Competitive Firms and Markets: Chapter 8 Study Notes

Competitive Firms and Markets

Learning Objectives

• Understand the characteristics of perfect competition.

• Analyze how firms maximize profit in competitive markets.

• Distinguish between short-run and long-run competition.

Market Structure

Definition and Types

Market structure refers to the organization of a market, defined by the number of firms, ease of entry and exit, and product differentiation.

• Competitive market structure: Many firms produce identical products and can easily enter or exit the market.

Price Taking

Characteristics of Price Takers

In a competitive market, each firm is a price taker, meaning it cannot influence the market price for its output or input prices.

• The demand curve faced by a price taker is horizontal at the market price.

Why the Firm's Demand Curve is Horizontal

Conditions for Perfect Competition

Five key characteristics ensure firms are price takers in perfectly competitive markets:

• Many small buyers and sellers

• Identical products produced by all firms

• Full information about prices and product characteristics

• Negligible transaction costs

• Free entry and exit for firms

Deviations from Perfect Competition

Highly Competitive Markets

Many real-world markets do not meet all criteria for perfect competition but remain highly competitive. In such markets, no buyer or seller can significantly affect the market price.

• Competition: All markets where participants are price takers, even if not perfectly competitive.

Derivation of a Competitive Firm's Demand Curve

Residual Demand Curve

The residual demand curve represents the market demand not met by other sellers at a given price.

• Formula: $D^r(p) = D(p) - S^o(p)$

Elasticity of Demand Facing a Firm

If the market has n identical firms, the elasticity of demand facing Firm i is:

• Formula: $\varepsilon_i = n\varepsilon - (n-1)\eta_o$

• Where $\varepsilon$ is market elasticity of demand (negative), $\eta_o$ is elasticity of supply of other firms (positive), and $n-1$ is the number of other firms.

Solved Problem 8.1

Given $n = 78$, $\eta_o = 3.1$, $\varepsilon = -1.1$:

• Calculation: $\varepsilon_i = [78 \times (-1.1)] - [77 \times 3.1] = -85.8 - 238.7 = -324.5$

• The residual demand curve is highly elastic, supporting the assumption of a horizontal demand curve for competitive firms.

Why We Study Perfect Competition

Benchmark for Real Markets

• Many markets (agriculture, commodities, stock exchanges) are reasonably competitive.

• Perfect competition serves as a benchmark for evaluating real-world market outcomes.

Profit

Economic Profit and Opportunity Cost

• Economic profit: $\pi = R - C$ (Revenue minus cost)

• If $\pi < 0$, the firm incurs a loss.

• Revenue is price times quantity.

• Opportunity cost: The value of the best alternative use of any input, including explicit and implicit costs.

Two Decisions for Maximizing Profit

Output and Shutdown Decisions

• Output decision: What output level $q^*$ maximizes profit or minimizes loss?

• Shutdown decision: Is it more profitable to produce $q^*$ or to shut down?

• Profit function: $\pi(q) = R(q) - C(q)$

Output Decision Rules

Rules for Profit Maximization

• Rule 1: Set output where profit is maximized.

• Rule 2: Set output where marginal profit is zero.

• Rule 3: Set output where marginal revenue equals marginal cost: $MR(q) = MC(q)$

Marginal Revenue and Marginal Profit

• Marginal revenue (MR): Change in revenue from selling one more unit: $MR = \frac{\Delta R}{\Delta q}$

• Marginal profit: Change in profit from selling one more unit: $\text{Marginal profit}(q) = MR(q) - MC(q)$

Shutdown Decision Rule

When Should a Firm Shut Down?

• Rule 1: Shut down only if it reduces loss.

• Example: $R = 2000$, $VC = 1000$, $F = 3000$; $\pi = 2000 - 1000 - 3000 = -2000$

• If shut down, loss is $F = 3000$; better to operate.

• Rule 2: Shut down only if revenue is less than avoidable cost.

Short-Run Output Decision

Profit Maximization in the Short Run

• In perfect competition, $MR = p$

• Profit-maximizing output: $MC(q) = p$

Short-Run Shutdown Decision

Shutdown Condition

• Shut down if $R(q) = pq < VC(q)$

• In average terms: $p < AVC(q)$

• Firm shuts down if market price is less than short-run average variable cost at profit-maximizing quantity.

Short-Run Firm Supply Curve

Supply Curve Definition

• If price falls below minimum average variable cost, firm shuts down.

• Short-run supply curve is marginal cost curve above minimum average variable cost.

Market Supply with Identical Firms

• Maximum number of firms is fixed in the short run.

• If all firms are identical, market supply at any price is $n$ times the supply of an individual firm.

Short-Run Market Supply with Identical Firms

• As number of firms increases, market supply curve becomes flatter (more elastic) at a given price.

Short-Run Market Supply with Different Firms

Supply Curve with Heterogeneous Firms

• Market supply curve is the horizontal sum of individual supply curves, which may differ if firms have different costs.

Short-Run Competitive Equilibrium

Equilibrium in Competitive Markets

• Equilibrium occurs where market supply equals market demand.

• Individual firm’s output and profit are determined by market price.

Solved Problems

Solved Problem 8.2: Tax on a Single Firm

• A per-unit tax increases the firm’s marginal and average costs, reducing profit-maximizing output and profit.

Solved Problem 8.3: Change in Fixed Costs

• Change in fixed costs does not affect output decision in the short run.

• Change in measurement of fixed costs does not affect economic profit.

Solved Problem 8.4: Tax on All Firms

• A per-unit tax on all firms shifts supply curves upward, increasing market price and reducing equilibrium quantity.

• Incidence of tax is shared between buyers and sellers depending on elasticities.

Long-Run Competitive Profit Maximization

Long-Run Output and Shutdown Decisions

• Firm chooses output to maximize long-run profit: $\pi = R - C$

• Operates where long-run marginal profit is zero and $MR = LRMC$

• Shuts down if revenue is less than avoidable (variable) cost; in long run, all costs are variable.

Long-Run Firm Supply Curve

Definition

• Long-run supply curve is long-run marginal cost curve above minimum long-run average cost curve.

• Firm can adjust capital in the long run, so supply curve may differ from short-run supply curve.

Long-Run Market Supply Curve

Market Supply in the Long Run

• Market supply curve is the horizontal sum of individual firms’ supply curves.

• Firms can enter or exit the market in the long run.

• Number of firms at each price must be determined to obtain the long-run market supply curve.

Entry and Exit

Conditions for Entry and Exit

• Free entry and exit: Firms enter if they can make long-run profit ($\pi > 0$), exit to avoid long-run loss ($\pi < 0$).

• If firms make zero long-run profit, they are indifferent between staying and exiting ($\pi = 0$).

Long-Run Market Supply with Identical Firms and Free Entry

Horizontal Supply Curve

• If firms have identical costs and input prices are constant, long-run market supply curve is flat at minimum long-run average cost.

Long-Run Market Supply with Limited Entry

Upward-Sloping Supply Curve

• If number of firms is limited (by government, scarce resources, or costly entry), long-run market supply curve slopes upward.

Long-Run Market Supply When Firms’ Cost Functions Differ

Heterogeneous Costs

• Firms with lower minimum long-run average costs enter at lower prices, resulting in upward-sloping supply curve.

Long-Run Market Supply When Input Prices Vary with Output

Increasing-Cost Markets

• If factor prices rise with output, long-run supply curve slopes upward even with identical firms and free entry.

Long-Run Market Supply Curve with a Large Buyer

Residual Supply Curve

• If a large buyer demands a significant share, the residual supply curve is the quantity supplied not consumed by other demanders.

• Formula: $S^r(p) = S(p) - D^o(p)$

Long-Run Competitive Equilibrium

Equilibrium Price and Quantity

• Intersection of long-run market supply and demand curves determines equilibrium.

• Equilibrium price equals minimum long-run average cost.

• Demand shifts affect equilibrium quantity, not price.

Tables

Summary Table: Key Decision Rules

Decision	Rule	Formula
Output Decision	Set output where profit is maximized	$MR(q) = MC(q)$
Shutdown Decision (Short Run)	Shut down if revenue < variable cost	$p < AVC(q)$
Shutdown Decision (Long Run)	Shut down if revenue < total cost	$p < AC(q)$

Summary Table: Causes of Upward-Sloping Long-Run Supply Curve

Cause	Description
Limited Entry	Government restrictions, scarce resources, costly entry
Different Cost Functions	Firms have varying minimum long-run average costs
Increasing Input Prices	Factor prices rise as output increases
Large Buyer	Buyer demands large share, affecting residual supply

Example

• In the Canadian metal chair market, with 78 identical firms, the elasticity of demand facing a single firm is highly elastic, supporting the horizontal demand curve assumption.

• A per-unit tax on all firms increases costs, shifts supply curves upward, and raises market price.