Chapter Notes - The Theory of the Firm under Perfect Competition

Table of Contents
1. Introduction
2. Perfect Competition: Defining Features
3. Revenue
4. Profit Maximisation
5. Supply Curve of a Firm
6. Determinants of the Firm's Supply Curve
7. Market Supply Curve
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Introduction

Perfect competition is a market form in which many buyers and many sellers trade a homogeneous product so that no single buyer or seller can influence the market price. In this market every economic agent is a price-taker; they accept the market price determined by overall demand and supply. Perfect competition is a useful theoretical benchmark in economics because it illustrates how markets allocate resources under ideal conditions and provides a standard for comparing other market structures.

Perfect Competition: Defining Features

A market is a place or system where buyers and sellers interact to exchange goods and services at agreed-upon prices. A perfectly competitive market is a type of market where many buyers and sellers come together to trade a single, identical product. No one-whether a buyer or a seller-has the power to control the price. 

Let's understand the key features that make this market "perfectly competitive":

1. Many Buyers and Sellers: There are a large number of buyers and sellers in the market. Each one is very small compared to the whole market. So, no single buyer or seller can influence the price.

2. Homogeneous Product (Identical Product): Every seller sells the exact same product. For example, if two farmers are selling wheat, there's no way to tell the difference between their wheat. This means buyers can buy from any seller and still get the same product.

3. Free Entry and Exit: Firms (sellers) are free to join or leave the market at any time.

• If making profits, new firms can enter easily.
• If facing losses, firms can exit without restrictions.
• This keeps the number of sellers balanced over time.

4. Perfect Information: Everyone in the market-both buyers and sellers-has complete knowledge about prices being charged, quality of the product and other important details. This helps buyers make smart choices and stops sellers from charging unfair prices.

What is Price-Taking?

The most important feature of perfect competition is price-taking.

For Sellers: A firm (seller) cannot choose its own price.

• If it tries to charge more than the market price, buyers will go to other sellers.
• If it charges the same or less, it can sell as much as it wants.

For Buyers: A buyer cannot offer a lower price than the market price.

• If she does, no seller will sell to her.
• If she agrees to pay the market price or more, she can buy as much as she needs.

Why Do Firms and Buyers Accept the Market Price?

Let's say every firm sells the product at ₹10 (market price). If one firm starts selling at ₹12:

• Buyers will not buy from this firm, because they can get the same product elsewhere for ₹10.
• Since there are many other sellers, buyers can easily switch without any problem.

This is why, in a perfectly competitive market, everyone accepts the market price and no one tries to set their own. That's what we mean by price-taking behaviour.

Revenue

Revenue is the income a firm receives from selling output. Revenue can be expressed at three levels: total, average and marginal.

Total Revenue (TR)

• Total Revenue is the product of price and quantity: TR = p × q.
• Graphically, for a firm facing a constant market price, the TR curve is a straight line through the origin with slope equal to the price.
• Example: If a candle box sells at Rs 10, TR when selling Q boxes is TR = 10 × Q. When Q = 0, TR = 0; when Q = 1, TR = 10; when Q = 2, TR = 20, and so on.

Average Revenue (AR)

• Average Revenue is revenue earned per unit of output: AR = TR / Q.
• In perfect competition AR equals the market price because each unit is sold at the same market price.

The price line that an individual firm faces is identical to its AR curve; it is a horizontal line at the market price because AR (price per unit) does not change with quantity.

Marginal Revenue

• The revenue generated by selling an additional unit of a commodity is known as marginal revenue. 
• When an additional unit of a commodity is sold on the market, it results in a change in overall revenue.
• The following equations can be used to describe the link between market price and marginal revenue:
  
  TR = Total Revenue
  MR = Marginal Revenue
  Q = Quantity
• In a perfectly competitive market, the price equals marginal revenue, according to the preceding equation.
  MR = PQ_n - PQ_n-1
  or
  

Understanding Marginal Revenue with an Example

Imagine you have a small bakery selling cupcakes.

• When you sell 2 cupcakes, you earn Rs. 30.
• When you sell 3 cupcakes, you earn Rs. 45.

Now, let's find out how much extra money you made by selling that 1 extra cupcake.

• Change in Total Revenue = Rs. 45 - Rs. 30 = Rs. 15.
• Change in Quantity = 3 - 2 = 1.

So, Marginal Revenue (MR) = 15/1 = Rs. 15.
That means, by selling 1 more cupcake, you earned an extra Rs. 15.

Is Marginal Revenue Always the Same as Price?

Yes! For a bakery in a perfectly competitive market, the Marginal Revenue (MR) is always equal to the market price (p).

The relationship between MR and Price

We can prove that MR = Price (p) under perfect competition:

The relationship between marginal revenue and pricing is depicted graphically as follows:

TR, MR and AR Curves in a perfectly competitive market can be seen in the graph below:

Profit Maximisation

Imagine a toy-making company that produces and sells a certain number of toys. The company's profit (π) is simply the difference between the money it earns from selling toys (Total Revenue, TR) and the money it spends on making them (Total Cost, TC). So,
Profit (π) = TR - TC.

The bigger the gap between TR and TC, the higher the profit. Naturally, the company wants to make this gap as big as possible. But how do they find the perfect number of toys to produce (q₀) to get the most profit?

To Maximise Profit, These Conditions Must Be Met:

1. Price (p) must equal Marginal Cost (MC): The company makes the most profit when the money earned from selling one more toy is exactly the same as the cost of making that toy.
2. Marginal Cost Should Not Decrease at q₀: The cost of making each extra toy shouldn't keep dropping at the profit-maximising point.
3. Price Must Cover Costs:
   • Short Run: The price should be higher than the Average Variable Cost (AVC).
   • Long Run: The price should be higher than the Average Cost (AC).

Condition 1: Maximising Profit by Comparing Revenue and Cost

A company's profit is the difference between the money it earns (Total Revenue) and the money it spends (Total Cost). As the company produces and sells more products, both Total Revenue and Total Cost increase.

Now, here's the key:

• If the extra revenue earned from selling one more unit (Marginal Revenue, MR) is greater than the extra cost of producing that unit (Marginal Cost or MC), then profits will keep increasing.
• But if the MR is less than the MC, the company's profit decreases.

To make the most profit, the company needs to produce up to the point where Marginal Revenue equals Marginal Cost (MR = MC).

In a perfectly competitive market, MR = Price (P). So, the company will earn the most profit when it produces up to the point where P = MC.

Supply Curve of a Firm

The firm's supply shows how much it is willing to sell at different market prices, holding technology and input prices constant. The supply decision depends on:

• Market price of the product
• Technology available
• Prices of factors of production (wages, raw materials, etc.)

A supply schedule is a table of quantity supplied at different prices. The supply curve is the graphical representation.

Short-Run Supply Curve of a Firm

In the short run the supply curve is derived from the upward-sloping portion of the short-run marginal cost (SMC) curve above the minimum of the average variable cost (AVC). Two cases arise:

• Case 1 - P ≥ minimum AVC: The firm produces where P intersects the upward-sloping part of SMC; that intersection gives the supply (output) at that price.
• Case 2 - P < minimum AVC: The firm produces zero output; it shuts down in the short run.

Combining the two cases: the firm's short-run supply curve is the rising part of the SMC curve that lies at or above the minimum of AVC; for prices below that minimum the supply is zero.

• When all inputs are variable, the long-run supply is the supply of commodities available. 
• The supply curve, in the long run, is always more elastic than the supply curve in the short run. 
• In a U-shaped curve, the long-run average cost curve encompasses the short-run average cost curves. 
• With the addition of increasing long-run marginal cost curves, the supply curve is upward-sloping.
  
  

Case 1: Price greater than or equal to the minimum LRAC 

• Presume the market cost price is P₁, which is greater than the minimum LRAC. We obtain the output degree Q₁ by equating P₁ with LRMC on the increasing part of the LRMC curve. 
• It's also worth noting that the LRAC in Q₁ does not exceed the market cost price, P₁. 
• As a result, at Q₁, all three of the conditions are met. When the market cost price is P₁, the firm's supplies are equal to Q₁ in the long run.
  

Case 2: Price less than the minimum LRAC 

• Assuming the market cost price is P₂, which is lower than the LRAC minimum.
• If a profit-maximising firm produces a positive output over time, the market cost price, P₂, must be larger than or equal to the LRAC at that production level.
• In other words, the firm is unable to produce a positive result. As a result, when the market cost price is P₂, the firm produces nothing. We reach an important conclusion by combining Cases 1 and 2.
• The long-run supply curve of a business is the increasing section of the LRMC curve from and above the minimum LRAC, as well as the zero production for all-cost prices less than the minimum LRAC.
  

The Shut Down Point

While deriving the supply curve, we noted that a firm continues to produce in the short run as long as the price is at least equal to the minimum of the Average Variable Cost (AVC). So, as we move down along the supply curve, the last price-output combination where the firm produces positive output occurs where the Short Run Marginal Cost (SMC) curve intersects the AVC curve at its minimum point.

If the price drops below this point, the firm ceases production. This point is known as the short-run shutdown point of the firm. In the long run, however, the shutdown point is determined by the minimum of the Long Run Average Cost (LRAC) curve.

The Normal Profit and Break-even Point

The normal profit is the minimum level of profit needed for a firm to continue operating in its current business. If a firm fails to earn this amount, it won't stay in business. Normal profit is considered a part of the firm's total costs and can be seen as the opportunity cost of entrepreneurship.

When a firm earns profit above normal profit, it is called super-normal profit.

• In the long run, a firm will not operate if it earns less than the normal profit.
• In the short run, however, the firm may continue producing even if profits are below normal profit.

The point on the supply curve where a firm earns only normal profit is called the break-even point. This occurs where the supply curve intersects the LRAC curve at its minimum point (or the SAC curve in the short run).

Opportunity Cost

Opportunity cost is the value of the next best alternative forgone when a choice is made. It represents the benefits that could have been obtained from the alternative use of resources.

Example: If you invest Rs 1,000 in the family business instead of depositing it in a bank that offers 10% interest, the opportunity cost of investing in the family business is the interest foregone (i.e., 10% of Rs 1,000 = Rs 100).

Determinants of the Firm's Supply Curve

The firm's supply curve is a segment of its marginal cost curve. Anything that shifts MC will change supply. Important determinants include:

• Technological progress: Improvements in technology increase productivity so that the same output can be produced with fewer inputs or more output with the same inputs. This lowers marginal cost at each output and shifts the firm's supply curve to the right (more supply at each price).
• Input prices: An increase in prices of inputs (e.g., wages, raw materials) raises marginal and average costs at each output; the MC curve shifts upward and the supply curve shifts left (less supply at each price).
• Taxes and subsidies: A per-unit tax (unit tax) increases MC and AC by the tax amount, shifting the supply curve left in both the short and long run. A subsidy lowers MC and shifts supply rightward.

Effect of a Unit Tax on Long-Run Supply

A unit tax raises long-run average cost (LRAC) and long-run marginal cost (LRMC) by the tax amount. Graphically LRAC and LRMC shift upward by the tax. Since the firm's long-run supply is the upward-sloping part of LRMC above minimum LRAC, the tax shifts the long-run supply curve leftwards and reduces quantity supplied at each market price.

Market Supply Curve

The market supply curve shows the total output produced by all firms in a market at different market prices.

How is the Market Supply Curve Derived?

Consider a market with n firms: firm 1, firm 2, firm 3, and so on. If the market price is fixed at p, then the total market supply at that price is calculated by adding up the supply of each firm at that price.

Market Supply = [Supply of firm 1 at price p] + [Supply of firm 2 at price p] + ... + [Supply of firm n at price p].

Geometric Representation (Two Firms Example)

Suppose there are two firms with different cost structures:

• Firm 1 will produce only if the market price is greater than or equal to p1.
• Firm 2 will produce only if the market price is greater than or equal to p2 (where p2 > p1).

How the Market Supply Curve is Constructed:

1. When the market price is below p1:

   • Neither firm produces anything.
   • Market supply is zero.

2. When the market price is between p1 and p2:

   • Only Firm 1 produces.
   • The market supply curve coincides with the supply curve of Firm 1.

3. When the market price is above p2:

   • Both Firm 1 and Firm 2 produce.
   • The total supply is the sum of the outputs of Firm 1 and Firm 2 at that price.
   • The market supply curve is obtained by horizontally adding the supply curves of the two firms.

Understanding Market Supply Curve with a Numerical Example

The market supply curve we derived before assumed a fixed number of firms. When the number of firms changes, the market supply curve shifts:

• If the number of firms increases, the market supply curve shifts to the right.
• If the number of firms decreases, the market supply curve shifts to the left.

Now, let's look at a numerical example involving two firms.

Supply Curves of the Firms

1. Firm 1's Supply Curve (S1(p))

When p < 10, the firm produces 0 units.

When p ≥ 10, the output produced is (p - 10).

So,

S1(p) = 0 if p < 10.

S1(p) = p - 10 if p ≥ 10.

2. Firm 2's Supply Curve (S2(p))

When p < 15, the firm produces 0 units.

When p ≥ 15, the output produced is (p - 15).

So,

S2(p) = 0 if p < 15.

S2(p) = p - 15 if p ≥ 15.

3. Market Supply Curve (Sm(p))

The market supply curve is the sum of the individual supply curves, i.e.,

Now, let's break down the calculation:

• When p < 10: Both firms produce 0 units.

When 10 ≤ p < 15:

• Only Firm 1 produces.

When p ≥ 15:

• Both firms produce.

The market supply curve can be summarised as: 

Price Elasticity of Supply

• The price elasticity of supply is a measurement of how sensitive a given good's quantity is to a change in price.

Measurement of Price Elasticity of Supply: 

• Price elasticity of supply curve,
  
  
  WhereΔQ = change in the quantity of the good supplied to the market
  ΔP = change in the price of the good

Extreme Cases of Price Elasticity of Supply: 

• Perfect elasticity supply (es = ∞): The extreme case of perfect elasticity is when the demanded quantity (Qd) or the supplied quantity (Qs) changes by an enormous amount in response to any change in price. The supply and demand curves are both horizontal in both instances. Ï 
• Perfect inelasticity supply (e_s = 0): If a given quantity of a service or commodity can be supplied at any price, it has a perfectly inelastic supply. The supply elasticity of such a service or commodity is zero. A straight line parallel to the Y-axis is a perfectly inelastic supply curve. This illustrates how supply remains constant regardless of price.
  

Equilibrium and Policy Applications

Equilibrium price is the price at which quantity demanded equals quantity supplied. At this price there is neither surplus nor shortage.

Equilibrium quantity is the quantity exchanged at the equilibrium price.

Applications: Price Controls

• Price ceiling (maximum price): Government imposes a maximum legal price below equilibrium to protect consumers when prices are considered too high. This may create shortages and require rationing or dual markets for allocation.
• Price floor (minimum price): Government sets a minimum price above equilibrium (for example, minimum support price) to protect producers. This can create surpluses; governments often buy the excess supply at the floor price.

Effect of Technological Advancement on Supply

• Technological progress lowers marginal cost of production and allows more output to be produced with the same inputs.
• Lower marginal costs shift the firm's MC curve downward and the supply curve rightward, increasing quantity supplied at each price.
• Thus, technological improvements generally increase supply and reduce equilibrium price, benefiting consumers and often expanding market output.