Behaviour of a Firm in a Perfectly Competitive Market

Firm Objectives and Profit Maximization

A firm’s primary goal is profit maximization – the difference between what it earns from selling output and what it spends on inputs. This assumption holds because even non‑profit or impact‑driven firms must eventually generate positive profits to remain financially sustainable.

$\text{Profit} = \text{Total Revenue} - \text{Total Cost}$

• Total Revenue (TR) = amount received from selling output – For a single price: $TR = P \times Q$ – If different batches are sold at different prices, sum over each batch: $TR = \sum (P_i \times Q_i)$

• Total Cost (TC) = market value of all inputs used, including opportunity costs.

Total Revenue and Total Cost – Example (Nidhi’s Samosa Shop)

On Tuesday the additional revenue from selling 500 extra samosas at ₹40 each was ₹20,000.

Costs for Monday: raw materials, labour, rent, electricity = ₹20,000 (explicit). But Nidhi also forgoes a daily wage of ₹10,000 as a computer programmer – this is an opportunity cost. Her ₹5,00,000 capital invested at 8% p.a. gives up ₹40,000 annual interest – another opportunity cost.

Explicit vs. Implicit Costs, Accounting vs. Economic Profit

• Explicit costs – direct monetary outlays (e.g., wages, rent, raw materials).
• Implicit costs – opportunity costs of using owner‑supplied resources (e.g., forgone salary, forgone interest).

$\text{Economic cost} = \text{Explicit costs} + \text{Implicit costs}$

$\text{Accounting profit} = TR - \text{Explicit costs only}$

$\text{Economic profit} = TR - \text{Economic cost}$

• Because economic cost always ≥ accounting cost, economic profit ≤ accounting profit.
• When economic profit is positive, the firm is covering all costs and rewarding owners. Negative economic profit (loss) means the firm fails to cover its full costs.

Exam tip: A question may ask you to distinguish accounting vs. economic profit. The key is whether implicit opportunity costs are included. For simplicity in later modules, opportunity costs are often assumed zero, making the two profits equal.

Production Function and Marginal Product

Production function = relationship between quantity of inputs (labour, capital) and maximum output attainable, holding other inputs fixed.

Example: Nidhi’s kitchen size is fixed (short run). Only the number of workers can vary.

Marginal product of an input $=$ change in output resulting from a one‑unit change in that input:

$MP_L = \frac{\Delta Q}{\Delta L}$

• From 0→1 workers: $MP = 50$
• From 1→2 workers: $MP = 90 - 50 = 40$
• etc.

Diminishing Marginal Product

As more workers join a fixed‑sized kitchen, each additional worker adds less to output – the diminishing marginal product:

• Reason: Crowding limits access to equipment and raw materials; greater coordination cost reduces individual productivity.
• Despite falling MP, total output still rises with each extra worker (output increases, but at a decreasing rate).

Graphically, the production function becomes flatter as L increases – slope = $MP_L$ decreases.

Total Cost Curve and Its Shape

Nidhi’s costs:

• Fixed cost: kitchen rent = ₹3000/hour (independent of output).
• Variable cost: wage = ₹1000 per worker per hour.
• $TC = FC + VC$

• The total cost curve (TC vs. Q) slopes upward and becomes steeper as output rises.
• Reason: Because of diminishing MP, each extra samosa requires hiring more workers than the previous one, so the additional cost (marginal cost) increases.

Worked example – rising marginal cost:

• First 50 samosas: cost increase = ₹1000 (from 3000 to 4000) → ₹20 per samosa.
• Next 40 samosas (50→90): cost increase = ₹1000 → ₹25 per samosa.
• Next 30 samosas (90→120): cost increase = ₹1000 → ₹33.3 per samosa.

Thus the cost curve gets steeper as Q rises – a direct consequence of diminishing marginal product.

Key takeaways

• A firm maximizes profit = total revenue – total cost (including opportunity cost).
• Economic profit is smaller than accounting profit because it subtracts implicit costs.
• Production function maps inputs to output; marginal product measures output change from one more unit of input.
• Most production processes exhibit diminishing marginal product – the production function flattens.
• Diminishing marginal product makes the total cost curve steeper as output increases, because additional units cost more to produce.

Variable, Fixed, and Sunk Costs

Not all costs behave the same. Some rise with every extra unit you produce; others stay fixed no matter how much you make. And some are gone the moment you pay them — they can never be recovered by a production decision. Understanding these categories is essential for calculating profit and choosing the right output level.

The three cost types

A firm’s explicit costs can be divided into three categories based on how they respond to the quantity of output $Q$.

Key insight: Fixed costs are unavoidable at any positive output, but they are still part of the total cost that affects profit. Sunk costs, by contrast, are irrelevant for any future production decision — they can never be undone, so they are excluded from the profit calculation.

How to classify a cost input

The flowchart below gives a decision rule for sorting any input cost:

• Sunk cost: The cost is already paid and cannot be retrieved — e.g., R&D, permit fees.
• Variable cost: The cost can be avoided by setting $Q = 0$, and it grows as output rises — e.g., raw materials, hourly labour.
• Fixed cost: The cost can also be avoided only by shutting down, but once the firm operates, it does not depend on the output level — e.g., monthly rent, salary of permanent staff.

Worked example: Arnav’s petrol pump

Arnav has already spent ₹10 lakh on a license and setup (sunk). He must decide whether to operate the pump next month.

Data for one month:

• Expected sales: 1 00 000 litres at ₹102/litre → Total revenue = ₹1 02 00 000
• Explicit costs:
  • Purchase of petrol: 1 00 000 litres × ₹100 = ₹1 00 00 000
  • Monthly wage: ₹40 000
  • Electricity: ₹30 000
  • Transportation: ₹80 000
• Implicit opportunity cost: ₹30 000 (return from investing the money elsewhere)

Calculation of total cost (excluding sunk cost):

$$\begin{aligned} \text{Total explicit cost} &= 1\,00\,00\,000 + 40\,000 + 30\,000 + 80\,000 = 1\,01\,50\,000 \\ \text{Total cost (including opportunity cost)} &= 1\,01\,50\,000 + 30\,000 = 1\,01\,80\,000 \end{aligned}$$

Profit:

$$\text{Profit} = \text{Revenue} - \text{Total cost} = 1\,02\,00\,000 - 1\,01\,80\,000 = ₹20\,000 > 0$$

Since profit is positive, Arnav should operate the pump. Notice the sunk ₹10 lakh was not included in total cost — it cannot affect the decision.

Exam tip: Fixed costs (like wages) are included because they must still be paid; sunk costs (like the license) are never added to total cost for an operating decision. A common trap is to include a sunk cost and wrongly conclude that the project is unprofitable.

Which cost dominates in different industries?

Key takeaways

• Variable costs change with output; fixed costs do not change with output but can be avoided only by shutting down; sunk costs cannot be recovered and are irrelevant for future decisions.
• Fixed costs are part of total cost and therefore affect profit; sunk costs are excluded from total cost.
• Use the “avoidable when Q = 0?” test to classify: unavoidable → sunk; avoidable and varies with Q → variable; avoidable and does not vary with Q → fixed.
• Always include implicit opportunity costs when calculating economic profit.
• The dominance of one cost category varies across industries (variable→PC, sunk→software, fixed→pizza).

Short Run vs. Long Run: Fixed and Variable Costs

The classification of a cost as fixed or variable depends on the time horizon available to adjust inputs.

Intuition: With more time, a firm can change more inputs. What is “fixed” in one week can become “variable” in a year.

The Ola Example

Ola Future Factory wants to increase daily scooter production from 1,000 to 3,000.

• Short run: a time horizon where at least one input’s quantity cannot be changed. → Fixed inputs → Fixed costs (e.g., rent on assembly lines).
• Long run: a time horizon where all inputs can be changed. → All costs are variable.

What counts as “short run” varies by industry (e.g., a scooter factory vs. a food truck).

Short Run Total Cost

In the short run, total cost is the sum of fixed cost and variable cost:

$TC = FC + VC$

Coffee Shop Example (all numbers are illustrative)

A boutique coffee shop has hourly fixed cost (rent) of ₹50.

Average Total Cost (ATC)

Average total cost measures the cost per unit of output:

$ATC = \frac{TC}{Q}$

The ATC curve is U‑shaped: initially falling as fixed costs are spread, then rising due to diminishing returns.

From the coffee shop data:

Average Fixed Cost (AFC)

Average fixed cost is the fixed cost per unit of output:

$AFC = \frac{FC}{Q}$

• AFC is downward sloping (decreases as output increases) because the same fixed cost is spread over more units.
• For the coffee shop: $AFC = \frac{50}{Q}$.

Exam tip: The U‑shape of ATC comes from two opposing forces: falling AFC (spreading fixed costs) and eventually rising average variable cost (diminishing returns). AFC always declines with output.

Key takeaways

• Fixed vs. variable classification depends on time horizon (short run vs. long run).
• Short run: $TC = FC + VC$ with positive fixed costs.
• $ATC = TC/Q$; the curve is U‑shaped.
• $AFC = FC/Q$; the curve slopes downward because fixed cost is spread over more output.
• In the long run all costs are variable (no fixed costs).

Average Variable Cost (AVC)

Average variable cost is variable cost per unit of output. Intuitively, it measures how much of the variable input cost is “spread” over each unit produced.

$\text{AVC} = \frac{\text{Variable cost}}{\text{Quantity}} = \frac{VC}{Q}$

From the coffee‑shop example, the variable cost at each output level is divided by output:

Plotted, the AVC curve first falls, then rises – a typical U‑shape driven by diminishing marginal product (see below).

Key points

• AVC is part of average total cost: $\text{ATC} = \text{AFC} + \text{AVC}$.
• At low output, AVC may decrease (specialization gains); at high output, it increases because each extra unit requires more inputs due to diminishing returns.

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Marginal Cost (MC)

Marginal cost is the cost of producing one additional unit of output. It tells the firm how much total cost changes when output expands by a tiny amount.

$\text{MC}(q+1) = TC(q+1) - TC(q)$

Using the same coffee shop (fixed cost = ₹50, so $TC(0)=50$):

The MC curve typically declines initially (due to increasing marginal returns) then rises, reflecting diminishing marginal product. As more variable input is added to a fixed input, extra output per additional input falls → producing one more unit requires more inputs → marginal cost rises.

Exam tip: The rising part of the MC curve is the supply curve of a perfectly competitive firm in the short run (above the shutdown point).

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Relationship Between MC and ATC

When the marginal cost curve and the average total cost curve are drawn together, three universal observations hold for most firms:

1. If $\text{MC} < \text{ATC}$, then ATC is falling.
2. If $\text{MC} > \text{ATC}$, then ATC is rising.
3. MC crosses ATC at ATC’s minimum – the efficient scale.

Intuition: ATC is an average; when the next unit costs less than the average, the average falls; when it costs more, the average rises. Therefore the crossing point must be where ATC is neither falling nor rising – the minimum.

In the coffee‑shop example, ATC is minimised at an output of 8 cups per hour – the efficient scale. Below that, high average fixed cost dominates; above that, rising average variable cost dominates.

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Long-Run Average Total Cost

In the short run, at least one input is fixed (e.g., factory size). In the long run, all inputs become variable – the firm can choose any scale of operation.

Because the firm has more freedom in the long run, it can always produce any given output at a cost no higher than in the short run. Hence the long-run average total cost curve (LRATC) lies below the short‑run average total cost curves (SRATC) at every level of output.

Each SRATC corresponds to a different level of the fixed input (e.g., a specific plant size). The LRATC is the envelope of all possible SRATC curves – it shows the lowest possible cost for each output when the firm can choose the optimal plant size.

The LRATC is also typically U‑shaped (economies of scale at low output, diseconomies at high output), but it is flatter than any individual SRATC.

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Key Takeaways

• AVC = $VC/Q$; first falls, then rises.
• MC = change in TC for one more unit; rises due to diminishing marginal product.
• MC‑ATC relationship: MC below ATC → ATC falls; MC above ATC → rises; MC crosses at ATC’s minimum (efficient scale).
• Long‑run costs: more flexibility → LRATC lies below all SRATC curves.
• Fixed vs. variable input distinction depends on the time horizon; in the long run all costs are variable.

Marginal Principle

A profit-maximizing firm in a perfectly competitive market faces three decisions:

1. What quantity to produce at the given market price?
2. When to temporarily shut down production?
3. When to exit the industry entirely?

All three are answered using marginal analysis — comparing the benefit of one more unit (marginal revenue) to its cost (marginal cost).

The Firm in a Perfectly Competitive Market

A perfectly competitive market has two defining features:

• Many buyers and many sellers — no single participant can influence price.
• Homogeneous goods — products are identical across sellers.

These features force every firm to sell at the equilibrium price determined by market supply and demand. If a firm charges above the equilibrium, buyers switch to others selling the identical good at the lower price. If a buyer offers below equilibrium, sellers refuse because many other buyers will pay the higher price.

Example: A small cattle farmer sells milk. Milk is identical across farmers, and there are many producers. The farmer must accept the prevailing market price — say ₹50 per litre.

Revenue in Perfect Competition

For a firm in perfect competition:

• Total revenue $TR = P \times Q$, where $P$ is fixed.
• Average revenue $AR = \frac{TR}{Q} = P$ — constant at all output levels.
• Marginal revenue $MR = \frac{\Delta TR}{\Delta Q} = P$ — constant at all output levels.

Thus for the cattle farmer at $P = \text{Rs. }50$:

$AR = MR = P$ holds for any price-taking firm.

Profit-Maximizing Quantity: Total Profit Method

Profit = $TR - TC$. The firm should produce the quantity that gives the highest profit.

Using the cattle farmer’s data at $P = \text{Rs. }50$:

Profit-maximizing quantity = 8 litres → maximum profit = ₹30.

Exam tip: The total profit method is straightforward but inefficient for large output ranges. The marginal principle gives the same answer faster.

Profit-Maximizing Quantity: Marginal Principle Method

The marginal principle (first seen in Module 1):

• If $MB > MC$, doing more of the activity increases net benefit.
• If $MB < MC$, doing more decreases net benefit.

Apply to the firm:

• Marginal benefit = marginal revenue ($MR = P$).
• Marginal cost ($MC$) is the cost of producing one extra unit.
• If $MR > MC$, producing another unit raises profit.
• If $MR < MC$, producing another unit lowers profit.

For the cattle farmer ($P = MR = \text{Rs. }50$):

Profit increases from Q=1 to Q=8, reaches maximum at Q=8, then falls. The profit-maximizing quantity is the largest quantity where $MR \geq MC$ — here, Q=8.

Because $MR = P$ in perfect competition, the rule simplifies:

Profit-maximizing quantity = largest $Q$ such that $P \geq MC$.

If the farmer produces fewer than 8 litres, $P > MC$ — he leaves potential profit on the table. If he produces more than 8 litres, $P < MC$ — each extra unit reduces profit.

Graphical Summary

The profit curve rises as long as $MR > MC$, peaks where $MR = MC$ (or last unit where $MR \geq MC$), and declines thereafter.

Key takeaways

• In perfect competition, $AR = MR = P$ — constant at the market price.
• Profit-maximizing quantity is found either by comparing total profit across outputs or by applying the marginal principle.
• The marginal principle rule: produce the largest quantity where $P \geq MC$.
• If $P > MC$, producing more raises profit; if $P < MC$, producing more lowers profit.
• The cattle farmer example: at $P=\text{Rs. }50$, profit max at Q=8, profit = ₹30.

Revenue in perfect competition

A firm in a perfectly competitive market is a price taker – it cannot influence the market price by changing its output. Therefore, for any quantity $Q$:

• Total revenue (TR) = $P \times Q$
• Average revenue (AR) = $\frac{TR}{Q} = P$
• Marginal revenue (MR) = $\frac{\Delta TR}{\Delta Q} = P$ (each additional unit sold adds exactly the price)

Thus AR = MR = P. Graphically, the revenue curves collapse into a single horizontal line at the market price $P$.

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Cost curves – shape and key intersections

The three central cost curves for a firm are:

• Average total cost (ATC) – U‑shaped (economies then diseconomies of scale)
• Average variable cost (AVC) – U‑shaped, lies below ATC because $ATC = AVC + AFC$ (average fixed cost is positive)
• Marginal cost (MC) – increasing due to diminishing marginal product

Critical property: The MC curve intersects both ATC and AVC at their respective minimum points.

MC cuts ATC at min ATC
MC cuts AVC at min AVC

Exam tip: The order of the curves from bottom to top is always AVC, then ATC, then MC in its rising portion (except near the vertical axis). Remember: AVC is lower because it excludes fixed cost.

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Profit‑maximising quantity (marginal principle)

The firm chooses the largest quantity $Q^*$ such that $P \ge MC$ (marginal revenue = marginal cost). Because in perfect competition $P = MR$, the condition simplifies to:

$P = MC$

Why it works:

• If $Q < Q^*$: $P > MC$ → increasing output raises profit.
• If $Q > Q^*$: $P < MC$ → decreasing output raises profit.
• At $Q = Q^*$: $P = MC$ → profit is maximised.

The supply curve of the firm is therefore its marginal cost curve – as price rises, the profit-maximising quantity moves up along the MC curve.

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Picturing profit – revenue and cost rectangles

With the cost curves and the price line $P_0$, profit can be visualised as the difference of two rectangles:

• Total revenue = $P_0 \times Q_0$ → green rectangle (height $P_0$, width $Q_0$)
• Total cost = $ATC(Q_0) \times Q_0$ → red rectangle (height $ATC$, width $Q_0$)
• Profit = $(P_0 - ATC(Q_0)) \times Q_0$ → striped rectangle

$$\pi = Q \cdot (P - ATC)$$

Worked example:

• Price $P_1$ above min ATC → green rectangle larger than red rectangle → positive profit.
• Price $P_2$ below min ATC but above min AVC → green rectangle smaller than red rectangle → loss, but firm may still operate in short run (see below).

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Short‑run shutdown decision (temporary)

In the short run, fixed costs are sunk – they must be paid regardless of production. The firm compares total revenue with total variable cost:

$\text{Shut down temporarily if } TR < TVC$

Dividing by $Q$ gives the shutdown rule:

$\boxed{P < AVC}$

• If $P > AVC$: operate even if making losses, because revenue covers variable costs and partly recovers fixed costs.
• If $P < AVC$: shut down immediately; producing adds loss beyond sunk fixed costs.

Graphically: The short‑run supply curve is the portion of the MC curve lying above the AVC curve. For any price below the minimum AVC, quantity supplied = 0.

Exam tip: A firm can be making losses but still operate in the short run – as long as price covers average variable cost. The shutdown point is the minimum AVC, not the minimum ATC.

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Long‑run exit decision (permanent)

In the long run, all costs are variable – no sunk costs. The firm can sell off assets and avoid fixed costs entirely. The decision rule becomes:

$\text{Exit if } TR < TC$

Dividing by $Q$:

$\boxed{P < ATC}$

• If $P > ATC$: enter the industry (positive profits).
• If $P < ATC$: exit (losses cannot be recovered).

The long‑run supply curve of the firm is the portion of the MC curve above the ATC curve.

Intuition: In the short run, the firm has already paid fixed costs – it will tolerate losses as long as the price covers variable costs, because shutting down entirely would waste the fixed cost recovery. In the long run, it avoids fixed costs altogether and will only stay if the price covers all costs.

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Summary of supply curves

• Short‑run supply: MC curve above $AVC$ (the part where $P \ge AVC$)
• Long‑run supply: MC curve above $ATC$ (the part where $P \ge ATC$)

The firm’s profit‑maximising behaviour is fully captured by these two supply curves.

Key takeaways

• In perfect competition, $P = MR = AR$; revenue curves are a horizontal line.
• Profit‑maximising quantity: $P = MC$. This defines the firm’s supply curve.
• Profit = $Q \cdot (P - ATC)$. Positive only if $P > \min ATC$.
• Short‑run shutdown rule: $P < AVC$ → stop production; otherwise operate even with losses.
• Long‑run exit rule: $P < ATC$ → leave the industry.
• The short‑run supply curve is the MC above AVC; the long‑run supply curve is the MC above ATC.

Practice Problem: Perfect Competition with Identical Firms

Given – a market with 9 identical firms, each with cost structure:

• Total cost: $TC = 50 + \frac{1}{2}Q^2$
• Marginal cost: $MC = Q$
• Market demand: $Q_d = 120 - P$

1. Fixed Cost, Variable Cost, ATC, AVC

• Fixed cost = 50 (independent of output).
• Variable cost = $\frac{1}{2}Q^2$.
• Average total cost: $ATC = \frac{TC}{Q} = \frac{50}{Q} + \frac{1}{2}Q$
• Average variable cost: $AVC = \frac{VC}{Q} = \frac{1}{2}Q$

2. Cost Curves for $Q \in [5,15]$

• ATC is U‑shaped, decreasing from $Q=5$ to $Q=10$, then rising.
• AVC rises linearly from 0 (at $Q=0$) – it is an increasing curve.
• MC = $Q$ is a 45° line through the origin.

3. Minimum of ATC

• Graphically: MC intersects ATC at its minimum.
• Mathematically: set $ATC = MC$ $\frac{50}{Q} + \frac{1}{2}Q = Q \quad\Rightarrow\quad \frac{50}{Q} = \frac{1}{2}Q \quad\Rightarrow\quad Q^2 = 100 \quad\Rightarrow\quad Q = 10$
• At $Q=10$: $MC = 10$, $ATC = 10$.

  Exam tip: The condition $MC = ATC$ always locates the minimum of the average total cost curve.

4. Minimum of AVC

• $AVC = \frac{1}{2}Q$ is increasing for $Q>0$; its minimum occurs at $Q=0$.
• Set $AVC = MC$: $\frac{1}{2}Q = Q \Rightarrow Q=0$.
• At $Q=0$: $AVC = 0$, $MC = 0$.

5. Short‑Run Supply Curves

Individual firm supply: the portion of MC above the minimum AVC. Since $MC = Q > \frac{1}{2}Q = AVC$ for all $Q>0$, the entire MC curve (from $Q=0$ upward) is the supply curve.

• Inverse supply: $P = Q$
• Supply equation: $q_i(P) = P$ (each firm supplies its marginal cost price).

Market supply with 9 firms: $Q_s(P) = 9 \times q_i(P) = 9P$

6. Short‑Run Equilibrium

Set quantity demanded equal to quantity supplied: $120 - P = 9P \quad\Rightarrow\quad 10P = 120 \quad\Rightarrow\quad P^* = 12$ $Q^* = 120 - 12 = 108 \quad (\text{or } 9 \times 12)$

Each firm’s output: $q_i = 108 / 9 = 12$ (consistent with $q_i = P = 12$).

Profit per firm: $\pi = P \cdot q_i - TC(12) = 12 \times 12 - \left(50 + \frac{1}{2} \times 144\right) = 144 - (50 + 72) = 22$

• Positive profits → firms outside have incentive to enter in the long run.

7. Long‑Run Equilibrium

In long‑run perfect competition, entry drives economic profit to zero. Zero‑profit condition: $P = \text{min } ATC$.

From earlier: min ATC = 10 at $Q=10$. Hence long‑run price $P^* = 10$.

Market demand at this price: $Q_d = 120 - 10 = 110$

Each firm produces at its efficient scale: $q_i = 10$ (because $P=10$ and supply $q_i=P$ gives $q_i=10$).

Number of firms: $N = \frac{Q_d}{q_i} = \frac{110}{10} = 11$

• Check zero profit: $P = 10$, $ATC = 10$, so $\pi = (10-10) \times 10 = 0$.

Key Takeaways

• Short‑run supply for a firm = MC above AVC; here $q_i = P$.
• Short‑run equilibrium found by $Q_d = Q_s$; positive profits trigger entry.
• Long‑run equilibrium occurs when $P = \min ATC$ and each firm earns zero profit.
• Fixed cost shifts ATC but does not affect short‑run supply (only AVC matters for shutdown).
• Given cost and demand, the long‑run number of firms is $N = \frac{\text{market demand at min ATC}}{\text{efficient scale}}$ (here 11 firms).

Exam tip: In long‑run perfect competition, always start by finding the minimum of ATC – that gives the long‑run price and efficient scale.