The Theory of the Firm under Perfect Competition

Perfect Competition: Defining Features

**Perfect competition** is a market structure where the firm's output decisions are analysed. A perfectly competitive market has four defining characteristics:

1. **Large number of buyers and sellers**: The market consists of many buyers and sellers, each individually small relative to the market size. No single participant can influence market price through their own actions.

2. **Homogeneous product**: All firms produce identical products. Buyers cannot differentiate between the product of one firm and another, so they are indifferent about which firm to purchase from.

3. **Free entry and exit**: New firms can easily enter the market, and existing firms can freely leave. There are no legal, technological, or financial barriers restricting entry or exit. This condition is essential for the existence of large numbers of firms.

4. **Perfect information**: All buyers and sellers have complete knowledge about prices, quality, and other relevant product details. No participant has information advantages over others.

**Price-taking behaviour** is the single most distinguishing characteristic that emerges from these four features:

**From a firm's perspective**: A price-taking firm believes that if it sets a price above the market price, it will sell zero units because buyers will purchase from competitors. If it sets a price at or below the market price, it can sell as many units as desired. Therefore, the firm has no incentive to price below the market price and will set its price exactly equal to the market price.

**From a buyer's perspective**: A price-taking buyer recognises that if they offer a price below the market price, no firm will sell to them. If they offer the market price or higher, they can purchase any quantity desired. Therefore, buyers will pay the market price.

**Why price-taking is reasonable under perfect competition**: When many firms produce identical goods and buyers have perfect information, any individual firm raising its price above market price loses all customers to competitors. Since many firms exist, this excess demand is easily accommodated elsewhere. The firm cannot sell any quantity at a supramarket price, confirming price-taking behaviour.

**Example**: The market for agricultural commodities like rice or wheat in India exhibits near-perfect competition features. Individual farmers are price-takers; they cannot influence the market price of wheat whether they grow 1 tonne or 100 tonnes.

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Revenue: Total Revenue, Average Revenue, and Marginal Revenue

**Total Revenue (TR)** is the amount a firm earns from selling its output. It is calculated as:

**TR = Price (p) × Quantity (q)**

For example, if a firm produces candles in a perfectly competitive market where the market price is Rs 10 per box, and the firm sells 5 boxes, then TR = 10 × 5 = Rs 50.

**The Total Revenue Curve** plots output on the x-axis and total revenue on the y-axis. Key observations about the TR curve under perfect competition:

The TR curve passes through the origin (when output = 0, TR = 0)

TR increases linearly with output because price (p) is constant

The slope of the TR curve equals the market price (p), which is the change in TR divided by change in output

The TR curve is an upward-sloping straight line

**Average Revenue (AR)** is total revenue per unit of output:

**AR = TR/q = (p × q)/q = p**

For a price-taking firm, average revenue always equals the market price. This is because the firm sells all units at the same market price.

**The Price Line** is the graphical representation of average revenue. It is a horizontal straight line at height p (the market price). This horizontal line is also the **demand curve facing the firm**, which is perfectly elastic. A perfectly elastic demand curve means the firm can sell any quantity at the given price, but zero quantity if it charges any price above the market price.

**Marginal Revenue (MR)** is the addition to total revenue from selling one additional unit of output:

**MR = Change in Total Revenue / Change in Quantity = ΔTR/Δq**

From the numerical example: when output increases from 2 to 3 boxes, TR increases from Rs 20 to Rs 30, so MR = (30 - 20)/(3 - 2) = Rs 10.

**Algebraically**, for a perfectly competitive firm:

**MR = (pq₂ - pq₁)/(q₂ - q₁) = p(q₂ - q₁)/(q₂ - q₁) = p**

**For a price-taking firm: MR = AR = p**

This means marginal revenue equals average revenue, which equals the market price. Intuitively, when a firm increases output by one unit, that extra unit is sold at the market price; therefore, the firm's revenue increase (MR) is precisely the market price.

**Key distinction**: The horizontal demand curve (price line) representing perfect elastic demand is unique to perfectly competitive firms. The firm is a price-taker, not a price-maker.

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Profit Maximisation: Conditions and Principles

**Profit (π)** is defined as the difference between total revenue and total cost:

**π = TR - TC**

A firm aims to identify the quantity q₀ at which profit is maximum. For profit to be at its maximum, **three conditions must hold simultaneously**:

**Condition 1: MR = MC**

Profit increases as long as the additional revenue from selling one more unit (MR) exceeds the additional cost of producing that unit (MC). Conversely, profit decreases when MR < MC.

**Logic**:

When MR > MC: producing one more unit adds more to revenue than to cost, so profit increases

When MR = MC: producing one more unit adds equally to revenue and cost, so profit is at maximum

When MR < MC: producing one more unit adds more to cost than to revenue, so profit decreases

For a perfectly competitive firm where MR = p, this condition becomes: **p = MC**

The firm's profit-maximising output is where price equals marginal cost (on the rising portion of the MC curve).

**Graphically**: The intersection point of the horizontal price line and the upward-sloping marginal cost curve determines the profit-maximising quantity.

**Condition 2: MC Must Be Non-Decreasing (Rising)**

At the profit-maximising output level, the marginal cost curve must be upward sloping, not downward sloping.

**Why this is necessary**: Suppose at output q₁, price equals MC, but MC is still declining (downward sloping). At output levels slightly less than q₁, price exceeds MC, meaning MR > MC and profit is still increasing. Therefore, q₁ cannot be the maximum profit point. The firm should continue producing beyond q₁.

Only when MC is rising can we be certain that profit is indeed at its maximum when MR = MC.

**In practice**: This condition rules out the left (declining) portion of the MC curve as a valid profit-maximising point.

**Condition 3: Price Must Exceed Minimum Average Variable Cost (Short Run) or Average Cost (Long Run)**

**Short-Run Case: p ≥ AVC (minimum)**

If the market price falls below the average variable cost at the profit-maximising output, the firm should shut down and produce zero output.

**Why**: Suppose price p < AVC at output q₁.

Total Revenue at q₁: TR = p × q₁ (area of rectangle OpAq₁)

Total Variable Cost at q₁: TVC = AVC × q₁ (area of rectangle OEBq₁)

Since p < AVC, the area OpAq₁ < area OEBq₁

The firm's profit at q₁ = TR - TVC - TFC = negative amount (loss greater than fixed cost)

By shutting down (q = 0), the firm's profit = -TFC (loss equals fixed cost only)

Since -TFC > -TFC - (loss from operations), the firm prefers to shut down.

**Short-Run Shut-Down Point**: The minimum AVC represents the shut-down price. Below this price, the firm exits the market in the short run.

**Long-Run Case: p ≥ AC (minimum)**

In the long run, the firm must cover all costs (fixed and variable). If price falls below average cost, the firm incurs a loss and will exit the market permanently.

Total Revenue at q₁: TR = p × q₁

Total Cost at q₁: TC = AC × q₁

If p < AC, then TR < TC, the firm operates at a loss

By shutting down, the firm's profit = 0 (in long run, no fixed costs if not operating)

Since 0 > negative profit, the firm chooses to exit.

**Long-Run Exit Point**: The minimum long-run average cost represents the exit price.

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Profit Maximisation: Graphical Representation (Short Run)

Consider a perfectly competitive firm facing market price p:

**Steps to identify profit-maximising output:**

1. Locate the horizontal price line at height p (this is both the demand curve and AR curve)

2. Identify where this price line intersects the upward-sloping short-run marginal cost (SMC) curve; this intersection point determines the profit-maximising output q₀

3. Verify that at q₀, the SMC curve is rising (Condition 2 satisfied)

4. Verify that p > AVC at q₀ (Condition 3 satisfied)

**Profit calculation at q₀**:

Total Revenue: TR = p × q₀ = area of rectangle OpAq₀ (height = p, width = q₀)

Total Cost: TC = AC × q₀ = area of rectangle OEBq₀ (height = AC at q₀, width = q₀)

**Profit = TR - TC = area of rectangle EpAB** (the shaded area between the price line and the AC curve)

When p > AC at q₀, the rectangle EpAB is above the x-axis, representing **supernormal profit** (economic profit).

When p = AC at q₀, the rectangles have equal area, so profit = 0, representing **normal profit** (break-even).

When p < AC but p > AVC at q₀, the firm incurs a loss but continues operating short-run because it covers variable costs and some fixed costs.

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Supply Curve of a Firm: Short Run

A **supply curve** shows the quantity a firm chooses to produce at different market prices, holding technology and factor prices constant.

**Short-Run Supply Curve Derivation**:

The derivation considers two cases based on the relationship between price and minimum average variable cost (AVC_min):

**Case 1: p ≥ AVC_min**

When the market price is high enough to cover average variable costs:

Apply the profit-maximising rule: set output where p = SMC (on the rising portion)

All three conditions are satisfied

The firm produces positive output

As price increases from p₁ to a higher level, the intersection point with the SMC curve shifts rightward, and the firm produces more output

The firm traces out the upward-sloping SMC curve

**Example**: If market price increases from Rs 10 to Rs 15 per unit, and each price level intersects the SMC curve at different quantities, the firm supplies more at the higher price.

**Case 2: p < AVC_min**

When the market price falls below the minimum average variable cost:

Even though MR = MC condition might be satisfied at some output level, Condition 3 is violated

The firm cannot cover its variable costs

The firm shuts down and produces zero output

No production occurs at any price below AVC_min

**Short-Run Supply Curve Conclusion**:

**The firm's short-run supply curve is the upward-sloping portion of the short-run marginal cost curve above and including the point of minimum average variable cost. For all prices below minimum AVC, the firm supplies zero output.**

**Graphically**: The short-run supply curve is:

The rising SMC curve from the point where it intersects minimum AVC and above

A vertical drop to zero output at all prices below AVC_min

The bold/highlighted portion of the SMC curve above minimum AVC represents the actual supply curve

**Key Point**: The short-run supply curve is uniquely determined by the marginal cost curve and the shut-down point (minimum AVC).

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Supply Curve of a Firm: Long Run

The **long-run supply curve** is derived by similar logic but with different conditions:

**Long-Run Supply Curve Derivation**:

In the long run, the firm can adjust all factors of production and has no fixed costs. The analysis proceeds by cases:

**Case 1: p ≥ LRAC_min**

When price exceeds or equals the minimum long-run average cost:

Apply profit maximisation: set output where p = LRMC (on the rising portion)

The firm can cover all costs and earn normal profit (at p = LRAC_min) or supernormal profit (at p > LRAC_min)

The firm produces positive output

As price increases, the intersection point with the LRMC curve shifts rightward, and output increases

**Case 2: p < LRAC_min**

When price falls below the minimum long-run average cost:

The firm cannot cover its total costs

The firm incurs losses in the long run

In the long run, there are no fixed costs to cover; all costs are variable

The firm exits the market completely

The firm supplies zero output

**Long-Run Supply Curve Conclusion**:

**The firm's long-run supply curve is the upward-sloping portion of the long-run marginal cost curve above and including the point of minimum long-run average cost. For all prices below minimum LRAC, the firm supplies zero output.**

**Key Distinction from Short Run**:

Short-run supply curve: relevant from minimum AVC upward

Long-run supply curve: relevant from minimum LRAC upward

Minimum LRAC > minimum AVC (always), so the long-run supply curve starts at a higher price point

Long-run supply curve is typically flatter (more elastic) than short-run supply curve because the firm has more flexibility to adjust all factors

**Example**: An Indian textile manufacturer's long-run supply curve would reflect prices where it can cover all costs including capacity investment. Below this price, the manufacturer exits the industry entirely.

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Key Exam-Important Points

**Price-taking behaviour** is the fundamental characteristic of perfect competition; firms are price-takers, not price-makers

**MR = AR = p** for perfectly competitive firms (horizontal demand curve)

**Three conditions for profit maximisation**: (1) MR = MC, (2) MC rising, (3) p ≥ min AVC (short run) or p ≥ min LRAC (long run)

**Profit is visually represented** as the area between price line and AC curve

**Shut-down point**: minimum AVC in short run; minimum LRAC in long run

**Supply curve = SMC curve above minimum AVC (short run) or LRMC curve above minimum LRAC (long run)**

Firms produce zero output if price falls below the relevant minimum cost level