Theory of the Firm Under Perfect Competition

Perfect Competition: Defining Features

The theory of the firm studies how a business makes decisions about production and pricing to achieve its objectives, primarily profit maximisation. The firm's behaviour is heavily influenced by the structure of the market in which it operates. Perfect Competition is a market structure that serves as a theoretical benchmark. It is characterised by a set of ideal conditions that result in a highly competitive environment.

The defining features of a perfectly competitive market are:

1. Large Number of Buyers and Sellers: The market consists of a very large number of buyers and sellers. The number is so large that the contribution of a single firm to the total market supply is negligible, and the purchase of a single buyer from the total market demand is insignificant. Consequently, no single firm or buyer can influence the market price.
2. Homogeneous Product: All firms in the market produce and sell an identical or homogeneous product. The products are perfect substitutes for one another. There is no differentiation based on brand, quality, or packaging. This means a buyer has no reason to prefer the product of one seller over another, except for the price.
3. Freedom of Entry and Exit: There are no barriers to the entry of new firms into the industry or the exit of existing firms. New firms can enter if they see an opportunity for profit, and existing firms can leave if they are incurring losses. This feature has significant implications for long-run profits.
4. Perfect Information: All buyers and sellers have perfect and complete information about the market, including the price and quality of the product. This ensures that no firm can charge a higher price than the market price, as buyers are aware of the prevailing price.

A crucial consequence of these features is that an individual firm under perfect competition is a price taker, not a price maker. The market price is determined by the intersection of the market demand and market supply curves. The firm must accept this price and can sell any quantity of output it wants at this given price.

Revenue

Revenue refers to the money that a firm receives from the sale of its output. Understanding a firm's revenue structure is essential for analysing its profit-maximising behaviour.

• Total Revenue (TR): It is the total amount of money a firm earns by selling a given quantity of its product.

  $ TR = \text{Price} (P) \times \text{Quantity} (q) $

• Average Revenue (AR): It is the revenue per unit of output sold.

  $ AR = \frac{TR}{q} = \frac{P \times q}{q} = P $

  Thus, the Average Revenue is always equal to the price of the commodity.

• Marginal Revenue (MR): It is the change in Total Revenue resulting from the sale of one additional unit of output.

  $ MR = \frac{\Delta TR}{\Delta q} $

Under perfect competition, the firm is a price taker, meaning the price (P) is constant regardless of the quantity the firm sells. This leads to a unique relationship between P, AR, and MR.

Answer:

Profit Maximisation

The primary objective of a rational firm is to maximise its economic profit. Profit ($\pi$) is the difference between Total Revenue (TR) and Total Cost (TC).

$ \pi = TR - TC $

A firm maximises its profit by choosing the level of output where the difference between TR and TC is the greatest. To find this output level, a firm compares the marginal revenue (MR) it gets from selling an extra unit with the marginal cost (MC) of producing that extra unit. A firm will continue to produce as long as the revenue from an additional unit (MR) is greater than or equal to the cost of that unit (MC).

This leads to the following conditions for profit maximisation:

Condition 1

For a firm to be in equilibrium (i.e., at the profit-maximising output level), its Marginal Revenue must be equal to its Marginal Cost. Under perfect competition, since P = MR, this condition becomes:

$ P = MC $

If P > MC, the firm can increase its profit by producing more. If P < MC, the firm is making a loss on the last unit produced and should reduce its output.

Condition 2

The Marginal Cost must be non-decreasing (i.e., the MC curve must be rising) at the point of equilibrium. If MC were falling, the firm could increase profit by producing more, as the cost of each additional unit would be less than the previous one. A rising MC ensures that producing beyond the equilibrium point would become unprofitable.

Condition 3

• In the short run, the price must be greater than or equal to the minimum Average Variable Cost (P ≥ min AVC). If the price falls below the minimum AVC, the firm cannot even cover its variable costs and is better off shutting down production.
• In the long run, the price must be greater than or equal to the minimum Average Cost (P ≥ min AC). If the price is below the long-run average cost, the firm will exit the industry.

The Profit Maximisation Problem: Graphical Representation

In the graph above, the profit-maximising output is $q^*$, where the horizontal price line ($P=MR$) intersects the rising portion of the MC curve. At this output level:

• Total Revenue (TR) = $P \times q^* = \text{Area of rectangle } O P E q^*$.
• Total Cost (TC) = $AC \times q^* = \text{Area of rectangle } O C B q^*$.
• Total Profit ($\pi$) = $TR - TC = \text{Area of rectangle } C P E B$.

Since Price (P) is greater than Average Cost (C) at the equilibrium output, the firm is earning supernormal profit.

Supply Curve Of A Firm

A firm's supply curve shows the quantity of output that the firm is willing to produce and sell at different market prices, assuming technology and input prices are constant. The supply curve is derived directly from the firm's profit-maximising behaviour.

Short Run Supply Curve Of A Firm

In the short run, a firm will only produce if the price is high enough to cover its average variable costs (P ≥ min AVC). The firm determines its output level by equating the price with its marginal cost (P = MC). Therefore, the quantity supplied at any given price is determined by the MC curve.

This means the firm's short-run supply curve is the rising portion of its Short-Run Marginal Cost (SMC) curve that lies above the minimum point of the Average Variable Cost (AVC) curve.

Long Run Supply Curve Of A Firm

Similarly, in the long run, a firm will only produce if the price is sufficient to cover its long-run average costs (P ≥ min LRAC). The output is determined by equating price with the long-run marginal cost (P = LRMC).

Thus, the firm's long-run supply curve is the rising portion of its Long-Run Marginal Cost (LRMC) curve that lies above the minimum point of the Long-Run Average Cost (LRAC) curve.

The Shut Down Point

The shut-down point is a short-run concept. It is the point where the price is exactly equal to the minimum average variable cost (P = min AVC). At this price, the firm's total revenue is just enough to cover its total variable costs. The firm is making a loss equal to its total fixed costs. If the price falls below this point, the firm will minimise its losses by shutting down production temporarily. By shutting down, its loss is limited to its fixed costs. If it continues to produce, it will lose its fixed costs plus a portion of its variable costs.

The Normal Profit And Break-even Point

The break-even point occurs where the price is equal to the minimum average total cost (P = min AC). At this point, Total Revenue equals Total Cost (TR = TC). The firm is earning zero economic profit. Zero economic profit is also known as normal profit, which is the minimum level of profit required to keep the entrepreneur in the business. It is considered a part of the total cost of production (as the opportunity cost of the entrepreneur's time and capital).

Determinants Of A Firm’s Supply Curve

A firm's supply curve shows the relationship between price and quantity supplied, assuming other factors are constant. When these other factors change, the entire supply curve shifts. A rightward shift indicates an increase in supply (more is supplied at each price), and a leftward shift indicates a decrease in supply.

Technological Progress

An improvement in technology allows a firm to produce a given level of output with fewer inputs, or more output with the same inputs. This lowers the firm's cost of production. A downward shift in the firm's Marginal Cost (MC) curve means that at any given price, the firm is now willing to supply more output. This results in a rightward shift of the supply curve.

Input Prices

The supply curve is derived from the MC curve, which in turn depends on input prices. If the price of an input (like labour wages or raw material costs) increases, the firm's marginal cost of production rises. The MC curve shifts upwards and to the left. Consequently, the firm will supply less at any given price, causing a leftward shift of the supply curve. Conversely, a fall in input prices will cause a rightward shift.

Market Supply Curve

The market supply curve shows the total quantity of a good that all firms in the market are willing to supply at different prices. It is derived by the horizontal summation of the individual supply curves of all the firms in the industry.

To obtain the market supply at a given price, we simply add up the quantities supplied by each individual firm at that price.

Price Elasticity Of Supply

The Price Elasticity of Supply ($e_s$) measures the degree of responsiveness of the quantity supplied of a good to a change in its price. It is calculated as the percentage change in quantity supplied divided by the percentage change in price.

Formula:

$ e_s = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}} = \frac{\frac{\Delta q}{q} \times 100}{\frac{\Delta P}{P} \times 100} = \frac{\Delta q}{\Delta P} \cdot \frac{P}{q} $

Unlike demand elasticity, the value of supply elasticity is positive because of the direct relationship between price and quantity supplied.

Geometric Method

For a linear supply curve, the elasticity can be measured geometrically. If the supply curve is extended to intersect the price (Y) or quantity (X) axis, its elasticity can be determined:

• If the supply curve starts from the origin, $e_s = 1$ (unitary elastic).
• If the supply curve intersects the positive Y-axis, $e_s > 1$ (elastic).
• If the supply curve intersects the positive X-axis, $e_s < 1$ (inelastic).

Key Concepts

• Perfect Competition: A market with many buyers and sellers, a homogeneous product, and free entry and exit.
• Price Taker: A firm that has no control over the market price and must accept it as given.
• Revenue: The income a firm earns from sales (TR, AR, MR). In perfect competition, P=AR=MR.
• Profit Maximisation: The process of finding the output level where the difference between total revenue and total cost is greatest. The key condition is P = MC.
• Supply Curve: A curve showing the quantity a firm is willing to sell at different prices. It is the rising part of the MC curve above AVC (in the short run) or AC (in the long run).
• Shut-down Point: The point where P = minimum AVC. Below this, the firm ceases production in the short run.
• Break-even Point: The point where P = minimum AC, and the firm earns zero economic profit (normal profit).
• Market Supply: The horizontal summation of individual firms' supply curves.
• Price Elasticity of Supply: A measure of the responsiveness of quantity supplied to a change in price.

Summary

This chapter examined the behaviour of a firm operating in a perfectly competitive market. Due to the market's defining features, such a firm acts as a price taker, facing a perfectly elastic (horizontal) demand curve where Price = AR = MR.

The firm's primary goal is profit maximisation, which it achieves by producing the quantity of output where the market price equals its marginal cost ($P=MC$), provided the MC is rising and the price covers the relevant average costs (AVC in the short run, AC in the long run). This profit-maximising logic allows us to derive the firm's supply curve, which is the upward-sloping portion of its marginal cost curve. Key decision points for the firm are the shut-down point (P = min AVC) and the break-even point (P = min AC).

The firm's supply curve can shift due to changes in technology or input prices. By aggregating the supply curves of all firms, we obtain the market supply curve. Finally, the responsiveness of supply to price changes is quantified by the price elasticity of supply. Understanding these principles is fundamental to analysing how competitive markets function.