The Theory of the Firm under Perfect Competition | CBSE Class 11 Economics Notes

This note covers perfect competition, price-taking behaviour, revenue, profit maximisation, short-run and long-run supply, shutdown and break-even points, supply determinants, market supply and price elasticity of supply.

What makes a market perfectly competitive?

Perfect competition is a market environment with many buyers and sellers, identical products, free entry and exit, and perfect information. A firm is a producer that produces and sells a good. These features explain why an individual firm takes the market price as given.

What are the four defining features?

1. Large number of buyers and sellers: each individual buyer and seller is very small relative to the market. No individual can influence the market by their size.
2. Homogeneous product: one firm's product cannot be differentiated from another firm's product. A buyer receives the same product whichever firm supplies it.
3. Free entry and exit: firms can easily enter or leave the market. This condition is essential for large numbers of firms to exist.
4. Perfect information: buyers and sellers are completely informed about price, quality and other relevant details of the product and market.

Why does a firm accept the market price?

A price-taking firm believes that it cannot sell anything above the market price. At a price less than or equal to that price, it believes it can sell as many units as it wants. There is therefore no reason to charge less than the market price.

If one firm raises its price, informed buyers can turn to other firms selling the identical product. With so many other firms, their purchases can be accommodated. Price-taking is often thought to be a reasonable assumption when there are many firms and buyers have perfect price information.

A price-taking buyer believes that no firm will sell below the market price. At or above that price, the buyer can obtain the desired quantity. The buyer would like to pay the lowest possible price.

Note: The analysis assumes that a firm maximises profit and sells whatever it produces. Profit means revenue, or sales receipts, minus production cost. Output means the quantity produced. Under the second assumption, output and quantity sold are often used interchangeably. Profit maximisation is a critical, if somewhat unreasonable, assumption about firm behaviour.

How are total, average and marginal revenue related?

Revenue is the money a firm earns by selling its output. Let p denote the market price per unit and q the quantity produced and sold. Total revenue (TR) is the value of all these sales.

TR = p × q

How does total revenue change with output?

At a constant market price, total revenue rises in direct proportion to output. With no sales, total revenue is zero. The candle example assumes a perfectly competitive market and a market price of 10 rupees (Rs 10) per box.

Output is on the horizontal axis and revenue on the vertical axis. The straight TR line rises from the origin, labelled O. Its slope equals the constant market price.

See Fig. 4.1 in your NCERT textbook

What do average and marginal revenue measure?

Average revenue (AR) means total revenue per unit of output. For positive output, dividing total revenue by quantity cancels the quantity factor. Thus, the average revenue of a price-taking firm equals the market price.

AR = TR/q = p

Marginal revenue (MR) is the increase in total revenue for a unit increase in output. The symbol Δ means “change in”, so ΔTR means the change in total revenue and Δq means the change in quantity.

MR = ΔTR/Δq = p

Each additional unit is sold at the same market price. The extra revenue from that unit is therefore the price itself. Consequently, MR = AR = p for a perfectly competitive firm.

Worked example 1. A candle producer sells boxes at Rs 10 each. Total revenue is Rs 20 from two boxes and Rs 30 from three boxes. Find marginal revenue for this increase and average revenue at three boxes.

Answer: Marginal revenue = (30 − 20)/(3 − 2) = Rs 10 per box. Average revenue = 30/3 = Rs 10 per box. Both equal the market price.

Perfectly elastic demand here means that the firm can sell as many units as it wants at the given price. This horizontal demand curve belongs to the individual firm.

Price is measured vertically and output horizontally. The price line is horizontal at height p. It is the firm's average revenue curve and the perfectly elastic demand curve facing the firm.

See Fig. 4.2 in your NCERT textbook

Which conditions identify the profit-maximising output?

Let π, the Greek letter pi, denote profit, and let total cost (TC) mean the total cost of producing the output. Profit is the difference between total revenue and total cost.

π = TR − TC

Let q₀ denote the profit-maximising output. The firm seeks the quantity at which the gap between revenue and cost is greatest. This requires comparing what an extra unit adds to revenue with what it adds to cost.

Why must marginal revenue equal marginal cost?

Marginal cost (MC) is the change in total cost per unit increase in output. If marginal revenue exceeds marginal cost, expanding output increases profit. If marginal revenue is below marginal cost, expanding output reduces profit.

At the profit-maximising positive output, marginal revenue equals marginal cost. Since marginal revenue equals price under perfect competition, the first condition becomes p = MC. Equality alone is insufficient: the direction of the marginal cost curve and the cost coverage condition also matter.

Why must marginal cost be non-decreasing?

Non-decreasing marginal cost means that marginal cost does not fall as output increases at the relevant output. An intersection between price and a downward-sloping marginal cost curve cannot identify the profit maximum.

At outputs slightly to the left of such an intersection, price is below marginal cost. Producing slightly less therefore gives a higher profit than producing at that intersection. On the rising portion, the firm instead reaches the relevant equality after the range where expansion adds to profit.

What is the cost coverage condition?

Inputs, or factors of production, are resources used in production. Average variable cost (AVC) is variable cost per unit of output; variable costs change with output. Average cost (AC) is total cost per unit. In the short run, some factors are fixed; in the long run, all factors can be varied.

Use SMC for short-run marginal cost, SAC for short-run average cost, LRMC for long-run marginal cost and LRAC for long-run average cost. These abbreviations identify the cost curves used to select output in each period.

The horizontal price line meets rising SMC at output q₀. SAC and AVC lie below price at that output. The rectangle between price and SAC, extending across q₀, represents profit.

See Fig. 4.6 in your NCERT textbook

The height of this profit rectangle is price minus average cost; its width is quantity. Multiplying the height by the width gives total revenue minus total cost. A revenue rectangle alone does not measure profit because production costs must also be deducted.

How is the firm's short-run supply curve derived?

A firm's supply is the quantity it chooses to sell at a given price, given technology and input prices. A supply schedule lists quantities supplied at different prices while technology and input prices remain unchanged.

A supply curve represents that relationship graphically, with output on the horizontal axis and market price on the vertical axis. To construct it, find the profit-maximising output at each possible price, including prices at which producing nothing is preferable.

What happens at or above minimum average variable cost?

1. Take the market price as given and compare it with minimum average variable cost.
2. If price is at least that minimum, find its intersection with the rising short-run marginal cost curve.
3. Check that average variable cost at the selected output does not exceed price.
4. The resulting output satisfies the profit-maximisation conditions and supplies the quantity associated with that price.

Why does supply become zero below the minimum?

Total variable cost (TVC) is the total cost of variable inputs. Total fixed cost (TFC) is the cost that remains even at zero output in the short run. Total cost is the sum of these two components.

TC = TVC + TFC

When price is below average variable cost, revenue does not cover variable cost. Producing then adds an uncovered variable cost to the fixed cost already incurred. At zero output, both revenue and variable cost are zero, leaving a loss equal to total fixed cost.

If price is below minimum AVC, it is below AVC at every positive output. No positive output passes the cost coverage condition, so the firm supplies zero. This conclusion depends on comparing production with the option of no production.

The bold supply curve follows rising SMC from its intersection with AVC at minimum AVC. The zero-output part lies on the vertical axis below that price. SAC is also drawn above AVC.

See Fig. 4.8 in your NCERT textbook

The short-run supply curve therefore combines the rising SMC segment from and above minimum AVC with zero output for lower prices. Calling the entire marginal cost curve the supply curve would wrongly include outputs that fail the other conditions.

How does the long-run supply decision differ?

In the long run, a firm compares price with long-run average cost. At a positive output where price is below average cost, total revenue is below total cost and the firm incurs a loss. Shutting down production in the long-run setting gives zero profit.

What happens when price covers average cost?

If market price is at least minimum LRAC, equate price with LRMC on its rising portion. The selected output also has LRAC no greater than price. The firm therefore meets the equality, non-decreasing marginal cost and cost coverage conditions.

If price is below minimum LRAC, every positive output has average cost above price. Producing cannot satisfy the long-run cost coverage requirement. The firm chooses zero output and exits rather than continuing to incur a loss.

The rising LRMC curve intersects the U-shaped LRAC curve at its minimum. The bold supply curve follows LRMC from that point upwards and shows zero output on the vertical axis for lower prices.

See Fig. 4.10 in your NCERT textbook

Which cost threshold changes between the two periods?

The long-run supply curve thus combines rising LRMC from and above minimum LRAC with zero output below that minimum. Both periods use marginal cost to choose a positive quantity, but they use different average cost thresholds to decide whether production should take place.

What are shutdown, normal profit and break-even?

The short-run shutdown point is the point of minimum AVC where SMC cuts AVC. Moving down the supply curve, it is the last price-output combination at which the firm produces positive output. Below this price there is no production.

The long-run shutdown point is the minimum of LRAC. Keep the two thresholds separate: the relevant comparison in the short run is with variable cost, whereas the long-run comparison is with average cost.

Why is normal profit included in cost?

Normal profit is the minimum profit needed to keep a firm in its existing business. It forms part of total cost. It may be useful to think of it as an opportunity cost of entrepreneurship, the activity of running the business.

Opportunity cost is the gain forgone from the second-best activity. Committing resources to one activity means giving up the best available alternative use. Thus, cost need not be restricted to money paid out to purchase inputs.

Super-normal profit is profit above normal profit. In the long run, a firm does not produce if it earns less than normal profit. In the short run, however, it may produce even if its profit is below this level.

How does break-even differ from shutdown?

The break-even point is the point on the supply curve at which a firm earns only normal profit. It occurs at minimum average cost, where supply cuts LRAC in the long run or SAC in the short run.

Since normal profit is included in total cost, earning only normal profit means revenue covers that total cost. The short-run shutdown point concerns minimum AVC, so it must not be confused with the short-run break-even point at minimum SAC.

Worked example 2. You invest Rs 1,000 in the family business. Alternatives are keeping it in a house-safe for zero return, depositing it in bank-1 at 10 per cent, or depositing it in bank-2 at 5 per cent. Identify the opportunity cost.

Answer: Bank-1 offers the best alternative return. The interest forgone is Rs 1,000 × 10/100 = Rs 100. This forgone interest is the opportunity cost of choosing the family business.

What causes a firm's supply curve to shift?

A firm's supply curve is a segment of its marginal cost curve, together with the zero-output range. A factor affecting marginal cost therefore affects supply. A shift changes the quantity supplied at a given market price; the price itself need not change.

How does technological progress affect supply?

Technological progress can take the form of an organisational innovation. Suppose the same amounts of capital, meaning produced inputs such as machinery, and labour, meaning human work, now produce more output. The firm can then produce a given output with fewer inputs.

It is expected that this lowers marginal cost at any output level. The marginal cost curve shifts rightwards, or downwards, and the supply curve shifts to the right. At a given market price, the firm now supplies more output.

What happens when an input becomes more expensive?

A rise in an input price, such as the wage rate, or payment for labour, raises production cost. The resulting increase in average cost is usually accompanied by an increase in marginal cost at any output level.

The marginal cost curve shifts leftwards, or upwards, and the supply curve shifts leftwards. At a given market price, the firm supplies fewer units. An increase or decrease in input prices is expected to shift supply left or right respectively.

How does a unit tax change costs?

A unit tax is a tax imposed by the government per unit sale of output. Let t denote the tax amount per unit. Because output is sold in this analysis, each additional unit produced brings an additional tax payment of t.

The unit tax raises long-run average cost and long-run marginal cost at every output by t. As the long-run supply curve is derived from these cost curves, the tax shifts supply to the left. At a given market price, the firm supplies fewer units.

Worked example 3. The government imposes a unit tax of Rs 2. A firm produces and sells 10 units. Calculate its total tax payment.

Answer: Total tax = tax per unit × units sold = Rs 2 × 10 = Rs 20. The payment arises on each unit sold.

The cost diagram shows both long-run cost curves moving upwards by t. In the supply diagram, S₀ denotes supply before the tax and S₁ supply afterwards; S₁ lies to the left of S₀.

See Figs. 4.11 and 4.12 in your NCERT textbook

How is market supply obtained from individual supplies?

Market supply is the total quantity supplied by all firms at a particular market price. Its curve plots total output horizontally and price vertically. To obtain it, add each firm's quantity at the same price.

Why is the summation horizontal?

Horizontal summation means adding quantities along the output axis while holding price constant. Do not add the firms' prices. If firms have different cost structures, their minimum prices for supplying output can differ, so some may supply while others supply nothing.

Let S₁(p) and S₂(p) denote the quantities supplied by firms 1 and 2 at price p. Let Sₘ(p) denote their combined market supply. The subscript m identifies the market total.

Sₘ(p) = S₁(p) + S₂(p)

Consider a market where firm 1 supplies zero below price 10 and supplies p − 10 at prices of 10 or more. Firm 2 supplies zero below price 15 and supplies p − 15 at prices of 15 or more.

Below the lower threshold, neither firm supplies anything. Between the two thresholds, the market quantity comes entirely from firm 1. At or above the higher threshold, the market expression adds the quantities given by both supply functions.

Three panels show firm 1's supply, firm 2's supply and market supply. At a common price, the two individual output distances add to the output distance in the market panel.

See Fig. 4.13 in your NCERT textbook

What if the number of firms changes?

This derivation holds the number of firms fixed. An increase in the number of firms shifts market supply to the right. A decrease shifts it to the left. This change concerns the market total and must be distinguished from a cost change affecting an individual firm.

How is price elasticity of supply calculated?

Price elasticity of supply measures how responsive quantity supplied is to a change in the good's price. Denote it by eₛ; the symbol % means per cent. It compares the percentage change in quantity supplied with the percentage change in price, rather than comparing their absolute changes.

eₛ = (% change in quantity)/(% change in price)

Here Q is the initial market quantity supplied and P the initial market price. The changes are ΔQ and ΔP respectively. Using the initial values as bases gives an equivalent expression.

eₛ = (ΔQ/ΔP) × (P/Q)

How do the percentage calculations work?

1. Find the change in quantity by subtracting initial quantity from final quantity.
2. Divide this change by initial quantity and multiply by 100 to obtain the percentage quantity change.
3. Subtract initial price from final price, divide by initial price and multiply by 100 to obtain the percentage price change.
4. Divide the percentage quantity change by the percentage price change to obtain elasticity.

Worked example 4. In a perfectly competitive market for cricket balls, price rises from Rs 10 to Rs 30. Aggregate production and sales rise from 200 to 1,000 balls. Calculate price elasticity of supply.

Answer: Quantity rises by 1,000 − 200 = 800 balls, or (800/200) × 100 = 400 per cent. Price rises by Rs 20, or (20/10) × 100 = 200 per cent. Therefore, eₛ = 400/200 = 2.

The result means quantity supplied responds by a larger percentage than price in this example. Price elasticity of supply is independent of units: the ratio compares percentage changes, so it does not carry a rupee or quantity unit.

A vertical supply curve has zero elasticity because supply is completely insensitive to price. For a positively sloped supply curve, quantity supplied rises with price and elasticity is positive. The slope's sign indicates the direction of the response, while elasticity measures its proportional size.

How can elasticity be read from a straight supply line?

The geometric method compares horizontal distances associated with a straight-line supply curve. Let S be the point considered, O the origin and M the point where the extended supply line meets the quantity axis. Here q₀ denotes the quantity at S.

The distance Mq₀ runs from M to q₀ on the quantity axis; Oq₀ runs from the origin to q₀. At a positive-output point on the line, elasticity is the ratio Mq₀/Oq₀. The intercept determines how these distances compare.

What do the three intercept cases imply?

When the line meets the positive price axis, its extension meets the negative quantity axis. M lies to the left of O, making Mq₀ longer than Oq₀. The resulting elasticity is greater than one.

For a line through the origin, M coincides with O and the distance ratio is one. When M lies on the positive quantity axis, Mq₀ is shorter than Oq₀ and elasticity is below one. These results classify straight supply lines by their intercepts.

Panels (a), (b) and (c) show rising straight supply lines cutting the positive price axis, passing through the origin and cutting the positive quantity axis respectively. Each marks S and its output projection.

See Fig. 4.14 in your NCERT textbook

Do not infer unit elasticity simply because a supply curve is straight. The straight line must pass through the origin for the two horizontal distances to be equal. A line with another intercept has the corresponding greater-than-one or less-than-one elasticity.

Glossary

• Perfect competition — A market with many buyers and sellers, homogeneous products, free entry and exit, and perfect information.
• Price-taker — A buyer or seller that accepts the prevailing market price as given.
• Total revenue — The firm's receipts from sales, equal to price multiplied by quantity sold.
• Average revenue — Total revenue per unit of output, equal to price for a competitive firm.
• Marginal revenue — The increase in total revenue for a unit increase in output.
• Marginal cost — The change in total production cost per unit increase in output.
• Profit — The difference between the firm's total revenue and its total production cost.
• Normal profit — The minimum profit needed to keep a firm in its existing business.
• Super-normal profit — The profit a firm earns over and above its normal profit.
• Opportunity cost — The gain forgone from the second-best activity when another activity is chosen.
• Shutdown point — Minimum AVC in the short run and minimum LRAC in the long run.
• Break-even point — The point on the supply curve where a firm earns only normal profit.
• Unit tax — A tax imposed by the government per unit sale of output.
• Market supply — The sum of individual firms' quantities supplied at the same market price.
• Price elasticity of supply — Percentage change in quantity supplied divided by the percentage change in price.

Common errors and misconceptions

• Misconception: A competitive firm can raise its price without losing sales. Correct: The price-taking assumption says it cannot sell above the market price; informed buyers can purchase the homogeneous product elsewhere.
• Misconception: Total revenue and profit are the same. Correct: Total revenue measures sales receipts. Profit deducts total production cost, which includes normal profit, from those receipts.
• Misconception: Any equality between price and marginal cost gives maximum profit. Correct: Marginal cost must also be non-decreasing and the relevant average cost coverage condition must hold.
• Misconception: A firm must shut down whenever short-run profit is below normal profit. Correct: It may continue producing; the short-run supply threshold is minimum average variable cost.
• Misconception: The entire marginal cost curve is the supply curve. Correct: Use the rising segment from the relevant minimum average cost threshold, together with zero output below that price.
• Misconception: Market supply is found by adding prices. Correct: Add quantities supplied by all firms at a common price. This is horizontal summation.
• Misconception: Every straight supply line has unit elasticity. Correct: A straight line through the origin has unit elasticity; lines with other intercepts have different elasticity classifications.

Exam-style questions with model answers

Q1. Define average revenue and state its relationship with price for a perfectly competitive firm. [2 marks]

1. Average revenue is total revenue divided by the positive quantity of output sold.
2. Since total revenue equals price multiplied by quantity, average revenue equals the market price for a perfectly competitive firm.

Q2. Explain the four defining features of perfect competition. [4 marks]

1. There are many buyers and sellers, each small relative to the market, so no individual influences the market through size.
2. Products are homogeneous: the good supplied by one firm cannot be differentiated from the good supplied by another.
3. Entry and exit are free, making it easy for firms to join or leave the market.
4. Information is perfect: buyers and sellers know the price, quality and other relevant product and market details.

Q3. State and explain the three conditions for a competitive firm's positive profit-maximising output in the short run. [3 marks]

1. Price equals short-run marginal cost. Marginal revenue equals price, so this is also the equality of marginal revenue and marginal cost.
2. Short-run marginal cost is non-decreasing at the chosen output. An equality on a downward-sloping marginal cost curve cannot identify maximum profit.
3. Price is at least average variable cost at that output. Otherwise, producing adds an uncovered variable cost to the fixed cost already incurred.

Q4. Explain why a competitive firm produces zero output in the short run when market price is below minimum average variable cost. [5 marks]

1. If price is below minimum average variable cost, price is below average variable cost at every positive output available to the firm.
2. At any such output, total revenue is price multiplied by quantity, while total variable cost is average variable cost multiplied by that quantity.
3. Total revenue therefore falls short of total variable cost. Production leaves an uncovered variable cost as well as the fixed cost.
4. At zero output, total revenue and total variable cost are both zero. The firm's loss is then equal to total fixed cost.
5. The loss from producing exceeds the loss from producing nothing. A profit-maximising firm consequently chooses zero output at this market price.

Q5. A perfectly competitive cricket-ball market supplies 200 balls at Rs 10 each and 1,000 balls at Rs 30 each. Calculate price elasticity of supply by the percentage-change method. [4 marks]

1. The change in quantity is 1,000 − 200 = 800 balls. Relative to the initial 200 balls, the quantity increase is (800/200) × 100 = 400 per cent.
2. The price increase is Rs 30 − Rs 10 = Rs 20. Relative to Rs 10, the percentage increase is (20/10) × 100 = 200 per cent.
3. Price elasticity of supply equals percentage quantity change divided by percentage price change, giving 400/200 = 2.
4. The elasticity is greater than one: quantity supplied changes proportionately more than price. The elasticity value has no unit.

Q6. Firm 1 supplies zero for p < 10 and p − 10 for p ≥ 10. Firm 2 supplies zero for p < 15 and p − 15 for p ≥ 15, where p is market price. Derive their market supply in the three price ranges. [3 marks]

1. For a price below 10, both firms supply zero. Adding their quantities gives market supply of zero throughout this price range.
2. For a price of at least 10 but below 15, firm 2 supplies zero. Market supply therefore equals firm 1's supply, p − 10.
3. For a price of at least 15, add both supply expressions. Market supply is (p − 10) + (p − 15) = 2p − 25.

Q7. Explain how a unit tax affects a firm's long-run costs and supply. Let t denote the tax per unit sold. [5 marks]

1. A unit tax is imposed per unit sale of output. Selling each unit therefore requires the firm to make an additional payment of t.
2. Long-run average cost at each output increases by t because the tax adds the same amount to cost per unit sold.
3. Long-run marginal cost also increases by t because producing and selling an additional unit adds that tax to the extra cost.
4. The firm's long-run supply uses the rising marginal cost segment from minimum long-run average cost, with zero output below the threshold price.
5. The changed cost curves shift the firm's long-run supply curve to the left. At a given market price, the firm supplies fewer units.

Q8. A firm sells each unit at Rs 10. For output levels 0, 1, 2, 3, 4 and 5, its total costs are respectively Rs 5, 15, 22, 27, 31 and 38. Calculate profit at each of these six output levels. [6 marks]

1. At zero output, revenue is Rs 10 × 0 = Rs 0. Deducting total cost of Rs 5 gives profit of −Rs 5.
2. At one unit, revenue is Rs 10 × 1 = Rs 10. Deducting total cost of Rs 15 gives profit of −Rs 5.
3. At two units, revenue is Rs 10 × 2 = Rs 20. Deducting total cost of Rs 22 gives profit of −Rs 2.
4. At three units, revenue is Rs 10 × 3 = Rs 30. Deducting total cost of Rs 27 gives profit of Rs 3.
5. At four units, revenue is Rs 10 × 4 = Rs 40. Deducting total cost of Rs 31 gives profit of Rs 9.
6. At five units, revenue is Rs 10 × 5 = Rs 50. Deducting total cost of Rs 38 gives profit of Rs 12.

Key takeaways

• Perfect competition combines many buyers and sellers, homogeneous products, free entry and exit, and perfect information.
• A price-taking firm's average and marginal revenue equal market price, while total revenue equals price multiplied by output.
• Profit-maximising positive output requires price to equal non-decreasing marginal cost and satisfy the relevant cost coverage condition.
• Short-run supply follows rising marginal cost from minimum average variable cost, with zero output below that price.
• Long-run supply follows rising marginal cost from minimum long-run average cost, with zero output below that price.
• Normal profit is included in total cost; break-even occurs where the firm earns only normal profit.
• Technological progress is expected to shift supply rightwards; an input-price increase is expected to shift it leftwards.
• Market supply adds individual quantities at a common price; supply elasticity compares percentage quantity and price changes.

Test yourself

Why does the competitive firm's total revenue curve pass through the origin?

At zero output, nothing is sold, so price multiplied by quantity gives zero total revenue.

What does the horizontal price line represent for a competitive firm?

It represents the fixed market price, average revenue and the perfectly elastic demand curve facing that firm.

Why is price equal to marginal cost insufficient by itself?

Marginal cost must also be non-decreasing, and price must cover the relevant average cost at the chosen output.

What loss remains at zero output in the short run?

The loss equals total fixed cost because total revenue and total variable cost are both zero.

What distinguishes normal profit from super-normal profit?

Normal profit keeps the firm in its existing business and enters total cost. Super-normal profit is the excess above normal profit.

How does an increase in the number of firms affect market supply?

It shifts market supply to the right because more firms contribute quantities at the given market prices.

What is price elasticity of supply for a vertical supply curve?

It is zero because quantity supplied is completely insensitive to changes in the market price.

Which straight supply line has elasticity equal to one?

A straight supply line passing through the origin has price elasticity equal to one at its positive-output points.