The Theory of the Firm under Perfect Competition Class 12 Notes Explained

Understanding Perfect Competition and the Firm

Perfect competition is a market structure characterized by:

• A large number of buyers and sellers
• Homogeneous (identical) products
• Free entry and exit of firms
• Perfect knowledge of prices and technology
• Firms are price takers, meaning they accept the market price without influence

In this market, the firm’s main goal is to maximise profit by deciding the quantity of output to produce. Since the product is identical across firms, no single firm can influence the market price. This makes the firm's demand curve perfectly elastic at the market price.

Key definitions:

• Total Revenue (TR): Price ($P$) × Quantity ($Q$)
• Marginal Revenue (MR): Change in TR from selling one more unit
• Average Revenue (AR): TR divided by $Q$, equal to price in perfect competition

The firm’s demand curve is also its AR and MR curve, a horizontal line at market price.

Profit Maximization: The Core Principle

The firm maximizes profit by producing the output level where Marginal Revenue (MR) equals Marginal Cost (MC):

$$ MR = MC $$

• If $MR > MC$, producing more increases profit
• If $MR < MC$, producing less increases profit

Profit is the difference between Total Revenue and Total Cost:

$$ \text{Profit} = TR - TC $$

• Total Cost (TC) includes fixed and variable costs

In perfect competition, since $MR = AR = P$, the profit maximization condition becomes:

$$ P = MC $$

This means the firm produces where the price equals marginal cost.

Example:

If the market price is ₹50 and the firm’s marginal cost at 100 units is ₹50, the firm should produce 100 units to maximize profit.

Short-Run Equilibrium of the Firm

In the short run, firms can make:

• Supernormal (abnormal) profits if price > average total cost (ATC)
• Normal profits if price = ATC
• Losses if price < ATC

The firm’s supply decision depends on the price relative to average variable cost (AVC):

• If $P extgreater AVC$, the firm produces where $P = MC$
• If $P extless AVC$, the firm shuts down to minimize losses

Graphically:

• The firm’s short-run supply curve is the portion of the MC curve above AVC

This means the firm covers its variable costs and contributes to fixed costs when operating.

Example:

If the market price is ₹40, AVC is ₹30, and MC at 80 units is ₹40, the firm produces 80 units. If price falls to ₹25 (below AVC), the firm shuts down.

Long-Run Equilibrium: Zero Economic Profit

In the long run, firms can enter or exit the industry freely. This leads to:

• Firms earning normal profits only (zero economic profit)
• Price equals minimum average total cost (ATC)
• No incentive for firms to enter or exit

The long-run equilibrium condition is:

$$ P = MC = ATC_{min} $$

Here, firms produce at the most efficient scale, minimizing costs.

Industry adjustment:

• If firms earn supernormal profits, new firms enter, increasing supply and lowering price
• If firms incur losses, some exit, reducing supply and raising price

Eventually, the market stabilizes at a price where firms earn normal profit.

Comparison Table: Short Run vs Long Run

Cost Curves and Their Role in Firm Decisions

Understanding cost curves is essential for analysing firm behaviour:

• Total Cost (TC): Sum of Fixed Cost (FC) and Variable Cost (VC)
• Average Total Cost (ATC): $ATC = \frac{TC}{Q}$
• Average Variable Cost (AVC): $AVC = \frac{VC}{Q}$
• Marginal Cost (MC): Change in TC when output changes by one unit

Key properties:

• MC curve cuts ATC and AVC curves at their minimum points
• MC curve is typically U-shaped due to increasing then decreasing marginal returns

Firms use these curves to decide output levels:

• Produce where $P = MC$ if $P extgreater AVC$
• Shut down if $P extless AVC$

Worked Example:

Suppose:

• At 50 units, TC = ₹2000
• At 51 units, TC = ₹2040

Calculate MC at 51 units:

$$ MC = TC_{51} - TC_{50} = 2040 - 2000 = ₹40 $$

Worked Example: Calculating Profit Maximizing Output

A firm in perfect competition faces a market price of ₹60 per unit. Its marginal cost (MC) at different output levels is:

Find the profit-maximizing output.

Solution:

• The firm produces where $P = MC$
• Price = ₹60
• MC equals ₹60 at 30 units

Therefore, the firm should produce 30 units to maximize profit.

Calculate profit:

If Average Total Cost (ATC) at 30 units is ₹55,

$$ TR = P \times Q = 60 \times 30 = ₹1800 $$

$$ TC = ATC \times Q = 55 \times 30 = ₹1650 $$

$$ Profit = TR - TC = 1800 - 1650 = ₹150 $$

The firm earns a supernormal profit of ₹150.