one more unit: MCn = TCn − TCn−1 (also = TVCn − TVCn−1) |
Worked example (TFC = ₹20)
Output | TFC | TVC | TC | AFC | AVC | AC | MC |
|---|---|---|---|---|---|---|---|
0 | 20 | 0 | 20 | – | – | – | – |
1 | 20 | 30 | 50 | 20 | 30 | 50 | 30 |
2 | 20 | 50 | 70 | 10 | 25 | 35 | 20 |
3 | 20 | 66 | 86 | 6.67 | 22 | 28.67 | 16 |
4 | 20 | 88 | 108 | 5 | 22 | 27 | 22 |
5 | 20 | 120 | 140 | 4 | 24 | 28 | 32 |
Shapes and relationships
TFC is a horizontal straight line; TVC starts from the origin; TC starts from the level of TFC and runs parallel to TVC.
AFC is a rectangular hyperbola: it falls continuously but never touches the X-axis.
AVC, AC and MC are U-shaped, because of the law of variable proportions.
MC cuts AVC and AC at their minimum points from below. When MC < AC, AC falls; when MC > AC, AC rises.
The gap between AC and AVC is AFC, which narrows as output rises.
6. Revenue
Concept | Meaning |
|---|---|
Total revenue (TR) | Price × Quantity sold |
Average revenue (AR) | TR ÷ Q = Price |
Marginal revenue (MR) | Change in TR from selling one more unit |
Market | AR and MR | TR |
|---|---|---|
Perfect competition (price is given; the firm is a price taker) | AR = MR = Price; both are a horizontal line | A straight line from the origin |
Imperfect competition (the firm must lower price to sell more) | AR and MR slope downward; MR lies below AR | Rises at a diminishing rate, is maximum when MR = 0, then falls |
Example (imperfect competition): price ₹10 for 1 unit, ₹9 for 2 units, ₹8 for 3 units. TR = 10, 18, 24; MR = 10, 8, 6; AR = 10, 9, 8.
7. Producer's equilibrium
A producer is in equilibrium when it maximises profit. Using the MR = MC approach, two conditions must hold:
MR = MC, and
MC is rising (MC cuts MR from below) at that output.
If MR > MC, producing one more unit adds more to revenue than to cost, so output should rise. If MR < MC, output should fall.
Example. With the cost table above and a market price of ₹32 (perfect competition, so MR = ₹32), MR = MC = 32 at 5 units, and MC is rising there. Profit = TR − TC = (5 × 32) − 140 = ₹20. (MR = MC could also occur on a falling MC curve, but that is not equilibrium, because producing more would add profit.)
8. Supply
Supply is the quantity of a good a producer is willing and able to sell at a given price during a given period.
Determinants of supply
Price of the good itself
Prices of other goods (a farmer may switch to a crop whose price has risen)
Prices of factors of production (higher input costs reduce supply)
State of technology (better technology increases supply)
Goals of the firm, government policy (taxes reduce supply, subsidies raise it), number of firms and expectations of future prices
Law of supply: other things being equal, the quantity supplied of a good rises when its price rises and falls when its price falls. The supply curve slopes upward, because a higher price makes it profitable to produce more (covering rising MC) and attracts new firms.
Basis | Movement along the supply curve | Shift of the supply curve |
|---|---|---|
Cause | Change in the good's own price | Change in other factors (technology, input prices, taxes) |
Types | Expansion (price rises) and contraction (price falls) | Increase (shift right) and decrease (shift left) |
Examples of shifts: improved technology shifts supply to the right; a rise in wages or raw material prices shifts it to the left; a new tax shifts it left; a subsidy shifts it right.
9. Price elasticity of supply
Price elasticity of supply (Es) = Percentage change in quantity supplied ÷ Percentage change in price.
Example. When price rises from ₹10 to ₹12, quantity supplied rises from 200 to 260 units.
% change in Qs = (260 - 200) / 200 x 100 = 30%
% change in P = (12 - 10) / 10 x 100 = 20%
Es = 30 / 20 = 1.5 (elastic supply)Geometric method (straight-line supply curves):
A supply curve that passes through the origin has Es = 1.
One that meets the Y-axis (price axis) when extended has Es > 1.
One that meets the X-axis (quantity axis) when extended has Es < 1.
Determinants: nature of the good (perishable goods have less elastic supply), time period (supply is more elastic in the long run), availability of facilities for expansion, and the cost of production as output changes.
A reliable problem-solving routine
For production tables, compute MP = TPn − TPn−1 and AP = TP ÷ L, then identify the three phases from MP.
For cost tables, use TC = TFC + TVC, then AFC, AVC, AC and MC; check that MC cuts AC at its minimum.
For revenue, compute TR = P × Q, AR = TR ÷ Q and MR = TRn − TRn−1.
For equilibrium, find where MR = MC and MC is rising; compute profit = TR − TC.
For elasticity of supply, use the percentage method, or the geometric rule based on where the curve meets an axis.
Connections that matter
Consumer equilibrium and demand provides the other side of the market.
Market price determination combines supply and demand to find equilibrium price.
Class 12 business studies: financial management discusses fixed and variable costs in business decisions.
Common mistakes
Saying TP falls as soon as MP falls. TP falls only when MP is negative.
Drawing AFC as U-shaped. It is a rectangular hyperbola that falls continuously.
Stating equilibrium as MR = MC without the rising-MC condition.
Calling a change in technology a movement along the supply curve. It is a shift.
Confusing returns to a factor (short run) with returns to scale (long run).
Revision checklist
I can compute TP, AP and MP and explain the law of variable proportions.
I can explain returns to scale.
I can compute all short-run costs and explain their relationships and shapes.
I can compute TR, AR and MR under perfect and imperfect competition.
I can find producer's equilibrium and profit.
I can explain supply, the law of supply, movements and shifts, and elasticity of supply.